Integer Points on A^4+B^4+49298*C^4=4*D^4
[2026.05.12]A^4+B^4+49298*C^4=4*D^4の整点
■Diophantine Equation
A^4+B^4+2*n^2*C^4=4*D^4 ----------(1)
を満たす自明でない整数の組(A,B,C,D) (ただし A*B*C*D!=0かつgcd(A,B,C,D)=1)を探す。
以下では、Elkiesの論文(参考文献[1])の方法によって、(1)を満たす整数の組(A,B,C,D)を探す。
■(1)およびD!=0より、A/D=x+y,B/D=x-y.C/D=tとすると、
2*(x^4+6*x^2*y^2+y^4)+2*n^2*t^4=4
x^4+6*x^2*y^2+y^4+n^2*t^4=2 ----------(2)
つまり、(2)を満たす有理数の組(x,y,t)を見つければ良い。
ここで、ある有理数uに対して、
(u^2+1)*y^2=--(u^2+4*u+5)*x^2-(u^2+2*u-1) ----------(5a)
±n*(u^2+1)*t^2=2*(u^2+2*u-1)*x^2+(u^2-2*u^1) ----------(5b±)
を満たす有理数の組(x,y,t)が存在すれば、(x,y,t)が(2)を満たすことが分かる。
[pari/gpによる計算]
gp > YY2(u,x)
%1 = ((-u^2 - 4*u - 5)/(u^2 + 1))*x^2 + ((-u^2 - 2*u + 1)/(u^2 + 1))
gp > TT2(n,u,x)
%2 = ((2*u^2 + 4*u - 2)/(n*u^2 + n))*x^2 + ((u^2 - 2*u - 1)/(n*u^2 + n))
gp > x^4+6*x^2*YY2(u,x)+YY2(u,x)^2+n^2*TT2(n,u,x)^2
%5 = 2
■２次曲線(5a),(5b±)は、常にnon-singularである。
２次曲線(5a)の右辺の判別式は
-4*(u^2+4*u+5)*(u^2*2+u-1)
となり、有理数の根を持たないので、任意の有理数uについて、non-singularである。
同様に、２次曲線(5b±)の右辺の判別式は
-4*2*(u^2+2*u-1)*(u^2-2*u-1)
となり、有理数の根を持たないので、任意の有理数uについて、non-singularである。
■以下では、n=157とする。
Pari/GPで簡単なプログラム(a221s.gp)を作成して、0 < x,y,z <= 10000, 0 < zの範囲で、整数解を調べると、
27^4+55^4+49298*3^4=4*43^4
2515^4+2519^4+49298*121^4=4*2183^4
が見つかった。
[Pari/GP(gp2c-run)による計算]
gp > sss(157,10000)
N=10000
2*n^2=49298
1:27^4+55^4+49298*3^4=4*43^4
2:2515^4+2519^4+49298*121^4=4*2183^4
time = 11h, 41min, 38,938 ms.
%3 = 2
■有理数uの高さが小さいものから、順に調べる。
例えば、有理数uの高さが200以下の範囲で、uの分子が偶数、uの分母が奇数であり、２つの２次曲線(5a)と(5b±)が共に有理点を持つようなuを選択すると、
以下のように(重複を含む)936個のuが抽出される。
[pari/gpによる計算]
> PP(157,1,200);
** u= -200/109 ; C1 -12205*x^2 + 51881*y^2 + 15481*z^2
(2236/2417 : -753/2417 : 1) C2b (31613/32267 : -2317/32267 : 1)
** u= -200/161 ; C1 -40805*x^2 + 65921*y^2 + 50321*z^2
(71453/71951 : -28134/71951 : 1) C2b (-216459/340685 : -20603/340685 : 1)
** u= -200/199 ; C1 -78805*x^2 + 79601*y^2 + 79201*z^2
(51671/51741 : 4526/51741 : 1) C2b (-704377/2663573 : -197803/2663573 : 1)
** u= -198/91 ; C1 -8537*x^2 - 47485*y^2 + 5113*z^2
(8249/10743 : 440/10743 : 1) C2a (-5011674/290117 : 183565/290117 : 1)
** u= -198/103 ; C1 -10673*x^2 - 49813*y^2 + 12193*z^2
(-13378/13293 : -2215/13293 : 1) C2a (2417444/2605 : 134991/2605 : 1)
** u= -198/125 ; C1 -18329*x^2 - 54829*y^2 + 25921*z^2
(13041/11125 : -1288/11125 : 1) C2a (-1179618/535325 : -479/3325 : 1)
** u= -197/89 ; C1 {+/-} -8282*x^2 + 46730*y^2 + 4178*z^2
(29622/42509 : 2459/42509 : 1) C2a (-94140109/11243203 : 2992885/11243203 : 1) C2b (588686/229953 : 8981/229953 : 1)
** u= -197/97 ; C1 {+/-} -9418*x^2 + 48218*y^2 + 8818*z^2
(-2375/2697 : -478/2697 : 1) C2a (8175501/347573 : -393233/347573 : 1) C2b (-2578/1415 : -49/1415 : 1)
** u= -196/103 ; C1 -10709*x^2 + 49025*y^2 + 12569*z^2
(-1473/1825 : -3082/9125 : 1) C2b (-25935/68501 : 31373/342505 : 1)
** u= -196/123 ; C1 -17629*x^2 + 53545*y^2 + 24929*z^2
(-7928/88723 : 3551/5219 : 1) C2b (-130193/171737 : -12261/171737 : 1)
** u= -196/177 ; C1 -56293*x^2 + 69745*y^2 + 62297*z^2
(118901/115987 : 24610/115987 : 1) C2b (56181/1540637 : -128609/1540637 : 1)
** u= -196/191 ; C1 -71077*x^2 + 74897*y^2 + 72937*z^2
(30341/32949 : 13550/32949 : 1) C2b (236141/675157 : -47809/675157 : 1)
** u= -196/195 ; C1 -75661*x^2 + 76441*y^2 + 76049*z^2
(347620/431383 : 255989/431383 : 1) C2b (188199/467089 : 30787/467089 : 1)
** u= -194/111 ; C1 -13105*x^2 - 49957*y^2 + 17753*z^2
(698/8173 : 4859/8173 : 1) C2a (50186/12773 : -3159/12773 : 1)
** u= -194/119 ; C1 -16097*x^2 - 51797*y^2 + 22697*z^2
(-13779/26095 : -15472/26095 : 1) C2a (-36147328/79609 : 2700671/79609 : 1)
** u= -194/129 ; C1 -20737*x^2 - 54277*y^2 + 29057*z^2
(46886/188855 : 135107/188855 : 1) C2a (3522968/2933469 : 16223/419067 : 1)
** u= -194/139 ; C1 -26377*x^2 - 56957*y^2 + 35617*z^2
(-146033/132347 : 32820/132347 : 1) C2a (2810904/1960027 : -178613/1960027 : 1)
** u= -194/165 ; C1 -45721*x^2 - 64861*y^2 + 53609*z^2
(-458/1715 : 1511/1715 : 1) C2a (7154/5829 : 539/5829 : 1)
** u= -194/175 ; C1 -54961*x^2 - 68261*y^2 + 60889*z^2
(103930/130253 : -80229/130253 : 1) C2a (-881738/1123995 : 1879/1123995 : 1)
** u= -194/181 ; C1 -60985*x^2 - 70397*y^2 + 65353*z^2
(671/51329 : 49452/51329 : 1) C2a (570506/130677 : 61099/130677 : 1)
** u= -194/195 ; C1 -76441*x^2 - 75661*y^2 + 76049*z^2
(-2842403/2947535 : 754964/2947535 : 1) C2a (338062/41163 : 38113/41163 : 1)
** u= -193/133 ; C1 {+/-} -23018*x^2 + 54938*y^2 + 31778*z^2
(-5595/5209 : 1606/5209 : 1) C2a (2744369/1592485 : 186149/1592485 : 1) C2b (1066482/1015631 : 9893/1015631 : 1)
** u= -192/95 ; C1 -9029*x^2 + 45889*y^2 + 8641*z^2
(-1845/7777 : 3274/7777 : 1) C2b (-673259/1009011 : -89453/1009011 : 1)
** u= -192/127 ; C1 -19973*x^2 + 52993*y^2 + 28033*z^2
(199308/171535 : -24361/171535 : 1) C2b (55661/477105 : -2551/28065 : 1)
** u= -192/143 ; C1 -29285*x^2 + 57313*y^2 + 38497*z^2
(-1884/7459 : 5963/7459 : 1) C2b (-606743/1269999 : -98159/1269999 : 1)
** u= -192/155 ; C1 -37949*x^2 + 60889*y^2 + 46681*z^2
(7204/59955 : 52187/59955 : 1) C2b (102073/165765 : 10307/165765 : 1)
** u= -192/175 ; C1 -55589*x^2 + 67489*y^2 + 60961*z^2
(-72049/75645 : -29882/75645 : 1) C2b (-15793/385643 : -32061/385643 : 1)
** u= -191/115 ; C1 -14746*x^2 + 49706*y^2 + 20674*z^2
(254/3983 : 2565/3983 : 1) C2b (33772/195143 : -17939/195143 : 1)
** u= -191/163 ; C1 -44794*x^2 + 63050*y^2 + 52354*z^2
(-562346/523023 : 248911/2615115 : 1) C2b (36772/88459 : 32693/442295 : 1)
** u= -190/99 ; C1 -9865*x^2 - 45901*y^2 + 11321*z^2
(1453/1451 : -256/1451 : 1) C2a (1161334/401595 : 52981/401595 : 1)
** u= -190/127 ; C1 -20225*x^2 - 52229*y^2 + 28289*z^2
(-5211/5875 : -572/1175 : 1) C2a (22258/14045 : 1333/14045 : 1)
** u= -190/161 ; C1 -43345*x^2 - 62021*y^2 + 51001*z^2
(8773/29273 : -25512/29273 : 1) C2a (161968/62265 : 15697/62265 : 1)
** u= -190/197 ; C1 -80425*x^2 - 74909*y^2 + 77569*z^2
(4217/7557 : -6328/7557 : 1) C2a (-991734/1454195 : 791/1454195 : 1)
** u= -189/113 ; C1 {+/-} -14138*x^2 + 48490*y^2 + 19762*z^2
(2222/7989 : -4957/7989 : 1) C2a (11898233/626251 : 855333/626251 : 1) C2b (76538/1271871 : 117995/1271871 : 1)
** u= -189/185 ; C1 -66986*x^2 - 69946*y^2 + 68434*z^2
(4454/26817 : 26165/26817 : 1) C2a (-3646491/1783031 : 380851/1783031 : 1)
** u= -188/83 ; C1 -7373*x^2 + 42233*y^2 + 2753*z^2
(-7872/13963 : -1375/13963 : 1) C2b (9171/3305 : -26479/518885 : 1)
** u= -188/99 ; C1 -9901*x^2 + 45145*y^2 + 11681*z^2
(1072/4703 : -2339/4703 : 1) C2b (214467/252997 : 20377/252997 : 1)
** u= -188/125 ; C1 -19469*x^2 + 50969*y^2 + 27281*z^2
(-4804/9353 : -6165/9353 : 1) C2b (3137/8205 : -703/8205 : 1)
** u= -188/127 ; C1 -20485*x^2 + 51473*y^2 + 28537*z^2
(-14320/12147 : -439/12147 : 1) C2b (-294751/509585 : -39221/509585 : 1)
** u= -188/191 ; C1 -74117*x^2 + 71825*y^2 + 72953*z^2
(24/35 : -1657/2275 : 1) C2b (-8955/56239 : -281731/3655535 : 1)
** u= -187/95 ; C1 -9034*x^2 + 43994*y^2 + 9586*z^2
(-10315/11147 : 2286/11147 : 1) C2b (798092/613385 : 39757/613385 : 1)
** u= -187/159 ; C1 -42442*x^2 - 60250*y^2 + 49778*z^2
(2282/3259 : -11299/16295 : 1) C2a (-51673/55599 : -11729/277995 : 1)
** u= -186/137 ; C1 -26513*x^2 - 53365*y^2 + 35137*z^2
(-21886/33147 : -22033/33147 : 1) C2a (7156788/2371121 : 620315/2371121 : 1)
** u= -186/191 ; C1 -74897*x^2 - 71077*y^2 + 72937*z^2
(78465/663659 : -667444/663659 : 1) C2a (-637236/117395 : 72269/117395 : 1)
** u= -186/193 ; C1 -77249*x^2 - 71845*y^2 + 74449*z^2
(-49459/111981 : -101804/111981 : 1) C2a (108880244/114608999 : -8716317/114608999 : 1)
** u= -185/101 ; C1 {+/-} -10490*x^2 + 44426*y^2 + 13346*z^2
(2921/3529 : 1314/3529 : 1) C2a (-110083/37985 : -5803/37985 : 1) C2b (2282646/1508941 : -10091/1508941 : 1)
** u= -185/141 ; C1 -29290*x^2 + 54106*y^2 + 37826*z^2
(1166/2681 : -2071/2681 : 1) C2b (-232506/260095 : 6947/260095 : 1)
** u= -184/77 ; C1 -6829*x^2 + 39785*y^2 + 409*z^2
(3992/23957 : -1779/23957 : 1) C2b (71693/101593 : -9607/101593 : 1)
** u= -184/105 ; C1 -11701*x^2 + 44881*y^2 + 15809*z^2
(26749/25183 : -6070/25183 : 1) C2b (-1850347/1328905 : -6567/1328905 : 1)
** u= -184/131 ; C1 -23245*x^2 + 51017*y^2 + 31513*z^2
(49009/61109 : -34818/61109 : 1) C2b (57683/1338875 : 120413/1338875 : 1)
** u= -184/175 ; C1 -58181*x^2 + 64481*y^2 + 61169*z^2
(-3207/19325 : -18574/19325 : 1) C2b (612769/932385 : 35639/932385 : 1)
** u= -182/85 ; C1 -7369*x^2 - 40349*y^2 + 5041*z^2
(11999/20485 : 5112/20485 : 1) C2a (-624/71 : 53/157 : 1)
** u= -182/151 ; C1 -37201*x^2 - 55925*y^2 + 44641*z^2
(8866/14457 : 53513/72285 : 1) C2a (-994152/718391 : 394097/3591955 : 1)
** u= -182/159 ; C1 -43777*x^2 - 58405*y^2 + 50033*z^2
(-9226/62213 : -57025/62213 : 1) C2a (2857088/2932051 : -165729/2932051 : 1)
** u= -182/163 ; C1 -47305*x^2 - 59693*y^2 + 52777*z^2
(-165589/159411 : -27172/159411 : 1) C2a (-898958/385575 : -89759/385575 : 1)
** u= -182/173 ; C1 -56825*x^2 - 63053*y^2 + 59777*z^2
(12558/12595 : -575/2519 : 1) C2a (-1342874/835843 : -5687/36341 : 1)
** u= -182/181 ; C1 -65161*x^2 - 65885*y^2 + 65521*z^2
(-16954/35111 : 30687/35111 : 1) C2a (-56052/60953 : -4001/60953 : 1)
** u= -182/193 ; C1 -78865*x^2 - 70373*y^2 + 74377*z^2
(-24145/24877 : 864/24877 : 1) C2a (261978/12379 : 30383/12379 : 1)
** u= -181/121 ; C1 -18362*x^2 + 47402*y^2 + 25682*z^2
(-10386/13181 : 7235/13181 : 1) C2b (558/1339 : 113/1339 : 1)
** u= -181/161 ; C1 {+/-} -45802*x^2 + 58682*y^2 + 51442*z^2
(18190/22853 : -14127/22853 : 1) C2a (68171/84405 : 73/4965 : 1) C2b (81934/667777 : -3263/39281 : 1)
** u= -181/185 ; C1 -69946*x^2 - 66986*y^2 + 68434*z^2
(-5455/8029 : 5898/8029 : 1) C2a (-108439/150999 : -3319/150999 : 1)
** u= -180/127 ; C1 -21605*x^2 + 48529*y^2 + 29449*z^2
(21/773 : -602/773 : 1) C2b (-64097/485877 : 6209/69411 : 1)
** u= -180/149 ; C1 -36125*x^2 + 54601*y^2 + 43441*z^2
(-24197/22083 : -46/1299 : 1) C2b (-24007/381705 : -32851/381705 : 1)
** u= -180/167 ; C1 -51605*x^2 + 60289*y^2 + 55609*z^2
(-70725/71029 : -19286/71029 : 1) C2b (200221/284901 : 9121/284901 : 1)
** u= -180/199 ; C1 -87125*x^2 + 72001*y^2 + 78841*z^2
(3192/3431 : 749/3431 : 1) C2b (418741/2506105 : 26091/358015 : 1)
** u= -178/77 ; C1 -6505*x^2 - 37613*y^2 + 1657*z^2
(4813/10221 : -772/10221 : 1) C2a (-190138/44175 : 1649/44175 : 1)
** u= -178/95 ; C1 -9169*x^2 - 40709*y^2 + 11161*z^2
(-746/6633 : -3455/6633 : 1) C2a (-275551926/6288415 : 16273787/6288415 : 1)
** u= -178/117 ; C1 -16825*x^2 - 45373*y^2 + 23657*z^2
(106/91 : -209/1547 : 1) C2a (-64/57 : -71/152133 : 1)
** u= -178/119 ; C1 -17761*x^2 - 45845*y^2 + 24841*z^2
(-19466/218689 : -160521/218689 : 1) C2a (-1908606/616739 : -148255/616739 : 1)
** u= -178/133 ; C1 -25433*x^2 - 49373*y^2 + 33353*z^2
(-7746/34175 : -27533/34175 : 1) C2a (7000154/1734683 : 630773/1734683 : 1)
** u= -178/143 ; C1 -32113*x^2 - 52133*y^2 + 39673*z^2
(217/3147 : -2740/3147 : 1) C2a (-3999982/4141989 : -157639/4141989 : 1)
** u= -178/145 ; C1 -33569*x^2 - 52709*y^2 + 40961*z^2
(-10935/55673 : 48296/55673 : 1) C2a (10295698/4087645 : 961051/4087645 : 1)
** u= -178/187 ; C1 -73385*x^2 - 66653*y^2 + 69857*z^2
(-8994/66373 : -67291/66373 : 1) C2a (3252896/392707 : -374621/392707 : 1)
** u= -178/193 ; C1 -80513*x^2 - 68933*y^2 + 74273*z^2
(-102/907 : 935/907 : 1) C2a (-163388/242675 : 281/14275 : 1)
** u= -176/97 ; C1 -9733*x^2 + 40385*y^2 + 12577*z^2
(-2071/19963 : 11094/19963 : 1) C2b (13993/9731 : 235/9731 : 1)
** u= -176/167 ; C1 -52853*x^2 + 58865*y^2 + 55697*z^2
(-297288/297199 : -64961/297199 : 1) C2b (876199/1182303 : -10223/1182303 : 1)
** u= -176/169 ; C1 -54805*x^2 + 59537*y^2 + 57073*z^2
(23300/22857 : -1039/22857 : 1) C2b (91849/189785 : 11641/189785 : 1)
** u= -175/107 ; C1 -12970*x^2 - 42074*y^2 + 18274*z^2
(4034/11411 : -7179/11411 : 1) C2a (552183/97493 : -40069/97493 : 1)
** u= -175/163 ; C1 {+/-} -49370*x^2 + 57194*y^2 + 52994*z^2
(1854/3119 : 2459/3119 : 1) C2a (-630361/479041 : -55933/479041 : 1) C2b (-195884/270321 : -6661/270321 : 1)
** u= -174/95 ; C1 -9281*x^2 - 39301*y^2 + 11809*z^2
(65849/67695 : 18788/67695 : 1) C2a (-66666/43435 : 91/6205 : 1)
** u= -174/97 ; C1 -9809*x^2 - 39685*y^2 + 12889*z^2
(10542/13687 : 5777/13687 : 1) C2a (-670194/279119 : 34283/279119 : 1)
** u= -174/101 ; C1 -10985*x^2 - 40477*y^2 + 15073*z^2
(-10949/21177 : -892/1629 : 1) C2a (378/269 : 7/269 : 1)
** u= -174/185 ; C1 -72641*x^2 - 64501*y^2 + 68329*z^2
(-42810/58363 : 39299/58363 : 1) C2a (-1133054/1129075 : -98577/1129075 : 1)
** u= -174/199 ; C1 -89777*x^2 - 69877*y^2 + 78577*z^2
(1961/81711 : -86620/81711 : 1) C2a (750728/162785 : -89043/162785 : 1)
** u= -172/101 ; C1 -11101*x^2 + 39785*y^2 + 15361*z^2
(-7151/21759 : 12982/21759 : 1) C2b (1610689/6487879 : 593291/6487879 : 1)
** u= -172/109 ; C1 -13997*x^2 + 41465*y^2 + 19793*z^2
(-31916/36713 : 17307/36713 : 1) C2b (-451571/385623 : 4573/385623 : 1)
** u= -172/111 ; C1 -14821*x^2 + 41905*y^2 + 20921*z^2
(-28/127 : -1499/2159 : 1) C2b (3471/3439 : 2581/58463 : 1)
** u= -172/127 ; C1 -22853*x^2 + 45713*y^2 + 30233*z^2
(-14728/28615 : -20811/28615 : 1) C2b (-101687/146301 : -9127/146301 : 1)
** u= -171/79 ; C1 {+/-} -6410*x^2 + 35482*y^2 + 4018*z^2
(-6517/11499 : 2702/11499 : 1) C2a (-462897/64855 : 369449/1454605 : 1) C2b (-2762/1365 : -1697/30615 : 1)
** u= -171/103 ; C1 -11834*x^2 - 39850*y^2 + 16594*z^2
(-11/15 : 38/75 : 1) C2a (-5855/1753 : -1971/8765 : 1)
** u= -171/119 ; C1 {+/-} -18650*x^2 + 43402*y^2 + 25618*z^2
(12426/15095 : 1651/3019 : 1) C2a (3507/2809 : -167/2809 : 1) C2b (1005674/967755 : 7849/967755 : 1)
** u= -171/151 ; C1 {+/-} -39962*x^2 + 52042*y^2 + 45202*z^2
(201/835 : -758/835 : 1) C2a (-2810291/3234017 : -114177/3234017 : 1) C2b (580804/735927 : -10841/735927 : 1)
** u= -171/167 ; C1 -54458*x^2 + 57130*y^2 + 55762*z^2
(15106/15003 : 1477/15003 : 1) C2b (-3446/16233 : 179/2319 : 1)
** u= -170/71 ; C1 -5825*x^2 - 33941*y^2 + 281*z^2
(-5087/39755 : -588/7951 : 1) C2a (-1540654/11081 : 15787/11081 : 1)
** u= -170/77 ; C1 -6185*x^2 - 34829*y^2 + 3209*z^2
(19353/26993 : 788/26993 : 1) C2a (-6682/2333 : -59/2333 : 1)
** u= -170/109 ; C1 -14185*x^2 - 40781*y^2 + 20041*z^2
(5677/8933 : -5292/8933 : 1) C2a (165556/2541 : -1871/363 : 1)
** u= -170/159 ; C1 -47185*x^2 - 54181*y^2 + 50441*z^2
(-10747/47087 : 44312/47087 : 1) C2a (5467348/2778225 : 549697/2778225 : 1)
** u= -170/163 ; C1 -50905*x^2 - 55469*y^2 + 53089*z^2
(-58030/211557 : -199363/211557 : 1) C2a (-1962306/975085 : 201601/975085 : 1)
** u= -170/169 ; C1 -56785*x^2 - 57461*y^2 + 57121*z^2
(10277/10941 : 3824/10941 : 1) C2a (-379724/413709 : -113/1731 : 1)
** u= -169/133 ; C1 -27098*x^2 - 46250*y^2 + 34082*z^2
(-94/877 : 3747/4385 : 1) C2a (-797/137 : 1907/3425 : 1)
** u= -169/149 ; C1 -38842*x^2 - 50762*y^2 + 44002*z^2
(19726/18645 : 1897/18645 : 1) C2a (49397/23961 : 683/3423 : 1)
** u= -168/79 ; C1 -6341*x^2 + 34465*y^2 + 4561*z^2
(-13932/27223 : -7897/27223 : 1) C2b (474503/213003 : 5227/213003 : 1)
** u= -168/151 ; C1 -40757*x^2 + 51025*y^2 + 45313*z^2
(20937/20621 : -5242/20621 : 1) C2b (-41/53 : 129/8321 : 1)
** u= -167/123 ; C1 {+/-} -21370*x^2 + 43018*y^2 + 28322*z^2
(-238/17747 : -14399/17747 : 1) C2a (49/17 : -39/157 : 1) C2b (482/595 : -39/785 : 1)
** u= -167/195 ; C1 -87754*x^2 + 65914*y^2 + 75266*z^2
(1547/1975 : 1126/1975 : 1) C2b (397904/1342439 : -85287/1342439 : 1)
** u= -166/73 ; C1 -5729*x^2 - 32885*y^2 + 2009*z^2
(-5558/9587 : -483/9587 : 1) C2a (3217906/214319 : 12491/30617 : 1)
** u= -166/75 ; C1 -5881*x^2 - 33181*y^2 + 2969*z^2
(5419/8467 : 1100/8467 : 1) C2a (-371264/39465 : 11963/39465 : 1)
** u= -166/97 ; C1 -10193*x^2 - 36965*y^2 + 14057*z^2
(-15566/13283 : -531/13283 : 1) C2a (3381212/319319 : -233449/319319 : 1)
** u= -166/107 ; C1 -13753*x^2 - 39005*y^2 + 19417*z^2
(7066/7177 : -2835/7177 : 1) C2a (221156/31323 : -17375/31323 : 1)
** u= -166/117 ; C1 -18313*x^2 - 41245*y^2 + 24977*z^2
(-3047/3341 : 1624/3341 : 1) C2a (3550016/117987 : 311621/117987 : 1)
** u= -166/175 ; C1 -64481*x^2 - 58181*y^2 + 61169*z^2
(62243/102275 : 81876/102275 : 1) C2a (670772/655205 : 58649/655205 : 1)
** u= -166/189 ; C1 -80665*x^2 - 63277*y^2 + 70913*z^2
(-5090/6311 : 3407/6311 : 1) C2a (-10524638/2246671 : 1246437/2246671 : 1)
** u= -165/113 ; C1 {+/-} -16490*x^2 + 39994*y^2 + 22834*z^2
(12467/10869 : 1834/10869 : 1) C2a (179737/163093 : 567/23299 : 1) C2b (-29258/32753 : -231/4679 : 1)
** u= -164/101 ; C1 -11645*x^2 + 37097*y^2 + 16433*z^2
(-2367/17623 : 11654/17623 : 1) C2b (-295269/422597 : -32183/422597 : 1)
** u= -164/107 ; C1 -13949*x^2 + 38345*y^2 + 19649*z^2
(-4956/6319 : -3395/6319 : 1) C2b (-2637/49483 : 647/7069 : 1)
** u= -164/113 ; C1 -16613*x^2 + 39665*y^2 + 22937*z^2
(-1272/1181 : -359/1181 : 1) C2b (327991/577677 : -44167/577677 : 1)
** u= -164/155 ; C1 -45341*x^2 + 50921*y^2 + 47969*z^2
(-10636/14087 : 9285/14087 : 1) C2b (-5437/10323 : -601/10323 : 1)
** u= -164/165 ; C1 -54781*x^2 + 54121*y^2 + 54449*z^2
(-10636/29257 : 27325/29257 : 1) C2b (122507/186877 : -5361/186877 : 1)
** u= -164/175 ; C1 -65221*x^2 + 57521*y^2 + 61129*z^2
(22945/26721 : -12722/26721 : 1) C2b (24373/132175 : -9787/132175 : 1)
** u= -164/199 ; C1 -94357*x^2 + 66497*y^2 + 77977*z^2
(88445/97389 : -4706/97389 : 1) C2b (-1884713/8531665 : 559859/8531665 : 1)
** u= -163/127 ; C1 {+/-} -24410*x^2 + 42698*y^2 + 30962*z^2
(4819/6871 : 4578/6871 : 1) C2a (-595217/445355 : -41699/445355 : 1) C2b (-51842/61455 : 2093/61455 : 1)
** u= -163/175 ; C1 {+/-} -65594*x^2 + 57194*y^2 + 61106*z^2
(-29210/45307 : -34851/45307 : 1) C2a (-861973/380537 : 96217/380537 : 1) C2b (31494/169259 : -12473/169259 : 1)
** u= -162/77 ; C1 -5993*x^2 - 32173*y^2 + 4633*z^2
(-14605/29493 : -9248/29493 : 1) C2a (1767754/123115 : 74811/123115 : 1)
** u= -161/85 ; C1 -7306*x^2 - 33146*y^2 + 8674*z^2
(67538/130885 : 58971/130885 : 1) C2a (391869/55759 : 22009/55759 : 1)
** u= -161/149 ; C1 {+/-} -40970*x^2 + 48122*y^2 + 44258*z^2
(-35049/33989 : -4078/33989 : 1) C2a (4142801/360245 : -447427/360245 : 1) C2b (-1843836/2567677 : -72683/2567677 :
1)
** u= -161/181 ; C1 {+/-} -73162*x^2 + 58682*y^2 + 65122*z^2
(-48658/55737 : -22265/55737 : 1) C2a (44727/24931 : 4981/24931 : 1) C2b (20638/34265 : 731/34265 : 1)
** u= -160/93 ; C1 -9325*x^2 + 34249*y^2 + 12809*z^2
(13391/15395 : 1262/3079 : 1) C2b (218649/170779 : -5059/170779 : 1)
** u= -160/113 ; C1 -17125*x^2 + 38369*y^2 + 23329*z^2
(99448/85245 : 409/17049 : 1) C2b (537599/537665 : -10607/537665 : 1)
** u= -160/147 ; C1 -39565*x^2 + 47209*y^2 + 43049*z^2
(-11720/12919 : 6089/12919 : 1) C2b (20721/27071 : -241/27071 : 1)
** u= -160/183 ; C1 -75925*x^2 + 59089*y^2 + 66449*z^2
(-176597/189505 : -3538/37901 : 1) C2b (-589339/981515 : -16923/981515 : 1)
** u= -160/191 ; C1 -85765*x^2 + 62081*y^2 + 72001*z^2
(40565/64273 : -50178/64273 : 1) C2b (-39311/116891 : -6899/116891 : 1)
** u= -159/131 ; C1 {+/-} -27770*x^2 + 42442*y^2 + 33538*z^2
(-911/5799 : 5102/5799 : 1) C2a (-218967/57035 : 21409/57035 : 1) C2b (3376/13195 : 1089/13195 : 1)
** u= -158/73 ; C1 -5473*x^2 - 30293*y^2 + 3433*z^2
(7507/21137 : -6360/21137 : 1) C2a (302748/120139 : -1651/120139 : 1)
** u= -158/91 ; C1 -8857*x^2 - 33245*y^2 + 12073*z^2
(31982/49809 : 25069/49809 : 1) C2a (-20095334/13135407 : 605039/13135407 : 1)
** u= -158/107 ; C1 -14585*x^2 - 36413*y^2 + 20297*z^2
(-6934/7729 : 3747/7729 : 1) C2a (158744/10435 : -13343/10435 : 1)
** u= -158/151 ; C1 -43537*x^2 - 47765*y^2 + 45553*z^2
(127/1639 : 1596/1639 : 1) C2a (-247986/294733 : -13013/294733 : 1)
** u= -158/163 ; C1 -54793*x^2 - 51533*y^2 + 53113*z^2
(-4202/19985 : 19821/19985 : 1) C2a (-3378612/2324365 : -341393/2324365 : 1)
** u= -158/175 ; C1 -67489*x^2 - 55589*y^2 + 60961*z^2
(-19295/30463 : -23784/30463 : 1) C2a (-1162454/212349 : -136459/212349 : 1)
** u= -158/185 ; C1 -79169*x^2 - 59189*y^2 + 67721*z^2
(-508965/598697 : -252224/598697 : 1) C2a (-62834/4349 : 1189933/682793 : 1)
** u= -156/77 ; C1 -5933*x^2 + 30265*y^2 + 5617*z^2
(-547/1011 : 362/1011 : 1) C2b (72047/63699 : -4895/63699 : 1)
** u= -156/163 ; C1 -55469*x^2 + 50905*y^2 + 53089*z^2
(2583/3137 : 1730/3137 : 1) C2b (166391/413211 : -25903/413211 : 1)
** u= -156/175 ; C1 -68261*x^2 + 54961*y^2 + 60889*z^2
(-20816/130995 : 135913/130995 : 1) C2b (3967039/10488995 : -627591/10488995 : 1)
** u= -156/179 ; C1 -72845*x^2 + 56377*y^2 + 63553*z^2
(-987/1133 : 434/1133 : 1) C2b (-6593/15965 : 873/15965 : 1)
** u= -154/65 ; C1 -4801*x^2 - 27941*y^2 + 529*z^2
(-2254/6955 : -207/6955 : 1) C2a (-907874/141495 : 4297/141495 : 1)
** u= -154/79 ; C1 -6257*x^2 - 29957*y^2 + 6857*z^2
(909/4655 : 2188/4655 : 1) C2a (2913772/34085 : -157307/34085 : 1)
** u= -154/83 ; C1 -7033*x^2 - 30605*y^2 + 8737*z^2
(-11822/23461 : 11181/23461 : 1) C2a (-41915784/473857 : -2527321/473857 : 1)
** u= -154/85 ; C1 -7481*x^2 - 30941*y^2 + 9689*z^2
(-6111/14425 : -7492/14425 : 1) C2a (5649752/2291005 : 285001/2291005 : 1)
** u= -154/89 ; C1 -8497*x^2 - 31637*y^2 + 11617*z^2
(84275/80661 : -21944/80661 : 1) C2a (2282104/47907 : -156017/47907 : 1)
** u= -154/115 ; C1 -19001*x^2 - 36941*y^2 + 24929*z^2
(11410/13609 : -7617/13609 : 1) C2a (863642/887543 : -13277/887543 : 1)
** u= -154/123 ; C1 -23593*x^2 - 38845*y^2 + 29297*z^2
(15131/37847 : -30680/37847 : 1) C2a (2670718/413751 : 259277/413751 : 1)
** u= -154/129 ; C1 -27457*x^2 - 40357*y^2 + 32657*z^2
(41854/50971 : 30175/50971 : 1) C2a (17903402/849575 : -106839/49975 : 1)
** u= -154/137 ; C1 -33169*x^2 - 42485*y^2 + 37249*z^2
(-1351/7529 : 6948/7529 : 1) C2a (876734/811179 : 325/4203 : 1)
** u= -154/155 ; C1 -48361*x^2 - 47741*y^2 + 48049*z^2
(-3271/4907 : -3660/4907 : 1) C2a (4999894/14085 : 566137/14085 : 1)
** u= -154/159 ; C1 -52177*x^2 - 48997*y^2 + 50537*z^2
(-16985/17339 : 1696/17339 : 1) C2a (-49909058/48862621 : -4244391/48862621 : 1)
** u= -154/183 ; C1 -78433*x^2 - 57205*y^2 + 66137*z^2
(7621/17423 : -16472/17423 : 1) C2a (109384/63003 : 12475/63003 : 1)
** u= -153/133 ; C1 {+/-} -30458*x^2 + 41098*y^2 + 34978*z^2
(2126/7869 : -7025/7869 : 1) C2a (754477/325799 : -73539/325799 : 1) C2b (-329726/404787 : -149/404787 : 1)
** u= -152/91 ; C1 -9181*x^2 + 31385*y^2 + 12841*z^2
(-1571/1329 : -26/1329 : 1) C2b (-31061/115321 : -10471/115321 : 1)
** u= -152/117 ; C1 -20413*x^2 + 36793*y^2 + 26153*z^2
(4736/6445 : -4133/6445 : 1) C2b (-27179/338953 : -29799/338953 : 1)
** u= -152/193 ; C1 -92005*x^2 + 60353*y^2 + 72817*z^2
(82831/143931 : -120562/143931 : 1) C2b (-4343/227981 : 15619/227981 : 1)
** u= -151/67 ; C1 {+/-} -4778*x^2 + 27290*y^2 + 1922*z^2
(-1271/2123 : 186/2123 : 1) C2a (-75689/20987 : -35/677 : 1) C2b (50336/18507 : 29/597 : 1)
** u= -151/171 ; C1 {+/-} -65722*x^2 + 52042*y^2 + 58082*z^2
(16138/37343 : 35035/37343 : 1) C2a (1544927/420969 : -181531/420969 : 1) C2b (1391634/7880045 : -562133/7880045 : 1)
** u= -150/143 ; C1 -38945*x^2 - 42949*y^2 + 40849*z^2
(-29757/29779 : 6364/29779 : 1) C2a (-2964154/169961 : 325977/169961 : 1)
** u= -150/199 ; C1 -101105*x^2 - 62101*y^2 + 76801*z^2
(4293/56603 : 62708/56603 : 1) C2a (-69742278/107846303 : -5080481/107846303 : 1)
** u= -149/73 ; C1 -5338*x^2 + 27530*y^2 + 4882*z^2
(5779/18273 : 7262/18273 : 1) C2b (-98632/49861 : -491/49861 : 1)
** u= -149/129 ; C1 {+/-} -28522*x^2 + 38842*y^2 + 32882*z^2
(21745/61817 : 53738/61817 : 1) C2a (-72611/61993 : 5397/61993 : 1) C2b (13602/31765 : -2299/31765 : 1)
** u= -149/161 ; C1 {+/-} -55850*x^2 + 48122*y^2 + 51698*z^2
(-13014/13673 : 2069/13673 : 1) C2a (-7116361/167357 : -832409/167357 : 1) C2b (-616934/1252863 : -63137/1252863 : 1)
** u= -148/107 ; C1 -15805*x^2 + 33353*y^2 + 21217*z^2
(-371/1389 : 1078/1389 : 1) C2b (-13667/203609 : 2603/29087 : 1)
** u= -148/113 ; C1 -18853*x^2 + 34673*y^2 + 24313*z^2
(14047/99975 : -83074/99975 : 1) C2b (213223/246935 : -8419/246935 : 1)
** u= -148/159 ; C1 -54181*x^2 + 47185*y^2 + 50441*z^2
(122269/163069 : -106114/163069 : 1) C2b (-70863/189013 : -11929/189013 : 1)
** u= -148/173 ; C1 -69133*x^2 + 51833*y^2 + 59233*z^2
(29380/47901 : 38351/47901 : 1) C2b (3156149/5411227 : -101831/5411227 : 1)
** u= -147/95 ; C1 -10874*x^2 - 30634*y^2 + 15346*z^2
(753/635 : -458/10795 : 1) C2a (1629/565 : -2029/9605 : 1)
** u= -146/69 ; C1 -4825*x^2 - 26077*y^2 + 3593*z^2
(-1109/4261 : 1508/4261 : 1) C2a (82688/19335 : -2941/19335 : 1)
** u= -146/85 ; C1 -7801*x^2 - 28541*y^2 + 10729*z^2
(-9290/8443 : 1791/8443 : 1) C2a (-459442/18483 : 31747/18483 : 1)
** u= -146/89 ; C1 -8945*x^2 - 29237*y^2 + 12593*z^2
(1995/1717 : 2968/22321 : 1) C2a (70796/55405 : 2003/102895 : 1)
** u= -146/139 ; C1 -36745*x^2 - 40637*y^2 + 38593*z^2
(4069/21839 : -20928/21839 : 1) C2a (435898/585315 : -3479/585315 : 1)
** u= -146/183 ; C1 -81889*x^2 - 54805*y^2 + 65609*z^2
(-84946/101329 : 38857/101329 : 1) C2a (3242692/225147 : 400141/225147 : 1)
** u= -146/197 ; C1 -100313*x^2 - 60125*y^2 + 75017*z^2
(2621/3397 : -8568/16985 : 1) C2a (534514/786523 : -218953/3932615 : 1)
** u= -145/77 ; C1 {+/-} -6010*x^2 + 26954*y^2 + 7234*z^2
(-7066/7937 : -2403/7937 : 1) C2a (34329/13339 : -1567/13339 : 1) C2b (-187696/262181 : -22079/262181 : 1)
** u= -144/65 ; C1 -4421*x^2 + 24961*y^2 + 2209*z^2
(5499/11087 : 2350/11087 : 1) C2b (25459/13771 : 21/293 : 1)
** u= -144/119 ; C1 -22997*x^2 + 34897*y^2 + 27697*z^2
(-9595/36033 : -31142/36033 : 1) C2b (426067/870011 : 61707/870011 : 1)
** u= -144/163 ; C1 -59693*x^2 + 47305*y^2 + 52777*z^2
(2851/12057 : 12326/12057 : 1) C2b (16597/45699 : 2765/45699 : 1)
** u= -142/75 ; C1 -5689*x^2 - 25789*y^2 + 6761*z^2
(-13250/15401 : -4843/15401 : 1) C2a (-197222/57673 : -10023/57673 : 1)
** u= -142/141 ; C1 -39481*x^2 - 40045*y^2 + 39761*z^2
(-2782/2803 : 413/2803 : 1) C2a (-16188088/20980867 : -700749/20980867 : 1)
** u= -142/187 ; C1 -88793*x^2 - 55133*y^2 + 67913*z^2
(-15097/20543 : -12360/20543 : 1) C2a (-3000016/3590533 : 290137/3590533 : 1)
** u= -142/189 ; C1 -91417*x^2 - 55885*y^2 + 69233*z^2
(-43906/65783 : 46985/65783 : 1) C2a (4232366/565377 : -530381/565377 : 1)
** u= -140/59 ; C1 -3965*x^2 + 23081*y^2 + 401*z^2
(265/1201 : -114/1201 : 1) C2b (-1913143/300423 : -1693/300423 : 1)
** u= -140/109 ; C1 -17965*x^2 + 31481*y^2 + 22801*z^2
(9664/9093 : 2567/9093 : 1) C2b (-1345631/1505621 : -191/9971 : 1)
** u= -140/129 ; C1 -30565*x^2 + 36241*y^2 + 33161*z^2
(-7808/8813 : -4433/8813 : 1) C2b (1248339/1929791 : -86101/1929791 : 1)
** u= -140/199 ; C1 -106165*x^2 + 59201*y^2 + 75721*z^2
(-19427/43029 : -41126/43029 : 1) C2b (-83567/403613 : -22633/403613 : 1)
** u= -138/83 ; C1 -7673*x^2 - 25933*y^2 + 10753*z^2
(1203/13295 : -8536/13295 : 1) C2a (4452198/559729 : -319381/559729 : 1)
** u= -138/107 ; C1 -17225*x^2 - 30493*y^2 + 21937*z^2
(6774/41005 : 6881/8201 : 1) C2a (559758/190349 : -50897/190349 : 1)
** u= -138/125 ; C1 -28169*x^2 - 34669*y^2 + 31081*z^2
(30610/29307 : 2951/29307 : 1) C2a (504144/632389 : -10799/632389 : 1)
** u= -138/145 ; C1 -44129*x^2 - 40069*y^2 + 42001*z^2
(14810/17247 : 8381/17247 : 1) C2a (476212/190067 : 53007/190067 : 1)
** u= -138/149 ; C1 -47801*x^2 - 41245*y^2 + 44281*z^2
(3473/14097 : 14120/14097 : 1) C2a (1140598/1706933 : 26637/1706933 : 1)
** u= -138/179 ; C1 -80441*x^2 - 51085*y^2 + 62401*z^2
(56439/64699 : 9868/64699 : 1) C2a (270116/447091 : 15099/447091 : 1)
** u= -137/149 ; C1 -48122*x^2 - 40970*y^2 + 44258*z^2
(30578/34121 : -12627/34121 : 1) C2a (-449867/568781 : -30071/568781 : 1)
** u= -136/63 ; C1 -4069*x^2 + 22465*y^2 + 2609*z^2
(-10361/44669 : -14570/44669 : 1) C2b (-1120193/458167 : 5295/458167 : 1)
** u= -136/95 ; C1 -11941*x^2 + 27521*y^2 + 16369*z^2
(2269/2577 : -1310/2577 : 1) C2b (-73829/81251 : 3557/81251 : 1)
** u= -136/105 ; C1 -16501*x^2 + 29521*y^2 + 21089*z^2
(17068/15485 : 2909/15485 : 1) C2b (-66069/847781 : 74483/847781 : 1)
** u= -136/121 ; C1 -25877*x^2 + 33137*y^2 + 29057*z^2
(-2513/4955 : -4074/4955 : 1) C2b (-96697/147399 : -1001/21057 : 1)
** u= -136/137 ; C1 -37813*x^2 + 37265*y^2 + 37537*z^2
(-37964/145257 : -140681/145257 : 1) C2b (-59207/105971 : -5101/105971 : 1)
** u= -136/143 ; C1 -42949*x^2 + 38945*y^2 + 40849*z^2
(11393/19077 : 15446/19077 : 1) C2b (-656489/4513481 : 342529/4513481 : 1)
** u= -136/169 ; C1 -69365*x^2 + 47057*y^2 + 56033*z^2
(24725/34343 : 22434/34343 : 1) C2b (-17313/523435 : 36427/523435 : 1)
** u= -136/175 ; C1 -76421*x^2 + 49121*y^2 + 59729*z^2
(-42120/50087 : -17041/50087 : 1) C2b (-546941/1723515 : -95021/1723515 : 1)
** u= -136/197 ; C1 -105373*x^2 + 57305*y^2 + 73897*z^2
(-51488/110289 : 103975/110289 : 1) C2b (-58289/160123 : -980497/25139311 : 1)
** u= -135/83 ; C1 -7850*x^2 + 25114*y^2 + 11074*z^2
(14/327 : 217/327 : 1) C2b (1306/1785 : -19/255 : 1)
** u= -135/187 ; C1 -92090*x^2 - 53194*y^2 + 67234*z^2
(-27075/80227 : 82862/80227 : 1) C2a (-1453017/1994945 : -133837/1994945 : 1)
** u= -134/57 ; C1 -3649*x^2 - 21205*y^2 + 569*z^2
(-134/8291 : -1357/8291 : 1) C2a (-609446/100159 : -6051/100159 : 1)
** u= -134/97 ; C1 -13009*x^2 - 27365*y^2 + 17449*z^2
(30323/26193 : -596/26193 : 1) C2a (1232096/1112781 : 48733/1112781 : 1)
** u= -134/111 ; C1 -20065*x^2 - 30277*y^2 + 24113*z^2
(-21185/70399 : 60412/70399 : 1) C2a (6658858/1606749 : 656227/1606749 : 1)
** u= -134/113 ; C1 -21233*x^2 - 30725*y^2 + 25097*z^2
(-243/937 : -4112/4685 : 1) C2a (-129994/33479 : -64729/167395 : 1)
** u= -134/119 ; C1 -24977*x^2 - 32117*y^2 + 28097*z^2
(-10922/38837 : -35025/38837 : 1) C2a (4936442/280289 : 520591/280289 : 1)
** u= -134/151 ; C1 -51025*x^2 - 40757*y^2 + 45313*z^2
(1126/1293 : 521/1293 : 1) C2a (168/251 : 7/251 : 1)
** u= -134/165 ; C1 -65641*x^2 - 45181*y^2 + 53489*z^2
(15886/27355 : -22787/27355 : 1) C2a (324262/124723 : 38847/124723 : 1)
** u= -134/169 ; C1 -70177*x^2 - 46517*y^2 + 55897*z^2
(-41435/48217 : 14268/48217 : 1) C2a (-113736/31537 : 13903/31537 : 1)
** u= -133/73 ; C1 {+/-} -5498*x^2 + 23018*y^2 + 7058*z^2
(-2598/2293 : 5/2293 : 1) C2a (-6197341/195443 : 386893/195443 : 1) C2b (-16374/37895 : -3403/37895 : 1)
** u= -133/97 ; C1 {+/-} -13130*x^2 + 27098*y^2 + 17522*z^2
(581/2389 : 1878/2389 : 1) C2a (411109/128633 : -35491/128633 : 1) C2b (-265756/339777 : 18523/339777 : 1)
** u= -133/113 ; C1 {+/-} -21418*x^2 + 30458*y^2 + 25138*z^2
(5050/6249 : 3781/6249 : 1) C2a (-2797/2211 : 33853/347127 : 1) C2b (194476/243845 : -958739/38283665 : 1)
** u= -133/129 ; C1 {+/-} -32266*x^2 + 34330*y^2 + 33266*z^2
(-21406/84629 : -80681/84629 : 1) C2a (-131081/39979 : 14199/39979 : 1) C2b (-33594/139871 : 10697/139871 : 1)
** u= -133/153 ; C1 {+/-} -53338*x^2 + 41098*y^2 + 46418*z^2
(767/8293 : 8770/8293 : 1) C2a (859477/1142889 : 59561/1142889 : 1) C2b (170372/475289 : -28407/475289 : 1)
** u= -133/193 ; C1 {+/-} -101258*x^2 + 54938*y^2 + 70898*z^2
(45081/56809 : 20470/56809 : 1) C2a (376897/795635 : -1727/795635 : 1) C2b (29344/85437 : -3569/85437 : 1)
** u= -132/61 ; C1 -3821*x^2 + 21145*y^2 + 2401*z^2
(16611/25019 : -4606/25019 : 1) C2b (-7993/3453 : 121/3453 : 1)
** u= -132/107 ; C1 -18173*x^2 + 28873*y^2 + 22273*z^2
(-6027/6805 : -3586/6805 : 1) C2b (-1007597/1221959 : 36003/1221959 : 1)
** u= -132/155 ; C1 -55709*x^2 + 41449*y^2 + 47521*z^2
(-41800/77067 : -66791/77067 : 1) C2b (-712991/1207005 : -16081/1207005 : 1)
** u= -131/55 ; C1 -3466*x^2 - 20186*y^2 + 274*z^2
(593/2471 : -150/2471 : 1) C2a (191181/4145 : -2483/4145 : 1)
** u= -131/79 ; C1 {+/-} -6970*x^2 + 23402*y^2 + 9778*z^2
(-1469/1551 : 602/1551 : 1) C2a (157049/8433 : -11431/8433 : 1) C2b (-1188046/1292923 : -82903/1292923 : 1)
** u= -131/159 ; C1 {+/-} -60250*x^2 + 42442*y^2 + 49778*z^2
(41587/45895 : 782/9179 : 1) C2a (-254351/183195 : 28243/183195 : 1) C2b (-1304638/4393201 : -267789/4393201 : 1)
** u= -130/67 ; C1 -4505*x^2 - 21389*y^2 + 5009*z^2
(2275/7247 : -3348/7247 : 1) C2a (793724/97325 : 42371/97325 : 1)
** u= -130/87 ; C1 -9505*x^2 - 24469*y^2 + 13289*z^2
(-4615/4531 : -1696/4531 : 1) C2a (119548/57633 : 8441/57633 : 1)
** u= -130/89 ; C1 -10225*x^2 - 24821*y^2 + 14161*z^2
(46529/43825 : 2856/8765 : 1) C2a (129932/105315 : -47/885 : 1)
** u= -130/109 ; C1 -19625*x^2 - 28781*y^2 + 23321*z^2
(-7014/10655 : -1529/2131 : 1) C2a (278308/272513 : 15851/272513 : 1)
** u= -130/141 ; C1 -42985*x^2 - 36781*y^2 + 39641*z^2
(-7847/8257 : -1232/8257 : 1) C2a (2381216/305949 : -39719/43707 : 1)
** u= -130/177 ; C1 -81505*x^2 - 48229*y^2 + 60449*z^2
(-14834/47111 : 49091/47111 : 1) C2a (-40274/77381 : -957/77381 : 1)
** u= -129/85 ; C1 -8906*x^2 + 23866*y^2 + 12514*z^2
(-3706/4305 : 2143/4305 : 1) C2b (38786/36499 : -1047/36499 : 1)
** u= -129/109 ; C1 {+/-} -19802*x^2 + 28522*y^2 + 23362*z^2
(3338/13545 : -11939/13545 : 1) C2a (418609/173033 : -40107/173033 : 1) C2b (958312/3754241 : 306453/3754241 : 1)
** u= -129/133 ; C1 {+/-} -36458*x^2 + 34330*y^2 + 35362*z^2
(-14817/65621 : 64826/65621 : 1) C2a (-571157/22211 : 65403/22211 : 1) C2b (-1231012/4279101 : -305171/4279101 : 1)
** u= -129/149 ; C1 {+/-} -50762*x^2 + 38842*y^2 + 44002*z^2
(21042/22853 : 3605/22853 : 1) C2a (13143/18839 : -761/18839 : 1) C2b (202066/663845 : -6039/94835 : 1)
** u= -129/173 ; C1 -77018*x^2 - 46570*y^2 + 57922*z^2
(7617/11009 : 7402/11009 : 1) C2a (-184999/225127 : 18027/225127 : 1)
** u= -129/197 ; C1 -109034*x^2 + 55450*y^2 + 72994*z^2
(10146/12401 : 151/12401 : 1) C2b (-31016/99229 : -4035/99229 : 1)
** u= -128/85 ; C1 -8989*x^2 + 23609*y^2 + 12601*z^2
(19736/22513 : 11055/22513 : 1) C2b (181853/165323 : 1771/165323 : 1)
** u= -128/87 ; C1 -9685*x^2 + 23953*y^2 + 13457*z^2
(8077/7337 : 1966/7337 : 1) C2b (-22751/62773 : -5373/62773 : 1)
** u= -128/93 ; C1 -12013*x^2 + 25033*y^2 + 16073*z^2
(-24184/24545 : -10303/24545 : 1) C2b (-291857/540481 : 40593/540481 : 1)
** u= -128/103 ; C1 -16693*x^2 + 26993*y^2 + 20593*z^2
(-9091/11641 : 7230/11641 : 1) C2b (-3295607/3901741 : -99563/3901741 : 1)
** u= -128/117 ; C1 -24925*x^2 + 30073*y^2 + 27257*z^2
(-107269/113455 : 9230/22691 : 1) C2b (-383389/649385 : -34911/649385 : 1)
** u= -128/123 ; C1 -29053*x^2 + 31513*y^2 + 30233*z^2
(40348/42683 : 15715/42683 : 1) C2b (-145481/219545 : -7767/219545 : 1)
** u= -128/145 ; C1 -47269*x^2 + 37409*y^2 + 41761*z^2
(39472/42069 : -2645/42069 : 1) C2b (8875267/14463805 : 191597/14463805 : 1)
** u= -128/177 ; C1 -82405*x^2 + 47713*y^2 + 60257*z^2
(-4717/60071 : -67222/60071 : 1) C2b (294939/589567 : -3097/589567 : 1)
** u= -128/187 ; C1 -95485*x^2 + 51353*y^2 + 66457*z^2
(-505/33397 : 2922/2569 : 1) C2b (-81413/646571 : 37541/646571 : 1)
** u= -127/123 ; C1 -29290*x^2 - 31258*y^2 + 30242*z^2
(-1450/1699 : -907/1699 : 1) C2a (239701/271875 : 14917/271875 : 1)
** u= -127/163 ; C1 {+/-} -66170*x^2 + 42698*y^2 + 51842*z^2
(34293/39139 : -6118/39139 : 1) C2a (853901/1307803 : 361/8123 : 1) C2b (176966/342447 : -47/2127 : 1)
** u= -126/59 ; C1 -3545*x^2 - 19357*y^2 + 2473*z^2
(-471/727 : 164/727 : 1) C2a (-1255302/33329 : -50543/33329 : 1)
** u= -126/85 ; C1 -9161*x^2 - 23101*y^2 + 12769*z^2
(18306/24055 : 13673/24055 : 1) C2a (57731068/24106855 : -38217/213335 : 1)
** u= -126/89 ; C1 -10625*x^2 - 23797*y^2 + 14473*z^2
(98102/236775 : -6905/9471 : 1) C2a (10792/8689 : 537/8689 : 1)
** u= -126/115 ; C1 -24041*x^2 - 29101*y^2 + 26329*z^2
(1813/1851 : -620/1851 : 1) C2a (-119582/136193 : -6033/136193 : 1)
** u= -126/127 ; C1 -32513*x^2 - 32005*y^2 + 32257*z^2
(3342/9149 : 8545/9149 : 1) C2a (71144/913 : 8061/913 : 1)
** u= -126/191 ; C1 -102017*x^2 - 52357*y^2 + 68737*z^2
(-1039167/8056895 : -536288/473935 : 1) C2a (146245418/49534115 : 18694293/49534115 : 1)
** u= -125/129 ; C1 -34330*x^2 - 32266*y^2 + 33266*z^2
(7214/11561 : -9079/11561 : 1) C2a (-312761/19905 : -35809/19905 : 1)
** u= -124/57 ; C1 -3349*x^2 + 18625*y^2 + 2009*z^2
(28/137 : 217/685 : 1) C2b (172511/80899 : 3021/57785 : 1)
** u= -124/65 ; C1 -4261*x^2 + 19601*y^2 + 4969*z^2
(143/591 : 290/591 : 1) C2b (-1339/6625 : -619/6625 : 1)
** u= -124/87 ; C1 -10069*x^2 + 22945*y^2 + 13769*z^2
(38668/33823 : -5509/33823 : 1) C2b (121077/354683 : 4319/50669 : 1)
** u= -124/91 ; C1 -11645*x^2 + 23657*y^2 + 15473*z^2
(-14955/23101 : 15458/23101 : 1) C2b (181821/185713 : -67/185713 : 1)
** u= -124/105 ; C1 -18421*x^2 + 26401*y^2 + 21689*z^2
(23/55 : -46/55 : 1) C2b (34147/51497 : 117/2239 : 1)
** u= -124/109 ; C1 -20717*x^2 + 27257*y^2 + 23537*z^2
(-5727/7183 : -4430/7183 : 1) C2b (-379463/730239 : -47117/730239 : 1)
** u= -124/117 ; C1 -25789*x^2 + 29065*y^2 + 27329*z^2
(5792/6557 : -3265/6557 : 1) C2b (83051/117751 : 3267/117751 : 1)
** u= -124/119 ; C1 -27157*x^2 + 29537*y^2 + 28297*z^2
(8000/12819 : -9929/12819 : 1) C2b (1630751/6162547 : 468169/6162547 : 1)
** u= -124/165 ; C1 -69661*x^2 + 42601*y^2 + 52769*z^2
(-47761/56543 : 15170/56543 : 1) C2b (-512469/1034291 : -22487/1034291 : 1)
** u= -124/177 ; C1 -84229*x^2 + 46705*y^2 + 59849*z^2
(10187/18587 : -15986/18587 : 1) C2b (-8601/18091 : -199/18091 : 1)
** u= -124/185 ; C1 -94741*x^2 + 49601*y^2 + 64729*z^2
(77420/94533 : 14609/94533 : 1) C2b (126211/281309 : 449/40187 : 1)
** u= -124/187 ; C1 -97469*x^2 + 50345*y^2 + 65969*z^2
(72392/100687 : -56019/100687 : 1) C2b (-595809/1627631 : 55237/1627631 : 1)
** u= -123/79 ; C1 {+/-} -7466*x^2 + 21370*y^2 + 10546*z^2
(-341/1299 : -890/1299 : 1) C2a (158627/123863 : 5355/123863 : 1) C2b (-1904/35009 : 3213/35009 : 1)
** u= -123/119 ; C1 {+/-} -27386*x^2 + 29290*y^2 + 28306*z^2
(-3834/31051 : -30299/31051 : 1) C2a (478917/581687 : 24463/581687 : 1) C2b (-48212/70113 : 1927/70113 : 1)
** u= -123/167 ; C1 {+/-} -72410*x^2 + 43018*y^2 + 53842*z^2
(-64698/84059 : -42403/84059 : 1) C2a (3213/575 : 63427/90275 : 1) C2b (-476/1503 : 12019/235971 : 1)
** u= -122/95 ; C1 -13649*x^2 - 23909*y^2 + 17321*z^2
(15954/29945 : -22457/29945 : 1) C2a (8373782/8462437 : 305153/8462437 : 1)
** u= -122/127 ; C1 -33553*x^2 - 31013*y^2 + 32233*z^2
(11894/21225 : 17753/21225 : 1) C2a (-416808/250009 : -43799/250009 : 1)
** u= -122/131 ; C1 -36761*x^2 - 32045*y^2 + 34241*z^2
(4119/13931 : 13708/13931 : 1) C2a (319538/361603 : 24865/361603 : 1)
** u= -122/159 ; C1 -63697*x^2 - 40165*y^2 + 49193*z^2
(-26122/39581 : 28925/39581 : 1) C2a (364036/333687 : -39575/333687 : 1)
** u= -122/171 ; C1 -77641*x^2 - 44125*y^2 + 56081*z^2
(-326/401 : -659/2005 : 1) C2a (-308/433 : -141/2165 : 1)
** u= -122/175 ; C1 -82609*x^2 - 45509*y^2 + 58441*z^2
(10555/38839 : 41652/38839 : 1) C2a (-1062516/685511 : -129209/685511 : 1)
** u= -122/177 ; C1 -85153*x^2 - 46213*y^2 + 59633*z^2
(255731/315149 : -87500/315149 : 1) C2a (-7262/189 : 133/27 : 1)
** u= -122/187 ; C1 -98473*x^2 - 49853*y^2 + 65713*z^2
(45383/58963 : -22680/58963 : 1) C2a (-12836808/12002561 : 1515529/12002561 : 1)
** u= -120/133 ; C1 -39005*x^2 + 32089*y^2 + 35209*z^2
(-11035/40647 : 40802/40647 : 1) C2b (3343567/5277903 : -45257/5277903 : 1)
** u= -120/139 ; C1 -44285*x^2 + 33721*y^2 + 38281*z^2
(-46852/75351 : -59689/75351 : 1) C2b (722561/1576669 : 76179/1576669 : 1)
** u= -120/167 ; C1 -73685*x^2 + 42289*y^2 + 53569*z^2
(-16223/20757 : -9338/20757 : 1) C2b (9839/369949 : -23379/369949 : 1)
** u= -120/193 ; C1 -108005*x^2 + 51649*y^2 + 69169*z^2
(282988/363321 : -96521/363321 : 1) C2b (2372951/7015525 : 819/26675 : 1)
** u= -119/67 ; C1 {+/-} -4714*x^2 + 18650*y^2 + 6274*z^2
(-154/615 : -1741/3075 : 1) C2a (115125/11131 : -37321/55655 : 1) C2b (-57214/44455 : 9031/222275 : 1)
** u= -119/123 ; C1 {+/-} -31258*x^2 + 29290*y^2 + 30242*z^2
(-6647/8111 : 4558/8111 : 1) C2a (-3987397/194991 : -457043/194991 : 1) C2b (130054/194327 : -3159/194327 : 1)
** u= -119/163 ; C1 -69418*x^2 + 40730*y^2 + 51202*z^2
(13487/57939 : -62530/57939 : 1) C2b (-13864/720377 : 46241/720377 : 1)
** u= -119/171 ; C1 {+/-} -78970*x^2 + 43402*y^2 + 55778*z^2
(-5177/6167 : 334/6167 : 1) C2a (881569/378255 : -661/2265 : 1) C2b (676294/1486133 : -171/8899 : 1)
** u= -118/71 ; C1 -5617*x^2 - 18965*y^2 + 7873*z^2
(1214/1173 : 367/1173 : 1) C2a (-2880156/194657 : 208667/194657 : 1)
** u= -118/101 ; C1 -17257*x^2 - 24125*y^2 + 20113*z^2
(-398/791 : 639/791 : 1) C2a (-25688/9471 : -2521/9471 : 1)
** u= -118/123 ; C1 -31513*x^2 - 29053*y^2 + 30233*z^2
(-9590/16853 : 13993/16853 : 1) C2a (4988/2801 : -531/2801 : 1)
** u= -118/155 ; C1 -60889*x^2 - 37949*y^2 + 46681*z^2
(40994/47245 : -7023/47245 : 1) C2a (-161558/274575 : 8599/274575 : 1)
** u= -118/181 ; C1 -92297*x^2 - 46685*y^2 + 61553*z^2
(7826/27743 : -29895/27743 : 1) C2a (-80038/176369 : -2501/176369 : 1)
** u= -117/49 ; C1 -2762*x^2 + 16090*y^2 + 178*z^2
(-2/561 : -59/561 : 1) C2b (2992/37649 : 3573/37649 : 1)
** u= -116/77 ; C1 -7373*x^2 + 19385*y^2 + 10337*z^2
(-21689/31327 : 18558/31327 : 1) C2b (61081/56673 : 1205/56673 : 1)
** u= -116/91 ; C1 -12637*x^2 + 21737*y^2 + 15937*z^2
(-6835/10477 : -7302/10477 : 1) C2b (41411/713827 : -62521/713827 : 1)
** u= -116/95 ; C1 -14501*x^2 + 22481*y^2 + 17609*z^2
(-12/3079 : -2725/3079 : 1) C2b (2211491/2913111 : 121843/2913111 : 1)
** u= -116/113 ; C1 -24869*x^2 + 26225*y^2 + 25529*z^2
(-12215/14863 : -42882/74315 : 1) C2b (29585/46893 : 1339/33495 : 1)
** u= -116/147 ; C1 -53293*x^2 + 35065*y^2 + 42257*z^2
(-2248/15979 : -17321/15979 : 1) C2b (-972501/1803763 : 28601/1803763 : 1)
** u= -116/181 ; C1 -93277*x^2 + 46217*y^2 + 61297*z^2
(-29464/197365 : 223407/197365 : 1) C2b (2821237/11280475 : 513209/11280475 : 1)
** u= -116/199 ; C1 -119125*x^2 + 53057*y^2 + 72313*z^2
(-1492/50835 : 11861/10167 : 1) C2b (101437/1167605 : -55663/1167605 : 1)
** u= -115/103 ; C1 -18890*x^2 - 23834*y^2 + 21074*z^2
(-942/5779 : 5369/5779 : 1) C2a (-328991/294371 : 24697/294371 : 1)
** u= -115/127 ; C1 -35450*x^2 + 29354*y^2 + 32114*z^2
(-1659/1879 : 734/1879 : 1) C2b (1382946/2228449 : 41131/2228449 : 1)
** u= -114/149 ; C1 -56057*x^2 - 35197*y^2 + 43177*z^2
(-1793/14697 : 16120/14697 : 1) C2a (-311214/397213 : 28397/397213 : 1)
** u= -114/175 ; C1 -86321*x^2 - 43621*y^2 + 57529*z^2
(27493/36399 : 15860/36399 : 1) C2a (-1304704/1188299 : -154941/1188299 : 1)
** u= -114/197 ; C1 -117209*x^2 - 51805*y^2 + 70729*z^2
(-45821/78309 : -60184/78309 : 1) C2a (-582/1013 : -59/1013 : 1)
** u= -113/117 ; C1 -28330*x^2 + 26458*y^2 + 27362*z^2
(-14665/14989 : -1438/14989 : 1) C2b (73932/281015 : 20327/281015 : 1)
** u= -113/133 ; C1 {+/-} -41098*x^2 + 30458*y^2 + 34978*z^2
(11122/33645 : -33661/33645 : 1) C2a (-4641/1867 : 85529/293119 : 1) C2b (4/13 : -127/2041 : 1)
** u= -113/165 ; C1 {+/-} -74314*x^2 + 39994*y^2 + 51746*z^2
(4190/31013 : -34811/31013 : 1) C2a (324449/358091 : 35619/358091 : 1) C2b (238896/519949 : 6517/519949 : 1)
** u= -113/189 ; C1 {+/-} -105946*x^2 + 48490*y^2 + 65666*z^2
(9407/15697 : -11846/15697 : 1) C2a (-333517/350813 : 39993/350813 : 1) C2b (-20388/466157 : 23599/466157 : 1)
** u= -112/59 ; C1 -3517*x^2 + 16025*y^2 + 4153*z^2
(2228/2051 : -27/2051 : 1) C2b (53887/33163 : 1951/165815 : 1)
** u= -112/65 ; C1 -4549*x^2 + 16769*y^2 + 6241*z^2
(3871/3315 : 158/3315 : 1) C2b (65509/102779 : -107/1301 : 1)
** u= -112/111 ; C1 -24421*x^2 + 24865*y^2 + 24641*z^2
(26629/27569 : -7534/27569 : 1) C2b (-232113/497897 : 30215/497897 : 1)
** u= -112/125 ; C1 -34669*x^2 + 28169*y^2 + 31081*z^2
(2951/29307 : 30610/29307 : 1) C2b (-335599/721351 : -36727/721351 : 1)
** u= -112/145 ; C1 -52709*x^2 + 33569*y^2 + 40961*z^2
(-38357/47759 : -21750/47759 : 1) C2b (-14943/37345 : -1697/37345 : 1)
** u= -112/183 ; C1 -98005*x^2 + 46033*y^2 + 61937*z^2
(-6049/7997 : 2854/7997 : 1) C2b (24503/321335 : -16617/321335 : 1)
** u= -110/61 ; C1 -3865*x^2 - 15821*y^2 + 5041*z^2
(20377/20997 : -6248/20997 : 1) C2a (-418162/279243 : -71/3933 : 1)
** u= -110/103 ; C1 -19825*x^2 - 22709*y^2 + 21169*z^2
(-10046/57345 : -10913/11469 : 1) C2a (-694782/162527 : -74521/162527 : 1)
** u= -110/173 ; C1 -85625*x^2 - 42029*y^2 + 55889*z^2
(-82293/103225 : 772/4129 : 1) C2a (3130396/67381 : -407413/67381 : 1)
** u= -110/177 ; C1 -90865*x^2 - 43429*y^2 + 58169*z^2
(-8041/19997 : -20008/19997 : 1) C2a (557656/143529 : -72433/143529 : 1)
** u= -110/189 ; C1 -107545*x^2 - 47821*y^2 + 65201*z^2
(65/1301 : 1516/1301 : 1) C2a (1804/4341 : -107/4341 : 1)
** u= -109/65 ; C1 -4666*x^2 - 16106*y^2 + 6514*z^2
(398/5349 : 3395/5349 : 1) C2a (411993/93173 : 28277/93173 : 1)
** u= -109/129 ; C1 {+/-} -38842*x^2 + 28522*y^2 + 32882*z^2
(11150/14029 : 7589/14029 : 1) C2a (-259589/196335 : 28081/196335 : 1) C2b (161415324/293315273 : -8136439/293315273
: 1)
** u= -109/153 ; C1 -62218*x^2 + 35290*y^2 + 44882*z^2
(-2419/2933 : 790/2933 : 1) C2b (139822/314189 : 8493/314189 : 1)
** u= -108/53 ; C1 -2813*x^2 + 14473*y^2 + 2593*z^2
(-1200/3397 : 1337/3397 : 1) C2b (87983/54711 : -3013/54711 : 1)
** u= -108/85 ; C1 -11069*x^2 + 18889*y^2 + 13921*z^2
(4335/4079 : -1118/4079 : 1) C2b (-21239/36031 : 2397/36031 : 1)
** u= -108/91 ; C1 -13757*x^2 + 19945*y^2 + 16273*z^2
(-5184/5563 : -2591/5563 : 1) C2b (-257233/315339 : 6625/315339 : 1)
** u= -108/95 ; C1 -15749*x^2 + 20689*y^2 + 17881*z^2
(13120/15951 : 9427/15951 : 1) C2b (174829/298761 : 17317/298761 : 1)
** u= -108/101 ; C1 -19037*x^2 + 21865*y^2 + 20353*z^2
(-6563/13011 : -10958/13011 : 1) C2b (93703/138291 : -5057/138291 : 1)
** u= -108/137 ; C1 -46325*x^2 + 30433*y^2 + 36697*z^2
(-22203/38395 : -6410/7679 : 1) C2b (16739/41773 : -1977/41773 : 1)
** u= -108/143 ; C1 -52133*x^2 + 32113*y^2 + 39673*z^2
(548751/858761 : -649790/858761 : 1) C2b (-133207/872109 : 55273/872109 : 1)
** u= -108/193 ; C1 -114533*x^2 + 48913*y^2 + 67273*z^2
(76635/136139 : -108346/136139 : 1) C2b (-62591/281625 : -9883/281625 : 1)
** u= -107/159 ; C1 -69802*x^2 - 36730*y^2 + 47858*z^2
(7241/8767 : -710/8767 : 1) C2a (-77461/6153 : 9973/6153 : 1)
** u= -106/49 ; C1 -2465*x^2 - 13637*y^2 + 1553*z^2
(2050/2663 : 219/2663 : 1) C2a (13976/4205 : 353/4205 : 1)
** u= -106/83 ; C1 -10489*x^2 - 18125*y^2 + 13249*z^2
(883/1455 : -26176/36375 : 1) C2a (388628/254865 : -752287/6371625 : 1)
** u= -106/141 ; C1 -50857*x^2 - 31117*y^2 + 38537*z^2
(-382/467 : 5155/13543 : 1) C2a (-12424/8655 : 42119/250995 : 1)
** u= -106/161 ; C1 -72577*x^2 - 37157*y^2 + 48817*z^2
(57718/191655 : 204331/191655 : 1) C2a (-92736/5477 : 11993/5477 : 1)
** u= -106/189 ; C1 -109705*x^2 - 46957*y^2 + 64553*z^2
(-55298/547271 : -636077/547271 : 1) C2a (-112714/322545 : 1607/322545 : 1)
** u= -105/61 ; C1 {+/-} -4010*x^2 + 14746*y^2 + 5506*z^2
(-2086/2109 : -691/2109 : 1) C2a (-41403/11855 : 2633/11855 : 1) C2b (236186/1455685 : -134703/1455685 : 1)
** u= -105/181 ; C1 -98810*x^2 + 43786*y^2 + 59746*z^2
(-6010/9693 : -6833/9693 : 1) C2b (-38/105 : -1/105 : 1)
** u= -104/63 ; C1 -4453*x^2 + 14785*y^2 + 6257*z^2
(6704/8263 : -3919/8263 : 1) C2b (30201/33853 : -2221/33853 : 1)
** u= -104/69 ; C1 -5917*x^2 + 15577*y^2 + 8297*z^2
(2501/2855 : 1402/2855 : 1) C2b (-241621/223403 : 4509/223403 : 1)
** u= -104/81 ; C1 -9925*x^2 + 17377*y^2 + 12593*z^2
(-1148/3973 : -3269/3973 : 1) C2b (-23167/44051 : -453/6293 : 1)
** u= -104/97 ; C1 -17509*x^2 + 20225*y^2 + 18769*z^2
(959/5035 : 23838/25175 : 1) C2b (5209/207829 : 125/1517 : 1)
** u= -104/103 ; C1 -21013*x^2 + 21425*y^2 + 21217*z^2
(1169/7477 : 7350/7477 : 1) C2b (21745/31423 : -443/22445 : 1)
** u= -104/115 ; C1 -29101*x^2 + 24041*y^2 + 26329*z^2
(-3569/12245 : 12198/12245 : 1) C2b (143437/481723 : 32179/481723 : 1)
** u= -104/153 ; C1 -64213*x^2 + 34225*y^2 + 44417*z^2
(64/101 : 13787/18685 : 1) C2b (-114153/376967 : -3167527/69738895 : 1)
** u= -103/179 ; C1 -97066*x^2 + 42650*y^2 + 58306*z^2
(262/1355 : -7671/6775 : 1) C2b (19304/257315 : 60457/1286575 : 1)
** u= -102/59 ; C1 -3737*x^2 - 13885*y^2 + 5113*z^2
(60422/52029 : 3775/52029 : 1) C2a (112972/61739 : 5169/61739 : 1)
** u= -102/107 ; C1 -23993*x^2 - 21853*y^2 + 22873*z^2
(2414/3369 : 95995/138129 : 1) C2a (-24834/35297 : 33713/1447177 : 1)
** u= -102/149 ; C1 -60617*x^2 - 32605*y^2 + 42193*z^2
(65382/82639 : -29833/82639 : 1) C2a (249132/506039 : -9631/506039 : 1)
** u= -102/161 ; C1 -74321*x^2 - 36325*y^2 + 48361*z^2
(-4897/13581 : -70088/67905 : 1) C2a (2562/5189 : -859/25945 : 1)
** u= -102/175 ; C1 -92129*x^2 - 41029*y^2 + 55921*z^2
(-20598/113861 : 129295/113861 : 1) C2a (254976/347771 : 28951/347771 : 1)
** u= -101/161 ; C1 -74762*x^2 + 36122*y^2 + 48242*z^2
(22889/42745 : 36822/42745 : 1) C2b (-61776/204367 : -7669/204367 : 1)
** u= -101/185 ; C1 {+/-} -106586*x^2 + 44426*y^2 + 61394*z^2
(-23205/57209 : -56842/57209 : 1) C2a (127907/53783 : 16807/53783 : 1) C2b (38666/127965 : -2239/127965 : 1)
** u= -100/47 ; C1 -2245*x^2 + 12209*y^2 + 1609*z^2
(16/27 : 7/27 : 1) C2b (-17041/12475 : -953/12475 : 1)
** u= -100/73 ; C1 -7445*x^2 + 15329*y^2 + 9929*z^2
(-1188/6529 : 5189/6529 : 1) C2b (23607/47125 : 3631/47125 : 1)
** u= -100/79 ; C1 -9605*x^2 + 16241*y^2 + 12041*z^2
(-9375/12721 : 8246/12721 : 1) C2b (53463/114947 : -8623/114947 : 1)
** u= -100/149 ; C1 -61405*x^2 + 32201*y^2 + 42001*z^2
(-12307/15403 : -4542/15403 : 1) C2b (337903/858445 : -25849/858445 : 1)
** u= -100/159 ; C1 -72805*x^2 + 35281*y^2 + 47081*z^2
(-78292/101167 : 31763/101167 : 1) C2b (-191253/471707 : -281/20509 : 1)
** u= -100/169 ; C1 -85205*x^2 + 38561*y^2 + 52361*z^2
(-24996/73409 : -77051/73409 : 1) C2b (-122913/1033603 : 49273/1033603 : 1)
** u= -100/171 ; C1 -87805*x^2 + 39241*y^2 + 53441*z^2
(15260/21431 : -10219/21431 : 1) C2b (3659/40705 : -1947/40705 : 1)
** u= -99/71 ; C1 {+/-} -6890*x^2 + 14842*y^2 + 9298*z^2
(-5610/4867 : -479/4867 : 1) C2a (-92829/90437 : 1649/90437 : 1) C2b (-36472/143885 : -12513/143885 : 1)
** u= -98/41 ; C1 -1937*x^2 - 11285*y^2 + 113*z^2
(-903/5329 : -380/5329 : 1) C2a (1675864/105113 : 16085/105113 : 1)
** u= -98/43 ; C1 -1993*x^2 - 11453*y^2 + 673*z^2
(758/2493 : 515/2493 : 1) C2a (-1624704/318343 : -32617/318343 : 1)
** u= -98/85 ; C1 -12409*x^2 - 16829*y^2 + 14281*z^2
(17483/17325 : 5416/17325 : 1) C2a (-231682/53463 : 23657/53463 : 1)
** u= -98/127 ; C1 -40465*x^2 - 25733*y^2 + 31417*z^2
(8413/9831 : 2588/9831 : 1) C2a (1814628/374849 : 224887/374849 : 1)
** u= -98/145 ; C1 -57889*x^2 - 30629*y^2 + 39841*z^2
(67510/110139 : -84647/110139 : 1) C2a (40176/23521 : -4979/23521 : 1)
** u= -98/187 ; C1 -111145*x^2 - 44573*y^2 + 62017*z^2
(-71/787 : -26724/22823 : 1) C2a (-58888/99891 : -195337/2896839 : 1)
** u= -97/133 ; C1 {+/-} -46250*x^2 + 27098*y^2 + 34082*z^2
(-5702/11425 : -417/457 : 1) C2a (-1925053/333335 : -242729/333335 : 1) C2b (20358/79979 : 4439/79979 : 1)
** u= -97/141 ; C1 -54106*x^2 + 29290*y^2 + 37826*z^2
(-1118/1477 : 713/1477 : 1) C2b (-347038/774587 : -14877/774587 : 1)
** u= -97/197 ; C1 {+/-} -127018*x^2 + 48218*y^2 + 67618*z^2
(-34778/55897 : 34575/55897 : 1) C2a (78873/116525 : 9763/116525 : 1) C2b (77798/468191 : 12133/468191 : 1)
** u= -96/103 ; C1 -22709*x^2 + 19825*y^2 + 21169*z^2
(22981/23889 : 2102/23889 : 1) C2b (1597/2757 : 101/2757 : 1)
** u= -96/109 ; C1 -26765*x^2 + 21097*y^2 + 23593*z^2
(-85/783 : -13982/13311 : 1) C2b (-6121/73505 : 5409/73505 : 1)
** u= -96/187 ; C1 -112253*x^2 + 44185*y^2 + 61657*z^2
(8333/21369 : 21466/21369 : 1) C2b (-389/1607 : -33/1607 : 1)
** u= -95/139 ; C1 -52810*x^2 + 28346*y^2 + 36706*z^2
(-11066/19439 : -16161/19439 : 1) C2b (12326/62735 : -3427/62735 : 1)
** u= -94/75 ; C1 -8761*x^2 - 14461*y^2 + 10889*z^2
(9815/10199 : 4468/10199 : 1) C2a (-5596858/405565 : 547011/405565 : 1)
** u= -94/81 ; C1 -11185*x^2 - 15397*y^2 + 12953*z^2
(20317/21553 : -9536/21553 : 1) C2a (205976/160307 : -16389/160307 : 1)
** u= -94/85 ; C1 -13001*x^2 - 16061*y^2 + 14369*z^2
(-19839/23597 : -13400/23597 : 1) C2a (149786/154009 : -9499/154009 : 1)
** u= -94/93 ; C1 -17113*x^2 - 17485*y^2 + 17297*z^2
(4039/7477 : 6272/7477 : 1) C2a (3161278/781711 : -49899/111673 : 1)
** u= -94/143 ; C1 -57313*x^2 - 29285*y^2 + 38497*z^2
(-23897/29159 : 288/29159 : 1) C2a (-5314664/5947017 : 596267/5947017 : 1)
** u= -94/171 ; C1 -90745*x^2 - 38077*y^2 + 52553*z^2
(5614/30577 : 34861/30577 : 1) C2a (27658/52159 : -2847/52159 : 1)
** u= -94/191 ; C1 -119425*x^2 - 45317*y^2 + 63553*z^2
(203/1795 : 420/359 : 1) C2a (65652/245441 : 379/35063 : 1)
** u= -92/41 ; C1 -1781*x^2 + 10145*y^2 + 761*z^2
(5088/7973 : 473/7973 : 1) C2b (-28567/33753 : -3077/33753 : 1)
** u= -92/57 ; C1 -3733*x^2 + 11713*y^2 + 5273*z^2
(-73/1447 : -970/1447 : 1) C2b (-19031/17843 : -801/17843 : 1)
** u= -92/75 ; C1 -8989*x^2 + 14089*y^2 + 10961*z^2
(-331/733 : 590/733 : 1) C2b (89853/1309267 : 113201/1309267 : 1)
** u= -92/93 ; C1 -17485*x^2 + 17113*y^2 + 17297*z^2
(18809/21143 : 9506/21143 : 1) C2b (563/805 : -27/18055 : 1)
** u= -92/119 ; C1 -35477*x^2 + 22625*y^2 + 27593*z^2
(269/4213 : -23202/21065 : 1) C2b (-19561/56913 : 2971/56913 : 1)
** u= -92/191 ; C1 -120581*x^2 + 44945*y^2 + 63161*z^2
(924/1279 : 91/1279 : 1) C2b (90213/383677 : -247/54811 : 1)
** u= -92/197 ; C1 -130013*x^2 + 47273*y^2 + 66593*z^2
(9067/24443 : -24810/24443 : 1) C2b (-2183/58755 : -1631/58755 : 1)
** u= -90/97 ; C1 -20225*x^2 - 17509*y^2 + 18769*z^2
(23838/25175 : 959/5035 : 1) C2a (-41156/50279 : 21/367 : 1)
** u= -90/113 ; C1 -31265*x^2 - 20869*y^2 + 25009*z^2
(-8210/9243 : 91/711 : 1) C2a (140134/230749 : 6717/230749 : 1)
** u= -90/133 ; C1 -48665*x^2 - 25789*y^2 + 33529*z^2
(75923/203493 : 207268/203493 : 1) C2a (-469412/795253 : -37521/795253 : 1)
** u= -90/139 ; C1 -54665*x^2 - 27421*y^2 + 36241*z^2
(1626/3277 : -103/113 : 1) C2a (1585136/16379 : -205677/16379 : 1)
** u= -89/165 ; C1 -85306*x^2 + 35146*y^2 + 48674*z^2
(13018/17605 : -4231/17605 : 1) C2b (-40554/857095 : -36209/857095 : 1)
** u= -89/197 ; C1 {+/-} -131834*x^2 + 46730*y^2 + 65954*z^2
(38794/65669 : -42903/65669 : 1) C2a (267073/16307 : 35809/16307 : 1) C2b (53036/321909 : -415/45987 : 1)
** u= -88/37 ; C1 -1565*x^2 + 9113*y^2 + 137*z^2
(-425/1571 : -78/1571 : 1) C2b (6909/7225 : -679/7225 : 1)
** u= -88/61 ; C1 -4877*x^2 + 11465*y^2 + 6713*z^2
(5208/4649 : -1057/4649 : 1) C2b (10049/22617 : -265/3231 : 1)
** u= -88/73 ; C1 -8693*x^2 + 13073*y^2 + 10433*z^2
(4516/5405 : -3123/5405 : 1) C2b (-801/1247 : -71/1247 : 1)
** u= -88/101 ; C1 -23197*x^2 + 17945*y^2 + 20233*z^2
(-3707/32151 : 33878/32151 : 1) C2b (22277/40241 : -1295/40241 : 1)
** u= -88/109 ; C1 -28781*x^2 + 19625*y^2 + 23321*z^2
(2313/2707 : -4642/13535 : 1) C2b (263/543 : -15559/426255 : 1)
** u= -88/111 ; C1 -30277*x^2 + 20065*y^2 + 24113*z^2
(4196/7847 : 6887/7847 : 1) C2b (-37969/89023 : -3945/89023 : 1)
** u= -88/133 ; C1 -49373*x^2 + 25433*y^2 + 33353*z^2
(5451/23015 : 25238/23015 : 1) C2b (239439/1697767 : 93599/1697767 : 1)
** u= -87/59 ; C1 {+/-} -4442*x^2 + 11050*y^2 + 6178*z^2
(-66/95 : -287/475 : 1) C2a (-94191/9397 : -7903/9397 : 1) C2b (6940/9251 : 3021/46255 : 1)
** u= -86/51 ; C1 -2857*x^2 - 9997*y^2 + 3977*z^2
(170/373 : -217/373 : 1) C2a (796318/79951 : -56199/79951 : 1)
** u= -86/65 ; C1 -6161*x^2 - 11621*y^2 + 8009*z^2
(4475/12857 : 10164/12857 : 1) C2a (-155272/6005 : 14539/6005 : 1)
** u= -86/99 ; C1 -22345*x^2 - 17197*y^2 + 19433*z^2
(107879/139247 : 82396/139247 : 1) C2a (-9838/15989 : 93/15989 : 1)
** u= -86/105 ; C1 -26401*x^2 - 18421*y^2 + 21689*z^2
(-2806/17743 : -246445/230659 : 1) C2a (2884/4761 : 61/2691 : 1)
** u= -86/133 ; C1 -50089*x^2 - 25085*y^2 + 33169*z^2
(-6782/22423 : 23937/22423 : 1) C2a (1195548/470603 : 152867/470603 : 1)
** u= -86/191 ; C1 -124097*x^2 - 43877*y^2 + 61937*z^2
(-495174/1611865 : -1724533/1611865 : 1) C2a (-11104/61963 : -343/61963 : 1)
** u= -85/193 ; C1 -127850*x^2 - 44474*y^2 + 62834*z^2
(62/125 : 21/25 : 1) C2a (-22133/43547 : 2839/43547 : 1)
** u= -84/37 ; C1 -1469*x^2 + 8425*y^2 + 529*z^2
(-92/381 : 437/1905 : 1) C2b (-7837/3197 : 9/139 : 1)
** u= -84/101 ; C1 -24125*x^2 + 17257*y^2 + 20113*z^2
(4709/5235 : -194/1047 : 1) C2b (202757/673149 : -41249/673149 : 1)
** u= -84/137 ; C1 -54869*x^2 + 25825*y^2 + 34729*z^2
(-1821/13387 : 76478/66935 : 1) C2b (-41599/162583 : -33183/812915 : 1)
** u= -84/181 ; C1 -110045*x^2 + 39817*y^2 + 56113*z^2
(1080/2281 : -2027/2281 : 1) C2b (114613/822031 : -16509/822031 : 1)
** u= -84/191 ; C1 -125285*x^2 + 43537*y^2 + 61513*z^2
(-37801/282153 : 329194/282153 : 1) C2b (8779/85803 : 1217/85803 : 1)
** u= -84/193 ; C1 -128453*x^2 + 44305*y^2 + 62617*z^2
(-58632/149041 : 146381/149041 : 1) C2b (384193/3024861 : -16649/3024861 : 1)
** u= -83/191 ; C1 -125882*x^2 + 43370*y^2 + 61298*z^2
(137/17539 : 20850/17539 : 1) C2b (-38922/413531 : 5081/413531 : 1)
** u= -82/65 ; C1 -6529*x^2 - 10949*y^2 + 8161*z^2
(2098/7455 : 6229/7455 : 1) C2a (-144506/158109 : 2629/158109 : 1)
** u= -82/95 ; C1 -20689*x^2 - 15749*y^2 + 17881*z^2
(-13862/15325 : 3771/15325 : 1) C2a (2473016/3999525 : -50477/3999525 : 1)
** u= -82/101 ; C1 -24601*x^2 - 16925*y^2 + 20041*z^2
(-2926/8331 : 8351/8331 : 1) C2a (19916/483 : 1747/345 : 1)
** u= -82/105 ; C1 -27409*x^2 - 17749*y^2 + 21521*z^2
(-20162/24151 : -8915/24151 : 1) C2a (-557218/16723 : 69243/16723 : 1)
** u= -82/107 ; C1 -28873*x^2 - 18173*y^2 + 22273*z^2
(-2302/7105 : -7311/7105 : 1) C2a (327584/131397 : -39973/131397 : 1)
** u= -82/127 ; C1 -45713*x^2 - 22853*y^2 + 30233*z^2
(-8302/14513 : 11865/14513 : 1) C2a (-303332/697879 : 23/99697 : 1)
** u= -82/131 ; C1 -49561*x^2 - 23885*y^2 + 31921*z^2
(-33851/42199 : -1476/42199 : 1) C2a (-4188/10063 : -17/10063 : 1)
** u= -82/187 ; C1 -120233*x^2 - 41693*y^2 + 58913*z^2
(8834/12625 : -417/12625 : 1) C2a (-508624/2543935 : -47551/2543935 : 1)
** u= -81/53 ; C1 -3434*x^2 + 9370*y^2 + 4834*z^2
(811/729 : -182/729 : 1) C2b (55526/49259 : 297/49259 : 1)
** u= -81/109 ; C1 -30650*x^2 - 18442*y^2 + 22978*z^2
(-5082/10961 : -10333/10961 : 1) C2a (1966477/2241439 : -199923/2241439 : 1)
** u= -81/149 ; C1 -69290*x^2 - 28762*y^2 + 39778*z^2
(-21121/30693 : -1162/2361 : 1) C2a (2217/629 : 293/629 : 1)
** u= -80/47 ; C1 -2405*x^2 + 8609*y^2 + 3329*z^2
(435/4457 : -2762/4457 : 1) C2b (-50911/68661 : 5299/68661 : 1)
** u= -80/73 ; C1 -9685*x^2 + 11729*y^2 + 10609*z^2
(-721/947 : -618/947 : 1) C2b (-5459/15865 : -1183/15865 : 1)
** u= -80/83 ; C1 -14285*x^2 + 13289*y^2 + 13769*z^2
(-1316/1367 : 273/1367 : 1) C2b (1437/10195 : 781/10195 : 1)
** u= -80/91 ; C1 -18685*x^2 + 14681*y^2 + 16441*z^2
(-20276/29331 : 20981/29331 : 1) C2b (163967/277625 : 6359/277625 : 1)
** u= -80/133 ; C1 -52285*x^2 + 24089*y^2 + 32569*z^2
(-1388/2393 : -1887/2393 : 1) C2b (-1577/7075 : -299/7075 : 1)
** u= -80/143 ; C1 -62885*x^2 + 26849*y^2 + 36929*z^2
(-5733/12289 : -11434/12289 : 1) C2b (85693/368925 : -12509/368925 : 1)
** u= -79/35 ; C1 {+/-} -1306*x^2 + 7466*y^2 + 514*z^2
(554/2083 : 495/2083 : 1) C2a (289053/56315 : -6689/56315 : 1) C2b (30838/17543 : -1391/17543 : 1)
** u= -79/123 ; C1 {+/-} -43018*x^2 + 21370*y^2 + 28322*z^2
(-14399/17747 : -238/17747 : 1) C2a (103121/40103 : -111/337 : 1) C2b (378/1751 : -5/103 : 1)
** u= -79/131 ; C1 {+/-} -50650*x^2 + 23402*y^2 + 31618*z^2
(2866/29095 : -6711/5819 : 1) C2a (629589/286993 : -81259/286993 : 1) C2b (-72394/264275 : 9781/264275 : 1)
** u= -79/171 ; C1 {+/-} -98410*x^2 + 35482*y^2 + 50018*z^2
(-8225/21467 : 21494/21467 : 1) C2a (-177583/376791 : 3381539/59156187 : 1) C2b (672/3361 : 973/527677 : 1)
** u= -78/109 ; C1 -31481*x^2 - 17965*y^2 + 22801*z^2
(2567/9093 : 9664/9093 : 1) C2a (637234/460399 : -501/3049 : 1)
** u= -78/113 ; C1 -34673*x^2 - 18853*y^2 + 24313*z^2
(-12003/17065 : -10516/17065 : 1) C2a (735262/342025 : 91917/342025 : 1)
** u= -78/131 ; C1 -51017*x^2 - 23245*y^2 + 31513*z^2
(-8623/18039 : 16672/18039 : 1) C2a (619388/794809 : -70749/794809 : 1)
** u= -78/179 ; C1 -110441*x^2 - 38125*y^2 + 53881*z^2
(-597/907 : 1804/4535 : 1) C2a (-190/1351 : 177/33775 : 1)
** u= -77/145 ; C1 {+/-} -66394*x^2 + 26954*y^2 + 37426*z^2
(12490/18773 : -10251/18773 : 1) C2a (22753/66195 : -1291/66195 : 1) C2b (457826/1590191 : 24803/1590191 : 1)
** u= -76/41 ; C1 -1717*x^2 + 7457*y^2 + 2137*z^2
(955/1179 : -434/1179 : 1) C2b (42683/143381 : -13217/143381 : 1)
** u= -76/43 ; C1 -1949*x^2 + 7625*y^2 + 2609*z^2
(16/131 : 381/655 : 1) C2b (81/911 : 85/911 : 1)
** u= -76/71 ; C1 -9397*x^2 + 10817*y^2 + 10057*z^2
(3005/5189 : 4146/5189 : 1) C2b (-121219/268817 : 17789/268817 : 1)
** u= -76/83 ; C1 -14989*x^2 + 12665*y^2 + 13729*z^2
(6251/7149 : 3026/7149 : 1) C2b (2833829/4431919 : -52291/4431919 : 1)
** u= -76/139 ; C1 -60125*x^2 + 25097*y^2 + 34673*z^2
(391/545 : 42/109 : 1) C2b (57329/277347 : 9497/277347 : 1)
** u= -76/145 ; C1 -66821*x^2 + 26801*y^2 + 37289*z^2
(-35469/67523 : -56630/67523 : 1) C2b (672351/2682505 : 8573/383215 : 1)
** u= -76/183 ; C1 -117589*x^2 + 39265*y^2 + 55529*z^2
(114608/198403 : 127799/198403 : 1) C2b (-14373/473147 : -137/473147 : 1)
** u= -75/191 ; C1 -130730*x^2 - 42106*y^2 + 59506*z^2
(-19815/29423 : -2102/29423 : 1) C2a (2631/8945 : 389/8945 : 1)
** u= -74/63 ; C1 -6673*x^2 - 9445*y^2 + 7817*z^2
(503/2131 : -1892/2131 : 1) C2a (-249748/228339 : 16637/228339 : 1)
** u= -74/65 ; C1 -7361*x^2 - 9701*y^2 + 8369*z^2
(-783/2521 : 2240/2521 : 1) C2a (25994/19649 : -2161/19649 : 1)
** u= -74/77 ; C1 -12329*x^2 - 11405*y^2 + 11849*z^2
(-1462/1627 : 663/1627 : 1) C2a (-247018/27013 : 1667/1589 : 1)
** u= -74/91 ; C1 -19945*x^2 - 13757*y^2 + 16273*z^2
(10634/11813 : -1059/11813 : 1) C2a (-932858/1531749 : 39113/1531749 : 1)
** u= -74/117 ; C1 -39289*x^2 - 19165*y^2 + 25529*z^2
(-1666/25019 : 28777/25019 : 1) C2a (1768598/652127 : 32511/93161 : 1)
** u= -74/193 ; C1 -134593*x^2 - 42725*y^2 + 60337*z^2
(-3349/6333 : -4616/6333 : 1) C2a (-59012/165393 : 43513/826965 : 1)
** u= -73/53 ; C1 -3898*x^2 + 8138*y^2 + 5218*z^2
(-214/185 : 3/185 : 1) C2b (-6152/6661 : -217/6661 : 1)
** u= -73/61 ; C1 -6122*x^2 - 9050*y^2 + 7298*z^2
(-1878/4025 : 16339/20125 : 1) C2a (22565/15029 : 9433/75145 : 1)
** u= -73/133 ; C1 {+/-} -54938*x^2 + 23018*y^2 + 31778*z^2
(9763/15893 : 11010/15893 : 1) C2a (-8537/25219 : 199/25219 : 1) C2b (-9484/67173 : -2689/67173 : 1)
** u= -72/73 ; C1 -10805*x^2 + 10513*y^2 + 10657*z^2
(-232/1869 : -1867/1869 : 1) C2b (-5107/10011 : 541/10011 : 1)
** u= -72/145 ; C1 -68549*x^2 + 26209*y^2 + 36721*z^2
(12535/17187 : 1706/17187 : 1) C2b (-103297/398325 : -1963/398325 : 1)
** u= -71/51 ; C1 -3562*x^2 - 7642*y^2 + 4802*z^2
(2450/2111 : 49/2111 : 1) C2a (-919/735 : 1/15 : 1)
** u= -71/99 ; C1 {+/-} -25930*x^2 + 14842*y^2 + 18818*z^2
(1358/2543 : 2231/2543 : 1) C2a (-5381/9797 : -3/101 : 1) C2b (26724/56357 : 11/581 : 1)
** u= -71/179 ; C1 -114410*x^2 - 37082*y^2 + 52418*z^2
(-158677/851983 : 973854/851983 : 1) C2a (9239/26225 : -1313/26225 : 1)
** u= -70/29 ; C1 -985*x^2 - 5741*y^2 + z^2
(-2/987 : 13/987 : 1) C2a (-698/3 : -1/3 : 1)
** u= -70/33 ; C1 -1105*x^2 - 5989*y^2 + 809*z^2
(70/103 : 23/103 : 1) C2a (-53818/23137 : -429/23137 : 1)
** u= -70/53 ; C1 -4105*x^2 - 7709*y^2 + 5329*z^2
(73/357 : 292/357 : 1) C2a (-215512/3723 : 277/51 : 1)
** u= -70/59 ; C1 -5785*x^2 - 8381*y^2 + 6841*z^2
(-47/63 : -704/1071 : 1) C2a (218874/28541 : 377131/485197 : 1)
** u= -70/69 ; C1 -9385*x^2 - 9661*y^2 + 9521*z^2
(-613/1129 : 944/1129 : 1) C2a (1200718/800983 : 118131/800983 : 1)
** u= -70/89 ; C1 -19585*x^2 - 12821*y^2 + 15481*z^2
(-1553/4077 : -4048/4077 : 1) C2a (14932/24327 : -809/24327 : 1)
** u= -70/113 ; C1 -37105*x^2 - 17669*y^2 + 23689*z^2
(-13643/22641 : 17216/22641 : 1) C2a (-97672/61185 : -12337/61185 : 1)
** u= -70/117 ; C1 -40585*x^2 - 18589*y^2 + 25169*z^2
(51797/99097 : -86248/99097 : 1) C2a (2081354/1399659 : -263863/1399659 : 1)
** u= -70/137 ; C1 -60385*x^2 - 23669*y^2 + 33049*z^2
(7811/11729 : -6036/11729 : 1) C2a (101224/323499 : 5717/323499 : 1)
** u= -70/171 ; C1 -103225*x^2 - 34141*y^2 + 48281*z^2
(2906/31465 : 7415/6293 : 1) C2a (-13738964/64434399 : -1926413/64434399 : 1)
** u= -70/193 ; C1 -137105*x^2 - 42149*y^2 + 59369*z^2
(-16477/77473 : -87012/77473 : 1) C2a (-1068136/1571555 : 149869/1571555 : 1)
** u= -69/121 ; C1 -44570*x^2 + 19402*y^2 + 26578*z^2
(-6035/9729 : 6782/9729 : 1) C2b (-51788/245379 : 9379/245379 : 1)
** u= -68/47 ; C1 -2885*x^2 + 6833*y^2 + 3977*z^2
(-339/733 : 514/733 : 1) C2b (143481/141463 : 3413/141463 : 1)
** u= -68/81 ; C1 -15397*x^2 + 11185*y^2 + 12953*z^2
(623/839 : -530/839 : 1) C2b (-1647/61409 : -4411/61409 : 1)
** u= -68/95 ; C1 -23909*x^2 + 13649*y^2 + 17321*z^2
(15705/19961 : 8578/19961 : 1) C2b (-14751/30341 : 377/30341 : 1)
** u= -68/117 ; C1 -41245*x^2 + 18313*y^2 + 24977*z^2
(-133259/173651 : 33658/173651 : 1) C2b (-117/146455 : 7147/146455 : 1)
** u= -68/123 ; C1 -46813*x^2 + 19753*y^2 + 27233*z^2
(-12095/18577 : -874/1429 : 1) C2b (-50337/205585 : -6349/205585 : 1)
** u= -67/119 ; C1 {+/-} -43402*x^2 + 18650*y^2 + 25618*z^2
(-2531/3323 : 510/3323 : 1) C2a (-81753/22837 : -53813/114185 : 1) C2b (206/4519 : 1037/22595 : 1)
** u= -67/151 ; C1 {+/-} -78026*x^2 + 27290*y^2 + 38546*z^2
(9741/24811 : -24458/24811 : 1) C2a (-14167/81923 : -775/81923 : 1) C2b (-2046/16519 : 217/16519 : 1)
** u= -66/43 ; C1 -2249*x^2 - 6205*y^2 + 3169*z^2
(-20206/22509 : -10525/22509 : 1) C2a (11508/10093 : 77/10093 : 1)
** u= -66/49 ; C1 -3425*x^2 - 6757*y^2 + 4513*z^2
(6033/5905 : -440/1181 : 1) C2a (-151266/73145 : -12337/73145 : 1)
** u= -66/73 ; C1 -11729*x^2 - 9685*y^2 + 10609*z^2
(-618/947 : -721/947 : 1) C2a (-1155064/1755841 : 315/17047 : 1)
** u= -66/115 ; C1 -40121*x^2 - 17581*y^2 + 24049*z^2
(1485/12863 : -14876/12863 : 1) C2a (-91996/191495 : 7977/191495 : 1)
** u= -66/145 ; C1 -71201*x^2 - 25381*y^2 + 35809*z^2
(-12570/39643 : -42119/39643 : 1) C2a (48774/262111 : 391/262111 : 1)
** u= -66/175 ; C1 -111281*x^2 - 34981*y^2 + 49369*z^2
(93897/192979 : -156560/192979 : 1) C2a (134288/197605 : 18621/197605 : 1)
** u= -66/179 ; C1 -117305*x^2 - 36397*y^2 + 51313*z^2
(-93150/143921 : -35167/143921 : 1) C2a (9372/216775 : -257/9425 : 1)
** u= -66/193 ; C1 -139649*x^2 - 41605*y^2 + 58369*z^2
(12542/24507 : -17737/24507 : 1) C2a (-928/1313 : -20679/206141 : 1)
** u= -66/199 ; C1 -149825*x^2 - 43957*y^2 + 61513*z^2
(1578/6053 : -6541/6053 : 1) C2a (-15956/145063 : 5649/145063 : 1)
** u= -65/189 ; C1 -133690*x^2 - 39946*y^2 + 56066*z^2
(2006/6917 : -7327/6917 : 1) C2a (156371/262905 : -1333/15465 : 1)
** u= -64/27 ; C1 -829*x^2 + 4825*y^2 + 89*z^2
(109/1193 : -778/5965 : 1) C2b (-2049/1481 : -137/1481 : 1)
** u= -64/35 ; C1 -1261*x^2 + 5321*y^2 + 1609*z^2
(-100/843 : -461/843 : 1) C2b (37319/24721 : 113/24721 : 1)
** u= -64/61 ; C1 -7085*x^2 + 7817*y^2 + 7433*z^2
(195/503 : -454/503 : 1) C2b (404439/598037 : -20083/598037 : 1)
** u= -64/63 ; C1 -7813*x^2 + 8065*y^2 + 7937*z^2
(1763/1769 : -262/1769 : 1) C2b (-52809/73667 : -379/73667 : 1)
** u= -64/69 ; C1 -10237*x^2 + 8857*y^2 + 9497*z^2
(12772/14917 : -7075/14917 : 1) C2b (-12721/44005 : -3027/44005 : 1)
** u= -64/97 ; C1 -26309*x^2 + 13505*y^2 + 17729*z^2
(-1991/7291 : 7878/7291 : 1) C2b (56147/152757 : 5045/152757 : 1)
** u= -64/119 ; C1 -44437*x^2 + 18257*y^2 + 25297*z^2
(3859/8649 : -8210/8649 : 1) C2b (179933/565805 : -2371/565805 : 1)
** u= -64/127 ; C1 -52229*x^2 + 20225*y^2 + 28289*z^2
(-18153/30757 : 21730/30757 : 1) C2b (2031/47611 : -1715/47611 : 1)
** u= -64/131 ; C1 -56365*x^2 + 21257*y^2 + 29833*z^2
(-7403/24881 : 26898/24881 : 1) C2b (-68977/1548841 : 50761/1548841 : 1)
** u= -64/153 ; C1 -81973*x^2 + 27505*y^2 + 38897*z^2
(-40748/158549 : -174931/158549 : 1) C2b (-1579/92203 : 699/92203 : 1)
** u= -63/139 ; C1 -65546*x^2 + 23290*y^2 + 32866*z^2
(-14266/119739 : 140213/119739 : 1) C2b (-112/185763 : 4517/185763 : 1)
** u= -62/27 ; C1 -793*x^2 - 4573*y^2 + 233*z^2
(383/895 : 124/895 : 1) C2a (688/45 : 17/45 : 1)
** u= -62/29 ; C1 -857*x^2 - 4685*y^2 + 593*z^2
(627/2329 : -784/2329 : 1) C2a (-70792/19121 : -2191/19121 : 1)
** u= -62/73 ; C1 -12385*x^2 - 9173*y^2 + 10537*z^2
(178/2163 : 2309/2163 : 1) C2a (1398/85 : -169/85 : 1)
** u= -62/85 ; C1 -18889*x^2 - 11069*y^2 + 13921*z^2
(6731/8857 : 4620/8857 : 1) C2a (-2757648/248603 : -348683/248603 : 1)
** u= -62/127 ; C1 -52993*x^2 - 19973*y^2 + 28033*z^2
(-1853/6915 : -7616/6915 : 1) C2a (-180896/571557 : -881/33621 : 1)
** u= -62/139 ; C1 -65977*x^2 - 23165*y^2 + 32713*z^2
(-12743/21999 : -14864/21999 : 1) C2a (-521416/3053733 : -19511/3053733 : 1)
** u= -62/147 ; C1 -75433*x^2 - 25453*y^2 + 35993*z^2
(-20015/39679 : 32236/39679 : 1) C2a (57212/500759 : -5469/500759 : 1)
** u= -62/153 ; C1 -82945*x^2 - 27253*y^2 + 38537*z^2
(41290/74611 : -51797/74611 : 1) C2a (-19832/505299 : 6517/505299 : 1)
** u= -62/167 ; C1 -101873*x^2 - 31733*y^2 + 44753*z^2
(-10593/16015 : 1216/16015 : 1) C2a (-1677722/444649 : -225169/444649 : 1)
** u= -62/175 ; C1 -113569*x^2 - 34469*y^2 + 48481*z^2
(-26282/59649 : -155/177 : 1) C2a (109969182/95385797 : 15007357/95385797 : 1)
** u= -62/177 ; C1 -116593*x^2 - 35173*y^2 + 49433*z^2
(-41950/66403 : 19067/66403 : 1) C2a (-1776712/22668045 : 756133/22668045 : 1)
** u= -62/197 ; C1 -149033*x^2 - 42653*y^2 + 59393*z^2
(8817/14845 : -5936/14845 : 1) C2a (-1188476/399385 : -159079/399385 : 1)
** u= -61/105 ; C1 {+/-} -33226*x^2 + 14746*y^2 + 20114*z^2
(-115/149 : 22/149 : 1) C2a (-5501447/2885217 : -711413/2885217 : 1) C2b (31428/430447 : -20579/430447 : 1)
** u= -61/161 ; C1 -94042*x^2 - 29642*y^2 + 41842*z^2
(-64018/96193 : -7695/96193 : 1) C2a (19463/43605 : -2803/43605 : 1)
** u= -60/67 ; C1 -9965*x^2 + 8089*y^2 + 8929*z^2
(504/551 : 149/551 : 1) C2b (-42449/237205 : 17073/237205 : 1)
** u= -60/139 ; C1 -66845*x^2 + 22921*y^2 + 32401*z^2
(-7524/11719 : 5389/11719 : 1) C2b (-133957/1612105 : -19221/1612105 : 1)
** u= -59/31 ; C1 {+/-} -970*x^2 + 4442*y^2 + 1138*z^2
(-401/1007 : -474/1007 : 1) C2a (-90351/1723 : 5159/1723 : 1) C2b (-106/1457 : 137/1457 : 1)
** u= -59/87 ; C1 {+/-} -20794*x^2 + 11050*y^2 + 14354*z^2
(-179/551 : -578/551 : 1) C2a (4163/6947 : -339/6947 : 1) C2b (-934/2417 : 399/12085 : 1)
** u= -58/49 ; C1 -4001*x^2 - 5765*y^2 + 4721*z^2
(-2234/2531 : 1335/2531 : 1) C2a (-83504/96071 : -2227/96071 : 1)
** u= -58/79 ; C1 -16241*x^2 - 9605*y^2 + 12041*z^2
(-3843/11623 : 12016/11623 : 1) C2a (277132/359897 : 26201/359897 : 1)
** u= -58/85 ; C1 -19769*x^2 - 10589*y^2 + 13721*z^2
(-1845/4397 : -4324/4397 : 1) C2a (53168/39437 : -6407/39437 : 1)
** u= -58/91 ; C1 -23657*x^2 - 11645*y^2 + 15473*z^2
(2967/4379 : -2756/4379 : 1) C2a (12502/22291 : -1055/22291 : 1)
** u= -58/97 ; C1 -27905*x^2 - 12773*y^2 + 17297*z^2
(11466/21331 : 18137/21331 : 1) C2a (-154388/251825 : 2243/35975 : 1)
** u= -58/133 ; C1 -60953*x^2 - 21053*y^2 + 29753*z^2
(29079/56921 : 46160/56921 : 1) C2a (-27274/97483 : -3197/97483 : 1)
** u= -58/177 ; C1 -118945*x^2 - 34693*y^2 + 48497*z^2
(-8666/39059 : -43303/39059 : 1) C2a (730576/310265 : 98163/310265 : 1)
** u= -58/197 ; C1 -151705*x^2 - 42173*y^2 + 58297*z^2
(34969/142089 : -153328/142089 : 1) C2a (-3192/65575 : 2891/65575 : 1)
** u= -57/29 ; C1 {+/-} -842*x^2 + 4090*y^2 + 898*z^2
(3026/4257 : -1447/4257 : 1) C2a (-155729/23837 : 7923/23837 : 1) C2b (8038/5031 : 211/5031 : 1)
** u= -56/47 ; C1 -3653*x^2 + 5345*y^2 + 4337*z^2
(-8859/11977 : 7922/11977 : 1) C2b (18127/21639 : -241/21639 : 1)
** u= -56/61 ; C1 -8077*x^2 + 6857*y^2 + 7417*z^2
(11984/18181 : -13725/18181 : 1) C2b (-1181297/2273671 : 103777/2273671 : 1)
** u= -56/71 ; C1 -12437*x^2 + 8177*y^2 + 9857*z^2
(6425/14717 : -14082/14717 : 1) C2b (-208817/655881 : 36833/655881 : 1)
** u= -56/75 ; C1 -14461*x^2 + 8761*y^2 + 10889*z^2
(-8533/10105 : 2594/10105 : 1) C2b (64771/127739 : -1923/127739 : 1)
** u= -56/107 ; C1 -36413*x^2 + 14585*y^2 + 20297*z^2
(-40668/58939 : -26555/58939 : 1) C2b (-712091/4543323 : 155251/4543323 : 1)
** u= -56/117 ; C1 -45373*x^2 + 16825*y^2 + 23657*z^2
(18248/25925 : 2017/7625 : 1) C2b (18931/84373 : -675/84373 : 1)
** u= -55/51 ; C1 -4810*x^2 + 5626*y^2 + 5186*z^2
(-61/271 : -254/271 : 1) C2b (44402/61673 : -1683/61673 : 1)
** u= -54/23 ; C1 -593*x^2 - 3445*y^2 + 97*z^2
(153/1711 : 280/1711 : 1) C2a (1706/187 : -27/187 : 1)
** u= -54/35 ; C1 -1481*x^2 - 4141*y^2 + 2089*z^2
(2851/2475 : -428/2475 : 1) C2a (6247064/625625 : 497493/625625 : 1)
** u= -54/61 ; C1 -8345*x^2 - 6637*y^2 + 7393*z^2
(198/4003 : 4219/4003 : 1) C2a (155402/49081 : 18147/49081 : 1)
** u= -54/125 ; C1 -54041*x^2 - 18541*y^2 + 26209*z^2
(2805/10273 : -11236/10273 : 1) C2a (-123418/295115 : -15831/295115 : 1)
** u= -54/139 ; C1 -69497*x^2 - 22237*y^2 + 31417*z^2
(25986/58285 : -51857/58285 : 1) C2a (22328/4855 : -2997/4855 : 1)
** u= -54/143 ; C1 -74273*x^2 - 23365*y^2 + 32977*z^2
(19089/67303 : -4256/3959 : 1) C2a (86612/817369 : 3243/116767 : 1)
** u= -54/173 ; C1 -115193*x^2 - 32845*y^2 + 45697*z^2
(567/901 : 44/901 : 1) C2a (-65414/411227 : -18681/411227 : 1)
** u= -53/25 ; C1 {+/-} -634*x^2 + 3434*y^2 + 466*z^2
(-149/785 : -282/785 : 1) C2a (585461/96261 : -22571/96261 : 1) C2b (33304/14965 : -301/14965 : 1)
** u= -53/137 ; C1 -67610*x^2 - 21578*y^2 + 30482*z^2
(-8850/17333 : 13379/17333 : 1) C2a (-144841/315583 : -20489/315583 : 1)
** u= -52/25 ; C1 -629*x^2 + 3329*y^2 + 521*z^2
(183/335 : 106/335 : 1) C2b (10407/10865 : 917/10865 : 1)
** u= -52/43 ; C1 -3005*x^2 + 4553*y^2 + 3617*z^2
(-3189/5173 : 3814/5173 : 1) C2b (117/301 : 3637/47257 : 1)
** u= -52/45 ; C1 -3469*x^2 + 4729*y^2 + 4001*z^2
(-15323/14851 : -3790/14851 : 1) C2b (-99801/307939 : 24023/307939 : 1)
** u= -52/53 ; C1 -5725*x^2 + 5513*y^2 + 5617*z^2
(68/69 : -7/69 : 1) C2b (-553/40381 : 3191/40381 : 1)
** u= -52/71 ; C1 -13141*x^2 + 7745*y^2 + 9721*z^2
(18023/21273 : -4106/21273 : 1) C2b (19243/106553 : -6419/106553 : 1)
** u= -52/113 ; C1 -43045*x^2 + 15473*y^2 + 21817*z^2
(-15551/100327 : -116274/100327 : 1) C2b (91253/937931 : -21479/937931 : 1)
** u= -52/119 ; C1 -48757*x^2 + 16865*y^2 + 23833*z^2
(-19352/28611 : 8609/28611 : 1) C2b (-69491/4738933 : 87793/4738933 : 1)
** u= -52/125 ; C1 -54829*x^2 + 18329*y^2 + 25921*z^2
(-1288/11125 : 13041/11125 : 1) C2b (2713/176663 : -37/7681 : 1)
** u= -51/23 ; C1 {+/-} -554*x^2 + 3130*y^2 + 274*z^2
(66/151 : 35/151 : 1) C2a (31067/8027 : 705/8027 : 1) C2b (6392/4997 : 423/4997 : 1)
** u= -51/31 ; C1 {+/-} -1082*x^2 + 3562*y^2 + 1522*z^2
(-242/903 : -575/903 : 1) C2a (-7791/2155 : -539/2155 : 1) C2b (98/65041 : 6027/65041 : 1)
** u= -51/127 ; C1 -57338*x^2 - 18730*y^2 + 26482*z^2
(-15074/27087 : 18487/27087 : 1) C2a (-14087/122801 : -2553/122801 : 1)
** u= -50/57 ; C1 -7345*x^2 - 5749*y^2 + 6449*z^2
(10199/44017 : 45172/44017 : 1) C2a (-870374/1096065 : 65081/1096065 : 1)
** u= -50/67 ; C1 -11545*x^2 - 6989*y^2 + 8689*z^2
(-5666/6549 : 539/6549 : 1) C2a (-71058/134965 : -1327/134965 : 1)
** u= -50/69 ; C1 -12505*x^2 - 7261*y^2 + 9161*z^2
(890/7927 : 8827/7927 : 1) C2a (128524/212075 : -9081/212075 : 1)
** u= -50/83 ; C1 -20345*x^2 - 9389*y^2 + 12689*z^2
(38642/70721 : 59361/70721 : 1) C2a (3914/9869 : -73/9869 : 1)
** u= -50/87 ; C1 -22945*x^2 - 10069*y^2 + 13769*z^2
(-10514/14309 : 5299/14309 : 1) C2a (91324/8169 : -1721/1167 : 1)
** u= -50/111 ; C1 -41905*x^2 - 14821*y^2 + 20921*z^2
(38443/57919 : 1388/3407 : 1) C2a (-359972/239615 : 47943/239615 : 1)
** u= -50/147 ; C1 -81145*x^2 - 24109*y^2 + 33809*z^2
(24326/43769 : 26359/43769 : 1) C2a (116774/2344449 : -81523/2344449 : 1)
** u= -50/151 ; C1 -86305*x^2 - 25301*y^2 + 35401*z^2
(2047/9747 : -10892/9747 : 1) C2a (442656/511391 : -61927/511391 : 1)
** u= -50/153 ; C1 -88945*x^2 - 25909*y^2 + 36209*z^2
(54034/185759 : -195451/185759 : 1) C2a (-124052/43587 : 16631/43587 : 1)
** u= -50/167 ; C1 -108545*x^2 - 30389*y^2 + 42089*z^2
(1274593/2444819 : 1573404/2444819 : 1) C2a (2657506/1524655 : -358939/1524655 : 1)
** u= -50/169 ; C1 -111505*x^2 - 31061*y^2 + 42961*z^2
(-56849/361593 : 411388/361593 : 1) C2a (1543142/278637 : 205189/278637 : 1)
** u= -49/69 ; C1 -12682*x^2 - 7162*y^2 + 9122*z^2
(65/5053 : -5702/5053 : 1) C2a (4847/2391 : -599/2391 : 1)
** u= -49/181 ; C1 -130730*x^2 - 35162*y^2 + 48098*z^2
(-1017/6349 : 7162/6349 : 1) C2a (-2963/7261 : -523/7261 : 1)
** u= -48/23 ; C1 -533*x^2 + 2833*y^2 + 433*z^2
(-141/1385 : -538/1385 : 1) C2b (-137807/344405 : 32019/344405 : 1)
** u= -48/41 ; C1 -2837*x^2 + 3985*y^2 + 3313*z^2
(-184/1917 : -1741/1917 : 1) C2b (-391/1583 : -129/1583 : 1)
** u= -48/65 ; C1 -10949*x^2 + 6529*y^2 + 8161*z^2
(-1571/5415 : -5702/5415 : 1) C2b (41747/82637 : 1011/82637 : 1)
** u= -48/71 ; C1 -13877*x^2 + 7345*y^2 + 9553*z^2
(2008/10371 : -11501/10371 : 1) C2b (10157/25469 : -765/25469 : 1)
** u= -48/79 ; C1 -18341*x^2 + 8545*y^2 + 11521*z^2
(7469/20649 : -21334/20649 : 1) C2b (-5479/69861 : 3571/69861 : 1)
** u= -48/107 ; C1 -39005*x^2 + 13753*y^2 + 19417*z^2
(1017/9301 : 10918/9301 : 1) C2b (581/6747 : 133/6747 : 1)
** u= -48/113 ; C1 -44453*x^2 + 15073*y^2 + 21313*z^2
(9965/46023 : -51982/46023 : 1) C2b (86129/977555 : 4587/977555 : 1)
** u= -47/27 ; C1 {+/-} -778*x^2 + 2938*y^2 + 1058*z^2
(46/55 : 23/55 : 1) C2a (-79037/7015 : 231/305 : 1) C2b (-18508/58489 : -231/2543 : 1)
** u= -47/187 ; C1 -141898*x^2 - 37178*y^2 + 50338*z^2
(-5594/10459 : -5355/10459 : 1) C2a (237019/194535 : 32671/194535 : 1)
** u= -46/37 ; C1 -2153*x^2 - 3485*y^2 + 2657*z^2
(1077/1769 : -1292/1769 : 1) C2a (-12106/4873 : 1115/4873 : 1)
** u= -46/45 ; C1 -3961*x^2 - 4141*y^2 + 4049*z^2
(7874/8015 : -1873/8015 : 1) C2a (-219796/181475 : 19683/181475 : 1)
** u= -46/49 ; C1 -5105*x^2 - 4517*y^2 + 4793*z^2
(685/1433 : 1284/1433 : 1) C2a (-5306/7423 : 229/7423 : 1)
** u= -46/73 ; C1 -15329*x^2 - 7445*y^2 + 9929*z^2
(-1689/28421 : 32732/28421 : 1) C2a (-32906/64421 : -2441/64421 : 1)
** u= -46/87 ; C1 -23953*x^2 - 9685*y^2 + 13457*z^2
(2566/4177 : -2821/4177 : 1) C2a (-93598/46019 : 12309/46019 : 1)
** u= -46/125 ; C1 -57241*x^2 - 17741*y^2 + 25009*z^2
(11159/21813 : 16400/21813 : 1) C2a (-14/111 : 553/17427 : 1)
** u= -44/45 ; C1 -4141*x^2 + 3961*y^2 + 4049*z^2
(172/941 : -935/941 : 1) C2b (85127/126745 : -2373/126745 : 1)
** u= -44/47 ; C1 -4709*x^2 + 4145*y^2 + 4409*z^2
(-796/1519 : 1317/1519 : 1) C2b (-30219/109651 : 7681/109651 : 1)
** u= -44/73 ; C1 -15733*x^2 + 7265*y^2 + 9817*z^2
(2692/3409 : -99/3409 : 1) C2b (-697/34711 : -1787/34711 : 1)
** u= -44/79 ; C1 -19237*x^2 + 8177*y^2 + 11257*z^2
(2500/3403 : -1113/3403 : 1) C2b (-310127/1170581 : -33743/1170581 : 1)
** u= -44/87 ; C1 -24469*x^2 + 9505*y^2 + 13289*z^2
(-12001/23849 : 20602/23849 : 1) C2b (78557/577837 : 18513/577837 : 1)
** u= -43/71 ; C1 -14842*x^2 + 6890*y^2 + 9298*z^2
(-479/4867 : -5610/4867 : 1) C2b (1072/3499 : -115/3499 : 1)
** u= -43/183 ; C1 -137818*x^2 - 35338*y^2 + 47378*z^2
(1379/15055 : 17218/15055 : 1) C2a (-796903/17259 : 104149/17259 : 1)
** u= -43/191 ; C1 -151402*x^2 - 38330*y^2 + 51058*z^2
(-14686/61367 : 64533/61367 : 1) C2a (-53/21 : -1/3 : 1)
** u= -42/41 ; C1 -3281*x^2 - 3445*y^2 + 3361*z^2
(42/83 : 71/83 : 1) C2a (813102/772367 : -65777/772367 : 1)
** u= -42/59 ; C1 -9257*x^2 - 5245*y^2 + 6673*z^2
(6042/7949 : 3995/7949 : 1) C2a (-29088/7759 : 3671/7759 : 1)
** u= -42/83 ; C1 -22265*x^2 - 8653*y^2 + 12097*z^2
(11839/16899 : 6212/16899 : 1) C2a (86532/234049 : -7673/234049 : 1)
** u= -42/95 ; C1 -30929*x^2 - 10789*y^2 + 15241*z^2
(9725/14511 : 5132/14511 : 1) C2a (-7226/42191 : 429/42191 : 1)
** u= -42/109 ; C1 -42857*x^2 - 13645*y^2 + 19273*z^2
(-9582/30551 : 32093/30551 : 1) C2a (372/18881 : -403/18881 : 1)
** u= -42/143 ; C1 -79985*x^2 - 22213*y^2 + 30697*z^2
(-1337/2187 : -416/2187 : 1) C2a (53114/34717 : 7209/34717 : 1)
** u= -42/167 ; C1 -113153*x^2 - 29653*y^2 + 40153*z^2
(42910/72357 : 7957/72357 : 1) C2a (-3926446/1536005 : 521601/1536005 : 1)
** u= -42/169 ; C1 -116177*x^2 - 30325*y^2 + 40993*z^2
(12779/22293 : 6796/22293 : 1) C2a (-4812/23479 : -1363/23479 : 1)
** u= -42/179 ; C1 -131897*x^2 - 33805*y^2 + 45313*z^2
(11438/29961 : 26321/29961 : 1) C2a (-1854/405757 : -21745/405757 : 1)
** u= -41/21 ; C1 {+/-} -442*x^2 + 2122*y^2 + 482*z^2
(443/437 : 50/437 : 1) C2a (-33607/6189 : 1711/6189 : 1) C2b (-7662/18665 : -1711/18665 : 1)
** u= -41/125 ; C1 -59306*x^2 - 17306*y^2 + 24194*z^2
(-15523/35065 : 29886/35065 : 1) C2a (-707521/232345 : 94807/232345 : 1)
** u= -41/133 ; C1 -68314*x^2 - 19370*y^2 + 26914*z^2
(2566/4101 : 383/4101 : 1) C2a (474689/74319 : 63227/74319 : 1)
** u= -40/17 ; C1 -325*x^2 + 1889*y^2 + 49*z^2
(-329/1555 : 42/311 : 1) C2b (4219/959 : -7/137 : 1)
** u= -40/37 ; C1 -2525*x^2 + 2969*y^2 + 2729*z^2
(-8895/8587 : 698/8587 : 1) C2b (-261/3991 : 329/3991 : 1)
** u= -40/49 ; C1 -5765*x^2 + 4001*y^2 + 4721*z^2
(-88/4997 : 5427/4997 : 1) C2b (26783/377217 : 26377/377217 : 1)
** u= -40/51 ; C1 -6445*x^2 + 4201*y^2 + 5081*z^2
(-256/5299 : 5819/5299 : 1) C2b (-7617/19115 : -901/19115 : 1)
** u= -39/107 ; C1 -42074*x^2 - 12970*y^2 + 18274*z^2
(-11267/17403 : -3862/17403 : 1) C2a (148587/621527 : 26389/621527 : 1)
** u= -39/155 ; C1 -97466*x^2 - 25546*y^2 + 34594*z^2
(-23506/222135 : 254387/222135 : 1) C2a (26051/1925 : -489/275 : 1)
** u= -38/21 ; C1 -457*x^2 - 1885*y^2 + 593*z^2
(94/83 : 5/83 : 1) C2a (22898/2331 : -1433/2331 : 1)
** u= -38/33 ; C1 -1873*x^2 - 2533*y^2 + 2153*z^2
(-1307/1897 : 1340/1897 : 1) C2a (25876/7167 : -2623/7167 : 1)
** u= -38/35 ; C1 -2249*x^2 - 2669*y^2 + 2441*z^2
(-46/457 : -435/457 : 1) C2a (-464/461 : -5083/72377 : 1)
** u= -38/47 ; C1 -5345*x^2 - 3653*y^2 + 4337*z^2
(5450/6089 : 747/6089 : 1) C2a (-724/37 : -89/37 : 1)
** u= -38/89 ; C1 -27521*x^2 - 9365*y^2 + 13241*z^2
(-3998/7447 : 5607/7447 : 1) C2a (21862/123107 : 2377/123107 : 1)
** u= -38/151 ; C1 -92497*x^2 - 24245*y^2 + 32833*z^2
(-4889/8223 : 616/8223 : 1) C2a (3572/3219 : -497/3219 : 1)
** u= -38/165 ; C1 -112489*x^2 - 28669*y^2 + 38321*z^2
(48451/84553 : 18580/84553 : 1) C2a (-495296/3698979 : -210779/3698979 : 1)
** u= -38/187 ; C1 -147865*x^2 - 36413*y^2 + 47737*z^2
(2822/32041 : 36243/32041 : 1) C2a (-1115028/609551 : 148387/609551 : 1)
** u= -37/17 ; C1 -298*x^2 + 1658*y^2 + 178*z^2
(67/165 : 46/165 : 1) C2b (7106/4075 : -283/4075 : 1)
** u= -37/137 ; C1 -74938*x^2 - 20138*y^2 + 27538*z^2
(5110/12329 : -10521/12329 : 1) C2a (1330101/556745 : -25367/79535 : 1)
** u= -36/19 ; C1 -365*x^2 + 1657*y^2 + 433*z^2
(2440/2439 : -493/2439 : 1) C2b (-19873/13595 : 567/13595 : 1)
** u= -36/43 ; C1 -4349*x^2 + 3145*y^2 + 3649*z^2
(308/1383 : -1445/1383 : 1) C2b (-4931/48039 : -3395/48039 : 1)
** u= -36/47 ; C1 -5573*x^2 + 3505*y^2 + 4297*z^2
(1716/2087 : -811/2087 : 1) C2b (-41/587 : -39/587 : 1)
** u= -36/49 ; C1 -6245*x^2 + 3697*y^2 + 4633*z^2
(-1367/1599 : -218/1599 : 1) C2b (-21781/43565 : -591/43565 : 1)
** u= -36/85 ; C1 -25181*x^2 + 8521*y^2 + 12049*z^2
(8231/14703 : -790/1131 : 1) C2b (-21667/383605 : -3543/383605 : 1)
** u= -35/79 ; C1 {+/-} -21370*x^2 + 7466*y^2 + 10546*z^2
(9553/15707 : 9342/15707 : 1) C2a (-13757/84165 : 547/84165 : 1) C2b (-52958/434975 : -5701/434975 : 1)
** u= -35/87 ; C1 -26890*x^2 - 8794*y^2 + 12434*z^2
(9295/14711 : 6466/14711 : 1) C2a (-22013/88917 : -3191/88917 : 1)
** u= -35/103 ; C1 -39850*x^2 - 11834*y^2 + 16594*z^2
(2723/14115 : 3190/2823 : 1) C2a (4981/28941 : 1193/28941 : 1)
** u= -35/191 ; C1 -156890*x^2 - 37706*y^2 + 48626*z^2
(10658/19171 : -1149/19171 : 1) C2a (-179881/338671 : 30913/338671 : 1)
** u= -34/29 ; C1 -1417*x^2 - 1997*y^2 + 1657*z^2
(1105/1049 : 216/1049 : 1) C2a (6658/3879 : 599/3879 : 1)
** u= -34/37 ; C1 -2969*x^2 - 2525*y^2 + 2729*z^2
(185/217 : 516/1085 : 1) C2a (95900/31961 : 54929/159805 : 1)
** u= -34/43 ; C1 -4553*x^2 - 3005*y^2 + 3617*z^2
(-10011/18143 : -15632/18143 : 1) C2a (131996/104597 : -14677/104597 : 1)
** u= -34/61 ; C1 -11465*x^2 - 4877*y^2 + 6713*z^2
(1554/2047 : 301/2047 : 1) C2a (6206/13643 : -77/1949 : 1)
** u= -34/69 ; C1 -15577*x^2 - 5917*y^2 + 8297*z^2
(646/37459 : -44345/37459 : 1) C2a (-11734/12485 : 1509/12485 : 1)
** u= -34/73 ; C1 -17873*x^2 - 6485*y^2 + 9137*z^2
(3242/5819 : -4329/5819 : 1) C2a (-34504/142537 : -2363/142537 : 1)
** u= -34/111 ; C1 -47665*x^2 - 13477*y^2 + 18713*z^2
(-10087/31523 : -31936/31523 : 1) C2a (-24278/48045 : -3791/48045 : 1)
** u= -34/115 ; C1 -51641*x^2 - 14381*y^2 + 19889*z^2
(21251/39863 : -24000/39863 : 1) C2a (-32836/295531 : -13541/295531 : 1)
** u= -34/199 ; C1 -172097*x^2 - 40757*y^2 + 51977*z^2
(-38530/78941 : 40971/78941 : 1) C2a (54842/131711 : 10789/131711 : 1)
** u= -33/133 ; C1 -71978*x^2 - 18778*y^2 + 25378*z^2
(4615/8061 : 2486/8061 : 1) C2a (1285941/125507 : 168853/125507 : 1)
** u= -33/149 ; C1 -92426*x^2 - 23290*y^2 + 30946*z^2
(1398/2417 : 79/2417 : 1) C2a (104323/232853 : 18747/232853 : 1)
** u= -32/17 ; C1 -293*x^2 + 1313*y^2 + 353*z^2
(-55/203 : 102/203 : 1) C2b (-17/15 : -1/15 : 1)
** u= -32/35 ; C1 -2669*x^2 + 2249*y^2 + 2441*z^2
(3376/3695 : -1137/3695 : 1) C2b (-17373/31025 : 1177/31025 : 1)
** u= -32/49 ; C1 -6757*x^2 + 3425*y^2 + 4513*z^2
(20/513 : 2941/2565 : 1) C2b (-1103/51901 : -2965/51901 : 1)
** u= -32/55 ; C1 -9109*x^2 + 4049*y^2 + 5521*z^2
(-1757/3385 : -2946/3385 : 1) C2b (-12257/44585 : -1463/44585 : 1)
** u= -32/63 ; C1 -12805*x^2 + 4993*y^2 + 6977*z^2
(-18220/33911 : -27487/33911 : 1) C2b (231087/873121 : -10321/873121 : 1)
** u= -31/19 ; C1 -410*x^2 - 1322*y^2 + 578*z^2
(374/1051 : -663/1051 : 1) C2a (-245117/99739 : -929/5867 : 1)
** u= -31/51 ; C1 {+/-} -7642*x^2 + 3562*y^2 + 4802*z^2
(49/2111 : 2450/2111 : 1) C2a (281/693 : -1/99 : 1) C2b (138688/376859 : 153/7691 : 1)
** u= -31/59 ; C1 {+/-} -11050*x^2 + 4442*y^2 + 6178*z^2
(2071/5379 : 5438/5379 : 1) C2a (38351/116715 : 1957/116715 : 1) C2b (25366/99937 : -2213/99937 : 1)
** u= -31/91 ; C1 -31082*x^2 - 9242*y^2 + 12962*z^2
(1383/8275 : 9466/8275 : 1) C2a (27473/146131 : -6179/146131 : 1)
** u= -31/187 ; C1 -152618*x^2 - 35930*y^2 + 45602*z^2
(-453/871 : 302/871 : 1) C2a (-311831/160513 : 271/1063 : 1)
** u= -30/13 ; C1 -185*x^2 - 1069*y^2 + 49*z^2
(-266/759 : 119/759 : 1) C2a (2186/145 : 51/145 : 1)
** u= -30/29 ; C1 -1625*x^2 - 1741*y^2 + 1681*z^2
(451/945 : 164/189 : 1) C2a (-50658/1435 : 137/35 : 1)
** u= -30/43 ; C1 -4985*x^2 - 2749*y^2 + 3529*z^2
(1/639 : 724/639 : 1) C2a (-19914/27565 : 1901/27565 : 1)
** u= -30/61 ; C1 -12185*x^2 - 4621*y^2 + 6481*z^2
(12493/17409 : -3676/17409 : 1) C2a (25532/3203 : 3411/3203 : 1)
** u= -30/103 ; C1 -41585*x^2 - 11509*y^2 + 15889*z^2
(4007/6639 : 1684/6639 : 1) C2a (-34722/292615 : 13727/292615 : 1)
** u= -30/163 ; C1 -114185*x^2 - 27469*y^2 + 35449*z^2
(-189/1531 : 1696/1531 : 1) C2a (133908/251663 : -22981/251663 : 1)
** u= -30/191 ; C1 -160385*x^2 - 37381*y^2 + 47041*z^2
(1845/5099 : 4256/5099 : 1) C2a (-348702/161435 : -45347/161435 : 1)
** u= -29/57 ; C1 {+/-} -10474*x^2 + 4090*y^2 + 5714*z^2
(2374/3749 : 2281/3749 : 1) C2a (11509/29829 : -1055/29829 : 1) C2b (-2804/13181 : 321/13181 : 1)
** u= -28/33 ; C1 -2533*x^2 + 1873*y^2 + 2153*z^2
(1340/1897 : -1307/1897 : 1) C2b (-19691/33065 : 243/33065 : 1)
** u= -28/37 ; C1 -3485*x^2 + 2153*y^2 + 2657*z^2
(-288/361 : 163/361 : 1) C2b (5203/10605 : 263/10605 : 1)
** u= -28/57 ; C1 -10645*x^2 + 4033*y^2 + 5657*z^2
(-541/1763 : 1894/1763 : 1) C2b (16671/136603 : -4057/136603 : 1)
** u= -28/67 ; C1 -15725*x^2 + 5273*y^2 + 7457*z^2
(45/341 : 398/341 : 1) C2b (2211/40897 : 83/40897 : 1)
** u= -27/23 ; C1 -890*x^2 + 1258*y^2 + 1042*z^2
(-21/31 : 22/31 : 1) C2b (-12364/14867 : 27/14867 : 1)
** u= -27/47 ; C1 {+/-} -6698*x^2 + 2938*y^2 + 4018*z^2
(-294/839 : 875/839 : 1) C2a (-4853/8785 : 69/1255 : 1) C2b (-2668/12481 : -69/1783 : 1)
** u= -27/95 ; C1 -35594*x^2 - 9754*y^2 + 13426*z^2
(59563/107115 : 1442/2895 : 1) C2a (634903/173285 : -12063/24755 : 1)
** u= -27/119 ; C1 -58682*x^2 - 14890*y^2 + 19858*z^2
(-11439/19667 : 394/19667 : 1) C2a (135517/325001 : -25071/325001 : 1)
** u= -27/143 ; C1 -87530*x^2 - 21178*y^2 + 27442*z^2
(-1374/4291 : 4007/4291 : 1) C2a (1297369/428845 : 168663/428845 : 1)
** u= -26/19 ; C1 -505*x^2 - 1037*y^2 + 673*z^2
(-481/723 : -476/723 : 1) C2a (1392/415 : 121/415 : 1)
** u= -26/21 ; C1 -697*x^2 - 1117*y^2 + 857*z^2
(254/631 : -515/631 : 1) C2a (2246/795 : 211/795 : 1)
** u= -26/41 ; C1 -4817*x^2 - 2357*y^2 + 3137*z^2
(-1362/4235 : 4481/4235 : 1) C2a (56/37 : 7/37 : 1)
** u= -26/61 ; C1 -12937*x^2 - 4397*y^2 + 6217*z^2
(-491/3165 : -3668/3165 : 1) C2a (-8456/51633 : -893/51633 : 1)
** u= -26/93 ; C1 -34249*x^2 - 9325*y^2 + 12809*z^2
(-2/163 : -191/163 : 1) C2a (9614/36313 : -10539/181565 : 1)
** u= -26/105 ; C1 -44881*x^2 - 11701*y^2 + 15809*z^2
(4541/8173 : 3340/8173 : 1) C2a (334666/265165 : -45987/265165 : 1)
** u= -26/133 ; C1 -75289*x^2 - 18365*y^2 + 23929*z^2
(7174/60259 : -67233/60259 : 1) C2a (-4552412/3239763 : 617047/3239763 : 1)
** u= -26/139 ; C1 -82825*x^2 - 19997*y^2 + 25873*z^2
(1409/2595 : -140/519 : 1) C2a (-815558/2259171 : 171823/2259171 : 1)
** u= -26/145 ; C1 -90721*x^2 - 21701*y^2 + 27889*z^2
(-28223/66265 : -48096/66265 : 1) C2a (-23526/38911 : -23/233 : 1)
** u= -26/161 ; C1 -113537*x^2 - 26597*y^2 + 33617*z^2
(35207/82385 : 57336/82385 : 1) C2a (-1523722/252581 : 194011/252581 : 1)
** u= -25/13 ; C1 -170*x^2 + 794*y^2 + 194*z^2
(98/121 : -39/121 : 1) C2b (-3506/2169 : -59/2169 : 1)
** u= -25/21 ; C1 {+/-} -730*x^2 + 1066*y^2 + 866*z^2
(157/149 : 34/149 : 1) C2a (-99391/57385 : 8829/57385 : 1) C2b (-5358/7853 : 397/7853 : 1)
** u= -25/37 ; C1 -3770*x^2 - 1994*y^2 + 2594*z^2
(194/521 : 531/521 : 1) C2a (12017/19553 : 1021/19553 : 1)
** u= -25/53 ; C1 {+/-} -9370*x^2 + 3434*y^2 + 4834*z^2
(469/829 : -606/829 : 1) C2a (-8469/4309 : -1127/4309 : 1) C2b (45554/471239 : 12439/471239 : 1)
** u= -25/189 ; C1 -160330*x^2 - 36346*y^2 + 44546*z^2
(56771/131009 : 82574/131009 : 1) C2a (186915907/56111153 : 23656401/56111153 : 1)
** u= -23/19 ; C1 {+/-} -586*x^2 + 890*y^2 + 706*z^2
(-242/243 : 91/243 : 1) C2a (-21981/1981 : -2203/1981 : 1) C2b (4784/10249 : -743/10249 : 1)
** u= -23/51 ; C1 {+/-} -8842*x^2 + 3130*y^2 + 4418*z^2
(-1363/2351 : 1598/2351 : 1) C2a (6629/16497 : 17/351 : 1) C2b (6512/37459 : 3/797 : 1)
** u= -23/147 ; C1 -95050*x^2 - 22138*y^2 + 27842*z^2
(54809/239075 : 48574/47815 : 1) C2a (2440753/423225 : -310129/423225 : 1)
** u= -23/187 ; C1 -158170*x^2 - 35498*y^2 + 43042*z^2
(-2215/12959 : -13482/12959 : 1) C2a (-206121/132923 : 27169/132923 : 1)
** u= -22/13 ; C1 -185*x^2 - 653*y^2 + 257*z^2
(-162/139 : -13/139 : 1) C2a (-91498/8435 : -6431/8435 : 1)
** u= -22/39 ; C1 -4657*x^2 - 2005*y^2 + 2753*z^2
(-2062/2801 : -947/2801 : 1) C2a (119542/44389 : -15675/44389 : 1)
** u= -22/57 ; C1 -11713*x^2 - 3733*y^2 + 5273*z^2
(-970/1447 : -73/1447 : 1) C2a (43492/24705 : 5857/24705 : 1)
** u= -22/83 ; C1 -27625*x^2 - 7373*y^2 + 10057*z^2
(4489/9695 : 1452/1939 : 1) C2a (151486/2247 : -19969/2247 : 1)
** u= -22/101 ; C1 -42601*x^2 - 10685*y^2 + 14161*z^2
(-18683/32993 : -7140/32993 : 1) C2a (4026/1139 : -31/67 : 1)
** u= -22/145 ; C1 -92849*x^2 - 21509*y^2 + 26921*z^2
(30531/56753 : -2740/56753 : 1) C2a (-13328/21817 : 344981/3425269 : 1)
** u= -22/151 ; C1 -101201*x^2 - 23285*y^2 + 28961*z^2
(-8098/20993 : 16221/20993 : 1) C2a (-174616/10859 : -21991/10859 : 1)
** u= -22/181 ; C1 -148361*x^2 - 33245*y^2 + 40241*z^2
(-921/2429 : 1832/2429 : 1) C2a (32566/385729 : 26635/385729 : 1)
** u= -22/183 ; C1 -151825*x^2 - 33973*y^2 + 41057*z^2
(67982/213905 : 37225/42781 : 1) C2a (-1603982/3609239 : 317097/3609239 : 1)
** u= -22/189 ; C1 -162457*x^2 - 36205*y^2 + 43553*z^2
(-39839/77053 : -4516/77053 : 1) C2a (7237076/685807 : -897129/685807 : 1)
** u= -21/17 ; C1 {+/-} -458*x^2 + 730*y^2 + 562*z^2
(-27/101 : 86/101 : 1) C2a (-29907/5051 : -2929/5051 : 1) C2b (326/373 : -3/373 : 1)
** u= -21/25 ; C1 {+/-} -1466*x^2 + 1066*y^2 + 1234*z^2
(-201/245 : -118/245 : 1) C2a (-243/257 : -23/257 : 1) C2b (2648/5775 : 263/5775 : 1)
** u= -21/41 ; C1 {+/-} -5402*x^2 + 2122*y^2 + 2962*z^2
(-1215/2021 : 1394/2021 : 1) C2a (8483/541 : 1131/541 : 1) C2b (1072/8571 : -293/8571 : 1)
** u= -21/137 ; C1 -82778*x^2 - 19210*y^2 + 24082*z^2
(11014/21873 : -8777/21873 : 1) C2a (349199/6604013 : -428691/6604013 : 1)
** u= -20/9 ; C1 -85*x^2 + 481*y^2 + 41*z^2
(224/421 : -79/421 : 1) C2b (-1761/1511 : 131/1511 : 1)
** u= -20/13 ; C1 -205*x^2 + 569*y^2 + 289*z^2
(119/111 : 34/111 : 1) C2b (-1163/1037 : 1/61 : 1)
** u= -20/29 ; C1 -2285*x^2 + 1241*y^2 + 1601*z^2
(456/869 : 769/869 : 1) C2b (-1797/59695 : 3619/59695 : 1)
** u= -20/33 ; C1 -3205*x^2 + 1489*y^2 + 2009*z^2
(-1736/2249 : -581/2249 : 1) C2b (417/14455 : -107/2065 : 1)
** u= -19/23 ; C1 {+/-} -1258*x^2 + 890*y^2 + 1042*z^2
(22/31 : -21/31 : 1) C2a (47633/24201 : -5557/24201 : 1) C2b (-39944/73097 : 1789/73097 : 1)
** u= -19/39 ; C1 -5002*x^2 + 1882*y^2 + 2642*z^2
(1087/1783 : 1150/1783 : 1) C2b (-13154/53675 : 213/53675 : 1)
** u= -19/55 ; C1 -11306*x^2 - 3386*y^2 + 4754*z^2
(662/1075 : 399/1075 : 1) C2a (-479581/1067231 : 73099/1067231 : 1)
** u= -19/119 ; C1 -62122*x^2 - 14522*y^2 + 18322*z^2
(-17587/32387 : 510/32387 : 1) C2a (19093/137529 : -9101/137529 : 1)
** u= -19/159 ; C1 -114682*x^2 - 25642*y^2 + 30962*z^2
(5318/10235 : -61/10235 : 1) C2a (188443/31551 : 23471/31551 : 1)
** u= -19/183 ; C1 -153898*x^2 - 33850*y^2 + 40082*z^2
(-1022/2207 : -5047/11035 : 1) C2a (2384723/200291 : 41889/28613 : 1)
** u= -19/191 ; C1 -168250*x^2 - 36842*y^2 + 43378*z^2
(-713/2115 : 4462/5499 : 1) C2a (3467/41469 : -1673/23439 : 1)
** u= -18/37 ; C1 -4505*x^2 - 1693*y^2 + 2377*z^2
(-353/1737 : 1976/1737 : 1) C2a (13624/25903 : 1611/25903 : 1)
** u= -18/115 ; C1 -58169*x^2 - 13549*y^2 + 17041*z^2
(1210/3273 : 2681/3273 : 1) C2a (-453154/55771 : -57471/55771 : 1)
** u= -18/145 ; C1 -95009*x^2 - 21349*y^2 + 25921*z^2
(161/18705 : -20608/18705 : 1) C2a (-2586432/25088147 : -10777/155827 : 1)
** u= -17/21 ; C1 {+/-} -1066*x^2 + 730*y^2 + 866*z^2
(359/1949 : -2078/1949 : 1) C2a (1667/1197 : 187/1197 : 1) C2b (1152/13787 : 955/13787 : 1)
** u= -17/61 ; C1 -14746*x^2 - 4010*y^2 + 5506*z^2
(118/237 : -161/237 : 1) C2a (208981/418581 : -33791/418581 : 1)
** u= -17/101 ; C1 -44426*x^2 - 10490*y^2 + 13346*z^2
(6042/11437 : -3437/11437 : 1) C2a (-21931/336419 : 21283/336419 : 1)
** u= -17/117 ; C1 -60778*x^2 - 13978*y^2 + 17378*z^2
(4330/81721 : 90671/81721 : 1) C2a (-149801/403337 : -32463/403337 : 1)
** u= -17/165 ; C1 -125194*x^2 - 27514*y^2 + 32546*z^2
(20087/39445 : 2126/39445 : 1) C2a (7097/15287 : 1383/15287 : 1)
** u= -16/9 ; C1 -85*x^2 + 337*y^2 + 113*z^2
(-20/53 : 29/53 : 1) C2b (-2621/2413 : 147/2413 : 1)
** u= -16/21 ; C1 -1117*x^2 + 697*y^2 + 857*z^2
(-337/2083 : -2270/2083 : 1) C2b (3831/51307 : -3389/51307 : 1)
** u= -16/35 ; C1 -4141*x^2 + 1481*y^2 + 2089*z^2
(-2528/3615 : 751/3615 : 1) C2b (-2027/13033 : -191/13033 : 1)
** u= -15/11 ; C1 -170*x^2 - 346*y^2 + 226*z^2
(54/59 : -29/59 : 1) C2a (3671/3745 : -9/3745 : 1)
** u= -15/19 ; C1 -890*x^2 + 586*y^2 + 706*z^2
(-9/79 : -86/79 : 1) C2b (704/1471 : -51/1471 : 1)
** u= -15/67 ; C1 -18650*x^2 - 4714*y^2 + 6274*z^2
(-71/231 : 226/231 : 1) C2a (30723/77915 : 5873/77915 : 1)
** u= -14/11 ; C1 -185*x^2 - 317*y^2 + 233*z^2
(49/71 : -48/71 : 1) C2a (99842/11639 : -9607/11639 : 1)
** u= -14/27 ; C1 -2329*x^2 - 925*y^2 + 1289*z^2
(-1118/2149 : -9067/10745 : 1) C2a (-6932/7983 : 869/7983 : 1)
** u= -14/37 ; C1 -4969*x^2 - 1565*y^2 + 2209*z^2
(-1081/1629 : -188/1629 : 1) C2a (516/25709 : 13/547 : 1)
** u= -14/39 ; C1 -5617*x^2 - 1717*y^2 + 2417*z^2
(-6857/13655 : -10424/13655 : 1) C2a (818/121815 : 3583/121815 : 1)
** u= -14/43 ; C1 -7033*x^2 - 2045*y^2 + 2857*z^2
(-658/2229 : -2335/2229 : 1) C2a (9924/1433 : -1325/1433 : 1)
** u= -14/45 ; C1 -7801*x^2 - 2221*y^2 + 3089*z^2
(2429/6905 : 6752/6905 : 1) C2a (-47512/140853 : 8507/140853 : 1)
** u= -14/73 ; C1 -22753*x^2 - 5525*y^2 + 7177*z^2
(-19/41 : -132/205 : 1) C2a (3046/22149 : 6893/110745 : 1)
** u= -14/85 ; C1 -31561*x^2 - 7421*y^2 + 9409*z^2
(4850/53379 : -59267/53379 : 1) C2a (-2289342/15065167 : -10259/155311 : 1)
** u= -14/95 ; C1 -40001*x^2 - 9221*y^2 + 11489*z^2
(-42933/105715 : 76996/105715 : 1) C2a (-138764/154325 : 20177/154325 : 1)
** u= -14/145 ; C1 -97201*x^2 - 21221*y^2 + 24889*z^2
(2518/25971 : 27605/25971 : 1) C2a (-424526/92151 : -52301/92151 : 1)
** u= -13/41 ; C1 -6442*x^2 - 1850*y^2 + 2578*z^2
(-43/69 : -14/69 : 1) C2a (59797/26601 : -8035/26601 : 1)
** u= -13/73 ; C1 -23018*x^2 - 5498*y^2 + 7058*z^2
(78/2233 : -2525/2233 : 1) C2a (-709609/268235 : 92231/268235 : 1)
** u= -13/177 ; C1 -147610*x^2 - 31498*y^2 + 35762*z^2
(214013/437449 : 51242/437449 : 1) C2a (-2394133/282951 : 288673/282951 : 1)
** u= -13/185 ; C1 -161674*x^2 - 34394*y^2 + 38866*z^2
(15230/55093 : -48369/55093 : 1) C2a (33273/31625 : -4621/31625 : 1)
** u= -12/11 ; C1 -221*x^2 + 265*y^2 + 241*z^2
(12/23 : 19/23 : 1) C2b (-2749/4461 : -223/4461 : 1)
** u= -12/19 ; C1 -1037*x^2 + 505*y^2 + 673*z^2
(-352/471 : 203/471 : 1) C2b (52013/123501 : -223/123501 : 1)
** u= -11/7 ; C1 {+/-} -58*x^2 + 170*y^2 + 82*z^2
(26/27 : -11/27 : 1) C2a (217/141 : 11/141 : 1) C2b (-2/11 : -1/11 : 1)
** u= -11/135 ; C1 -85306*x^2 - 18346*y^2 + 21074*z^2
(-583/1435 : -886/1435 : 1) C2a (-167/1953 : 143/1953 : 1)
** u= -10/7 ; C1 -65*x^2 - 149*y^2 + 89*z^2
(375/331 : -64/331 : 1) C2a (-10234/6491 : 673/6491 : 1)
** u= -10/11 ; C1 -265*x^2 - 221*y^2 + 241*z^2
(89/131 : 96/131 : 1) C2a (-13788/18425 : 833/18425 : 1)
** u= -10/17 ; C1 -865*x^2 - 389*y^2 + 529*z^2
(575/969 : 736/969 : 1) C2a (-1224/115 : 7/5 : 1)
** u= -10/31 ; C1 -3665*x^2 - 1061*y^2 + 1481*z^2
(498/1193 : 1063/1193 : 1) C2a (-4594/34639 : -1453/34639 : 1)
** u= -10/37 ; C1 -5465*x^2 - 1469*y^2 + 2009*z^2
(11634/19403 : -3367/19403 : 1) C2a (-7682/27943 : -1679/27943 : 1)
** u= -10/41 ; C1 -6865*x^2 - 1781*y^2 + 2401*z^2
(1519/2761 : -1176/2761 : 1) C2a (-26268/9653 : 71/197 : 1)
** u= -10/59 ; C1 -15145*x^2 - 3581*y^2 + 4561*z^2
(-10661/33511 : 30816/33511 : 1) C2a (30552/3827 : 3899/3827 : 1)
** u= -10/119 ; C1 -66145*x^2 - 14261*y^2 + 16441*z^2
(-8501/126447 : -134528/126447 : 1) C2a (-322812/349567 : 46561/349567 : 1)
** u= -10/123 ; C1 -70825*x^2 - 15229*y^2 + 17489*z^2
(78538/167365 : 11801/33473 : 1) C2a (1174/1491 : -28019/234087 : 1)
** u= -10/139 ; C1 -91145*x^2 - 19421*y^2 + 22001*z^2
(399/4003 : -4172/4003 : 1) C2a (73898/48643 : -1367/6949 : 1)
** u= -10/143 ; C1 -96625*x^2 - 20549*y^2 + 23209*z^2
(-1346/4065 : 637/813 : 1) C2a (918/22265 : 1643/22265 : 1)
** u= -10/161 ; C1 -123265*x^2 - 26021*y^2 + 29041*z^2
(21454/44203 : 543/44203 : 1) C2a (-102778/397035 : 31973/397035 : 1)
** u= -10/171 ; C1 -139465*x^2 - 29341*y^2 + 32561*z^2
(-28870/64273 : -24953/64273 : 1) C2a (550834/252309 : -68153/252309 : 1)
** u= -9/77 ; C1 -26954*x^2 - 6010*y^2 + 7234*z^2
(173/417 : 274/417 : 1) C2a (-27873/179197 : 12797/179197 : 1)
** u= -9/85 ; C1 -33146*x^2 - 7306*y^2 + 8674*z^2
(1779/5117 : 4090/5117 : 1) C2a (533613/2103535 : 161131/2103535 : 1)
** u= -8/7 ; C1 -85*x^2 + 113*y^2 + 97*z^2
(548/519 : -73/519 : 1) C2b (-647/1061 : -59/1061 : 1)
** u= -8/19 ; C1 -1261*x^2 + 425*y^2 + 601*z^2
(49/181 : 198/181 : 1) C2b (-121/5077 : -247/25385 : 1)
** u= -7/3 ; C1 {+/-} -10*x^2 + 58*y^2 + 2*z^2
(-2/7 : 1/7 : 1) C2a (1751/237 : 29/237 : 1) C2b (-68/35 : 3/35 : 1)
** u= -7/11 ; C1 {+/-} -346*x^2 + 170*y^2 + 226*z^2
(-634/791 : 117/791 : 1) C2a (9/11 : -1/11 : 1) C2b (-52/233 : -11/233 : 1)
** u= -7/19 ; C1 -1322*x^2 - 410*y^2 + 578*z^2
(-663/1051 : 374/1051 : 1) C2a (-4549/5797 : 37/341 : 1)
** u= -7/27 ; C1 -2938*x^2 - 778*y^2 + 1058*z^2
(23/55 : 46/55 : 1) C2a (-503/391 : 3/17 : 1)
** u= -7/107 ; C1 -54298*x^2 - 11498*y^2 + 12898*z^2
(2455/12879 : -12554/12879 : 1) C2a (159223/235149 : -25799/235149 : 1)
** u= -7/115 ; C1 -62954*x^2 - 13274*y^2 + 14786*z^2
(7147/14815 : 1494/14815 : 1) C2a (841/28009 : 2089/28009 : 1)
** u= -7/139 ; C1 -92762*x^2 - 19370*y^2 + 21218*z^2
(19467/42019 : -10918/42019 : 1) C2a (1431481/480083 : 1679/4661 : 1)
** u= -7/187 ; C1 -169658*x^2 - 35018*y^2 + 37538*z^2
(22194/47299 : 3425/47299 : 1) C2a (-105407/122341 : -113/893 : 1)
** u= -6/7 ; C1 -113*x^2 - 85*y^2 + 97*z^2
(-18/29 : 23/29 : 1) C2a (-42/11 : 5/11 : 1)
** u= -6/13 ; C1 -569*x^2 - 205*y^2 + 289*z^2
(34/111 : 119/111 : 1) C2a (864/2941 : -5/173 : 1)
** u= -6/31 ; C1 -4097*x^2 - 997*y^2 + 1297*z^2
(-754/5985 : 6653/5985 : 1) C2a (596/3343 : -213/3343 : 1)
** u= -6/143 ; C1 -98849*x^2 - 20485*y^2 + 22129*z^2
(-4406/11409 : -6851/11409 : 1) C2a (37476/24911 : 4789/24911 : 1)
** u= -6/155 ; C1 -116441*x^2 - 24061*y^2 + 25849*z^2
(-3713/23439 : -1760/1803 : 1) C2a (7754028/4438175 : -968621/4438175 : 1)
** u= -6/169 ; C1 -138785*x^2 - 28597*y^2 + 30553*z^2
(-12062/84903 : 83639/84903 : 1) C2a (391296/454955 : 57493/454955 : 1)
** u= -4/7 ; C1 -149*x^2 + 65*y^2 + 89*z^2
(-19/29 : 18/29 : 1) C2b (-109/321 : -5/321 : 1)
** u= -3/7 ; C1 {+/-} -170*x^2 + 58*y^2 + 82*z^2
(2/3 : 1/3 : 1) C2a (231/13 : -31/13 : 1) C2b (-122/1905 : 23/1905 : 1)
** u= -3/71 ; C1 -24362*x^2 - 5050*y^2 + 5458*z^2
(-175/3999 : -20698/19995 : 1) C2a (357/87485 : 33341/437425 : 1)
** u= -3/95 ; C1 -43994*x^2 - 9034*y^2 + 9586*z^2
(685/6231 : 6238/6231 : 1) C2a (323749/121961 : 38799/121961 : 1)
** u= -3/151 ; C1 -112202*x^2 - 22810*y^2 + 23698*z^2
(4539/16307 : 13226/16307 : 1) C2a (-963/38029 : -175/2237 : 1)
** u= -2 ; C1 -x^2 - 5*y^2 + z^2
(1 : 0 : 1) C2a (26/9 : -1/9 : 1)
** u= -2/5 ; C1 -89*x^2 - 29*y^2 + 41*z^2
(-11/53 : -60/53 : 1) C2a (-2/65 : 1/65 : 1)
** u= -2/9 ; C1 -337*x^2 - 85*y^2 + 113*z^2
(-43/109 : -92/109 : 1) C2a (-1118/379 : 147/379 : 1)
** u= -2/19 ; C1 -1657*x^2 - 365*y^2 + 433*z^2
(-131/463 : -420/463 : 1) C2a (-5736/733 : -707/733 : 1)
** u= -2/21 ; C1 -2041*x^2 - 445*y^2 + 521*z^2
(389/869 : 436/869 : 1) C2a (-8/3 : 1/3 : 1)
** u= -2/23 ; C1 -2465*x^2 - 533*y^2 + 617*z^2
(297/859 : -668/859 : 1) C2a (2266/2507 : -329/2507 : 1)
** u= -2/121 ; C1 -72241*x^2 - 14645*y^2 + 15121*z^2
(-182/523 : 345/523 : 1) C2a (35622/8143 : 4135/8143 : 1)
** u= -2/127 ; C1 -79633*x^2 - 16133*y^2 + 16633*z^2
(-5806/12705 : -167/12705 : 1) C2a (-14614/25377 : -2603/25377 : 1)
** u= -2/131 ; C1 -84761*x^2 - 17165*y^2 + 17681*z^2
(3274/22589 : 21741/22589 : 1) C2a (154456/31109 : 17861/31109 : 1)
** u= -2/183 ; C1 -165985*x^2 - 33493*y^2 + 34217*z^2
(186707/507151 : 300008/507151 : 1) C2a (-3069251672/25534509 : -350145707/25534509 : 1)
** u= -1/13 ; C1 -794*x^2 - 170*y^2 + 194*z^2
(26/61 : 33/61 : 1) C2a (-1987/703 : 245/703 : 1)
** u= -1/21 ; C1 -2122*x^2 - 442*y^2 + 482*z^2
(19/41 : 10/41 : 1) C2a (2569/1047 : -313/1047 : 1)
** u= 1/3 ; C1 -58*x^2 - 10*y^2 + 2*z^2
(1/7 : -2/7 : 1) C2a (257/9 : 13/9 : 1)
** u= 1/59 ; C1 -17642*x^2 - 3482*y^2 + 3362*z^2
(1066/4375 : -3567/4375 : 1) C2a (422767/266131 : -1259/6491 : 1)
** u= 1/83 ; C1 -34778*x^2 - 6890*y^2 + 6722*z^2
(714/6907 : -6631/6907 : 1) C2a (-469687/83981 : 52799/83981 : 1)
** u= 1/91 ; C1 -41770*x^2 - 8282*y^2 + 8098*z^2
(-1469/3839 : -1878/3839 : 1) C2a (-4053/47731 : -3877/47731 : 1)
** u= 1/139 ; C1 -97162*x^2 - 19322*y^2 + 19042*z^2
(-9055/22643 : -9642/22643 : 1) C2a (-114213/62269 : -13741/62269 : 1)
** u= 1/187 ; C1 -175594*x^2 - 34970*y^2 + 34594*z^2
(6377/14627 : 2730/14627 : 1) C2a (-170069/212289 : 3655/30327 : 1)
** u= 2/5 ; C1 -169*x^2 - 29*y^2 + z^2
(1/13 : 0 : 1) C2a (212/57 : 7/57 : 1)
** u= 2/9 ; C1 -481*x^2 - 85*y^2 + 41*z^2
(-1/29 : 20/29 : 1) C2a (-472/3 : 37/3 : 1)
** u= 2/13 ; C1 -953*x^2 - 173*y^2 + 113*z^2
(54/395 : -293/395 : 1) C2a (7568/39859 : 3629/39859 : 1)
** u= 2/19 ; C1 -1961*x^2 - 365*y^2 + 281*z^2
(-7/23 : -12/23 : 1) C2a (7492/2237 : 767/2237 : 1)
** u= 2/21 ; C1 -2377*x^2 - 445*y^2 + 353*z^2
(134/383 : 143/383 : 1) C2a (-1334/2457 : -251/2457 : 1)
** u= 2/23 ; C1 -2833*x^2 - 533*y^2 + 433*z^2
(554/1645 : 753/1645 : 1) C2a (-1012/5829 : -511/5829 : 1)
** u= 2/121 ; C1 -74177*x^2 - 14645*y^2 + 14153*z^2
(-1198/6439 : -5727/6439 : 1) C2a (-14663794/879277 : 1628575/879277 : 1)
** u= 2/125 ; C1 -79129*x^2 - 15629*y^2 + 15121*z^2
(7334/49087 : 45375/49087 : 1) C2a (-3002/2925 : -409/2925 : 1)
** u= 2/131 ; C1 -86857*x^2 - 17165*y^2 + 16633*z^2
(1214/2777 : 123/2777 : 1) C2a (24988/35979 : -4025/35979 : 1)
** u= 2/187 ; C1 -176345*x^2 - 34973*y^2 + 34217*z^2
(-41431/107743 : 51984/107743 : 1) C2a (-9924614/9987823 : 1369841/9987823 : 1)
** u= 3/17 ; C1 -1658*x^2 - 298*y^2 + 178*z^2
(18/233 : 175/233 : 1) C2a (4889/515 : 429/515 : 1)
** u= 3/25 ; C1 -3434*x^2 - 634*y^2 + 466*z^2
(90/977 : -811/977 : 1) C2a (-61/715 : 63/715 : 1)
** u= 3/73 ; C1 -27530*x^2 - 5338*y^2 + 4882*z^2
(-2150/6573 : 3959/6573 : 1) C2a (-711/763 : -15613/119791 : 1)
** u= 5/47 ; C1 -12010*x^2 - 2234*y^2 + 1714*z^2
(-374/1131 : 479/1131 : 1) C2a (-28233/24257 : -3499/24257 : 1)
** u= 5/63 ; C1 -21130*x^2 - 3994*y^2 + 3314*z^2
(2342/5983 : -827/5983 : 1) C2a (6229/4029 : 727/4029 : 1)
** u= 5/71 ; C1 -26650*x^2 - 5066*y^2 + 4306*z^2
(26/75 : -7/15 : 1) C2a (25271/15939 : -2957/15939 : 1)
** u= 6/25 ; C1 -3761*x^2 - 661*y^2 + 289*z^2
(-17/825 : -544/825 : 1) C2a (17932/9095 : -93/535 : 1)
** u= 6/67 ; C1 -24089*x^2 - 4525*y^2 + 3649*z^2
(90/5621 : -25217/28105 : 1) C2a (-26490/5443 : 13627/27215 : 1)
** u= 6/109 ; C1 -62057*x^2 - 11917*y^2 + 10537*z^2
(27474/66731 : 2585/66731 : 1) C2a (82944/191933 : -18343/191933 : 1)
** u= 6/155 ; C1 -123881*x^2 - 24061*y^2 + 22129*z^2
(-8622/21625 : -6881/21625 : 1) C2a (81214/469489 : -39819/469489 : 1)
** u= 6/169 ; C1 -146897*x^2 - 28597*y^2 + 26497*z^2
(24835/69381 : -35944/69381 : 1) C2a (6707896/649757 : -730737/649757 : 1)
** u= 7/45 ; C1 -11434*x^2 - 2074*y^2 + 1346*z^2
(-118/1085 : 829/1085 : 1) C2a (50591/19479 : -4919/19479 : 1)
** u= 9/35 ; C1 -7466*x^2 - 1306*y^2 + 514*z^2
(186/755 : -163/755 : 1) C2a (43533/6263 : 3137/6263 : 1)
** u= 9/83 ; C1 -37514*x^2 - 6970*y^2 + 5314*z^2
(-1077/3047 : 914/3047 : 1) C2a (921/559 : -103/559 : 1)
** u= 9/107 ; C1 -61178*x^2 - 11530*y^2 + 9442*z^2
(29331/78403 : -1666/6031 : 1) C2a (282183/130759 : 30923/130759 : 1)
** u= 9/139 ; C1 -101690*x^2 - 19402*y^2 + 16738*z^2
(543/30479 : 28282/30479 : 1) C2a (-32349/53357 : 5641/53357 : 1)
** u= 9/179 ; C1 -166730*x^2 - 32122*y^2 + 28738*z^2
(15987/39647 : 8926/39647 : 1) C2a (-576457/184535 : 63441/184535 : 1)
** u= 10/31 ; C1 -6145*x^2 - 1061*y^2 + 241*z^2
(34/353 : -147/353 : 1) C2a (-4504/3729 : -427/3729 : 1)
** u= 10/37 ; C1 -8425*x^2 - 1469*y^2 + 529*z^2
(437/1905 : -92/381 : 1) C2a (16548/1265 : -49/55 : 1)
** u= 10/41 ; C1 -10145*x^2 - 1781*y^2 + 761*z^2
(-1075/22033 : -14172/22033 : 1) C2a (-33908/15637 : -2891/15637 : 1)
** u= 10/61 ; C1 -21145*x^2 - 3821*y^2 + 2401*z^2
(-4606/25019 : 16611/25019 : 1) C2a (-60278/13965 : 113/285 : 1)
** u= 10/119 ; C1 -75665*x^2 - 14261*y^2 + 11681*z^2
(-1566/12769 : 10979/12769 : 1) C2a (-235544/152911 : 27397/152911 : 1)
** u= 10/123 ; C1 -80665*x^2 - 15229*y^2 + 12569*z^2
(5066/21317 : 15463/21317 : 1) C2a (2416/2139 : 48349/335823 : 1)
** u= 10/139 ; C1 -102265*x^2 - 19421*y^2 + 16441*z^2
(27005/69187 : -14568/69187 : 1) C2a (7658/75483 : -6461/75483 : 1)
** u= 10/143 ; C1 -108065*x^2 - 20549*y^2 + 17489*z^2
(-3258/10453 : -6097/10453 : 1) C2a (-173926/69265 : -19039/69265 : 1)
** u= 10/159 ; C1 -132865*x^2 - 25381*y^2 + 22001*z^2
(-2702/16969 : 14539/16969 : 1) C2a (-19954/2895 : -2111/2895 : 1)
** u= 10/161 ; C1 -136145*x^2 - 26021*y^2 + 22601*z^2
(-37578/234359 : -200791/234359 : 1) C2a (-1825622/1931003 : -251761/1931003 : 1)
** u= 10/171 ; C1 -153145*x^2 - 29341*y^2 + 25721*z^2
(-26282/139661 : 116161/139661 : 1) C2a (104086/161789 : 1029/9517 : 1)
** u= 10/191 ; C1 -190145*x^2 - 36581*y^2 + 32561*z^2
(-55046/133021 : -249/133021 : 1) C2a (346028/216763 : 6447643/34031791 : 1)
** u= 11/129 ; C1 -89002*x^2 - 16762*y^2 + 13682*z^2
(142/677 : -8785/11509 : 1) C2a (-259/3 : 449/51 : 1)
** u= 11/137 ; C1 -99994*x^2 - 18890*y^2 + 15634*z^2
(37267/96033 : 986/5649 : 1) C2a (-8881/34239 : 3065/34239 : 1)
** u= 13/175 ; C1 -162394*x^2 - 30794*y^2 + 25906*z^2
(-13295/38947 : -18546/38947 : 1) C2a (-2324619/1167269 : -260341/1167269 : 1)
** u= 13/183 ; C1 -177130*x^2 - 33658*y^2 + 28562*z^2
(17483/48683 : -20066/48683 : 1) C2a (-42540479/6733747 : 4459791/6733747 : 1)
** u= 14/37 ; C1 -9113*x^2 - 1565*y^2 + 137*z^2
(262/2219 : 177/2219 : 1) C2a (102272/3461 : -3431/3461 : 1)
** u= 14/39 ; C1 -9985*x^2 - 1717*y^2 + 233*z^2
(-58/421 : 67/421 : 1) C2a (3616/2705 : 297/2705 : 1)
** u= 14/43 ; C1 -11849*x^2 - 2045*y^2 + 449*z^2
(439/3451 : -72/203 : 1) C2a (-3008/3293 : -349/3293 : 1)
** u= 14/45 ; C1 -12841*x^2 - 2221*y^2 + 569*z^2
(-401/2633 : 920/2633 : 1) C2a (-272/285 : -31/285 : 1)
** u= 14/73 ; C1 -30929*x^2 - 5525*y^2 + 3089*z^2
(-314/1795 : 5589/8975 : 1) C2a (-26828/31835 : -18379/159175 : 1)
** u= 14/85 ; C1 -41081*x^2 - 7421*y^2 + 4649*z^2
(5331/21205 : -11152/21205 : 1) C2a (152/383 : 37/383 : 1)
** u= 14/145 ; C1 -113441*x^2 - 21221*y^2 + 16769*z^2
(-15858/45635 : -17359/45635 : 1) C2a (70246/26735 : 7417/26735 : 1)
** u= 14/173 ; C1 -159529*x^2 - 30125*y^2 + 24889*z^2
(3491/9981 : 21076/49905 : 1) C2a (56358/119153 : 58571/595765 : 1)
** u= 17/43 ; C1 -12458*x^2 - 2138*y^2 + 98*z^2
(-42/5155 : -1099/5155 : 1) C2a (-31523/30919 : 433/4417 : 1)
** u= 17/59 ; C1 -21706*x^2 - 3770*y^2 + 1186*z^2
(131/6951 : 3886/6951 : 1) C2a (51/329 : -31/329 : 1)
** u= 17/115 ; C1 -74234*x^2 - 13514*y^2 + 9026*z^2
(-190/643 : 279/643 : 1) C2a (16721/1345 : -1547/1345 : 1)
** u= 17/123 ; C1 -84298*x^2 - 15418*y^2 + 10658*z^2
(-2555/10943 : -6862/10943 : 1) C2a (-184343/197319 : -337/2703 : 1)
** u= 17/147 ; C1 -118330*x^2 - 21898*y^2 + 16322*z^2
(-4810/65623 : -55541/65623 : 1) C2a (-15845941/2745295 : -1562643/2745295 : 1)
** u= 18/115 ; C1 -74729*x^2 - 13549*y^2 + 8761*z^2
(12310/36033 : 1939/36033 : 1) C2a (54406/89195 : 9387/89195 : 1)
** u= 18/145 ; C1 -115889*x^2 - 21349*y^2 + 15481*z^2
(-1307/3825 : -68/225 : 1) C2a (-2484/38875 : -3427/38875 : 1)
** u= 18/151 ; C1 -125201*x^2 - 23125*y^2 + 17041*z^2
(1009/6471 : -25172/32355 : 1) C2a (1404/6017 : -13621/150425 : 1)
** u= 19/89 ; C1 -46730*x^2 - 8282*y^2 + 4178*z^2
(-18/61 : 7/61 : 1) C2a (-223273/1375 : -17899/1375 : 1)
** u= 19/169 ; C1 -156010*x^2 - 28922*y^2 + 21778*z^2
(1742/52569 : 45437/52569 : 1) C2a (19302243/3373135 : -1913269/3373135 : 1)
** u= 21/151 ; C1 -127130*x^2 - 23242*y^2 + 16018*z^2
(2034/15631 : 12073/15631 : 1) C2a (21393/28601 : 3233/28601 : 1)
** u= 22/57 ; C1 -21745*x^2 - 3733*y^2 + 257*z^2
(-482/4663 : -379/4663 : 1) C2a (63592/10559 : -2133/10559 : 1)
** u= 22/83 ; C1 -42233*x^2 - 7373*y^2 + 2753*z^2
(-10053/43543 : 11360/43543 : 1) C2a (-5342/5575 : -637/5575 : 1)
** u= 22/87 ; C1 -45985*x^2 - 8053*y^2 + 3257*z^2
(6341/36671 : 17728/36671 : 1) C2a (1423804/30115 : 102237/30115 : 1)
** u= 22/101 ; C1 -60377*x^2 - 10685*y^2 + 5273*z^2
(414/8227 : -5695/8227 : 1) C2a (-793492/171389 : -64855/171389 : 1)
** u= 22/145 ; C1 -118369*x^2 - 21509*y^2 + 14161*z^2
(-595/2461 : 1428/2461 : 1) C2a (-1068/2023 : -271/2669 : 1)
** u= 22/181 ; C1 -180217*x^2 - 33245*y^2 + 24313*z^2
(-42634/143727 : -72485/143727 : 1) C2a (-50008/17631 : 5069/17631 : 1)
** u= 22/183 ; C1 -184033*x^2 - 33973*y^2 + 24953*z^2
(-8243/27895 : 14264/27895 : 1) C2a (66506/56865 : 8141/56865 : 1)
** u= 22/189 ; C1 -195721*x^2 - 36205*y^2 + 26921*z^2
(-802/23203 : -19921/23203 : 1) C2a (-135674/103041 : 15991/103041 : 1)
** u= 23/109 ; C1 -69962*x^2 - 12410*y^2 + 6338*z^2
(-14286/62593 : 29161/62593 : 1) C2a (459319/341797 : -48517/341797 : 1)
** u= 23/189 ; C1 -196522*x^2 - 36250*y^2 + 26498*z^2
(-262/1265 : 22327/31625 : 1) C2a (7/19 : -9/95 : 1)
** u= 26/93 ; C1 -53593*x^2 - 9325*y^2 + 3137*z^2
(-154/1315 : 3337/6575 : 1) C2a (-403184/102945 : -140477/514725 : 1)
** u= 26/105 ; C1 -66721*x^2 - 11701*y^2 + 4889*z^2
(-24125/89161 : 1688/89161 : 1) C2a (1229462/38157 : 89767/38157 : 1)
** u= 26/121 ; C1 -86465*x^2 - 15317*y^2 + 7673*z^2
(39/149 : -856/2533 : 1) C2a (115954/485 : -9263/485 : 1)
** u= 26/139 ; C1 -111737*x^2 - 19997*y^2 + 11417*z^2
(9695/50927 : -30912/50927 : 1) C2a (328844/378595 : -6337/54085 : 1)
** u= 26/145 ; C1 -120881*x^2 - 21701*y^2 + 12809*z^2
(-5374/27935 : -17313/27935 : 1) C2a (1621904/4370329 : 419671/4370329 : 1)
** u= 26/197 ; C1 -215209*x^2 - 39485*y^2 + 27889*z^2
(13694/91899 : 70307/91899 : 1) C2a (-867192/1970767 : 1153/11801 : 1)
** u= 30/103 ; C1 -66305*x^2 - 11509*y^2 + 3529*z^2
(-1743/8371 : 1996/8371 : 1) C2a (-7806/64489 : -6067/64489 : 1)
** u= 30/163 ; C1 -153305*x^2 - 27469*y^2 + 15889*z^2
(810/33173 : -25157/33173 : 1) C2a (1548272/875623 : 154809/875623 : 1)
** u= 30/191 ; C1 -206225*x^2 - 37381*y^2 + 24121*z^2
(36513/181595 : -23600/36319 : 1) C2a (-298374/132845 : -29551/132845 : 1)
** u= 31/77 ; C1 -40154*x^2 - 6890*y^2 + 194*z^2
(-186/11989 : -1961/11989 : 1) C2a (-7739/1771 : -223/1771 : 1)
** u= 33/91 ; C1 -54506*x^2 - 9370*y^2 + 1186*z^2
(-498/4027 : 781/4027 : 1) C2a (-11295623/2436667 : -508917/2436667 : 1)
** u= 34/111 ; C1 -77857*x^2 - 13477*y^2 + 3617*z^2
(-10541/91475 : 40048/91475 : 1) C2a (67864/5445 : -4001/5445 : 1)
** u= 34/137 ; C1 -113633*x^2 - 19925*y^2 + 8297*z^2
(3030/29827 : -89177/149135 : 1) C2a (-7160/52211 : 24361/261055 : 1)
** u= 34/141 ; C1 -119737*x^2 - 21037*y^2 + 9137*z^2
(17527/65677 : 11180/65677 : 1) C2a (-127252/187329 : -19759/187329 : 1)
** u= 35/89 ; C1 -53290*x^2 - 9146*y^2 + 466*z^2
(-1922/26353 : 51/361 : 1) C2a (55479/1061 : 1417/1061 : 1)
** u= 35/137 ; C1 -114250*x^2 - 19994*y^2 + 7954*z^2
(4601/26865 : -2578/5373 : 1) C2a (-205407/133715 : -19193/133715 : 1)
** u= 37/103 ; C1 -69658*x^2 - 11978*y^2 + 1618*z^2
(-3094/26179 : 6075/26179 : 1) C2a (331581/103715 : -16901/103715 : 1)
** u= 38/93 ; C1 -58825*x^2 - 10093*y^2 + 137*z^2
(-118/10795 : 245/2159 : 1) C2a (12382/1985 : 249/1985 : 1)
** u= 38/123 ; C1 -95785*x^2 - 16573*y^2 + 4337*z^2
(-1615/11899 : 4688/11899 : 1) C2a (2590046/202413 : 150751/202413 : 1)
** u= 38/151 ; C1 -138401*x^2 - 24245*y^2 + 9881*z^2
(1269/20599 : 12796/20599 : 1) C2a (-41336746/2388539 : -2986703/2388539 : 1)
** u= 38/165 ; C1 -162649*x^2 - 28669*y^2 + 13241*z^2
(-7913/34745 : 14224/34745 : 1) C2a (-144902/64805 : 12621/64805 : 1)
** u= 38/177 ; C1 -184993*x^2 - 32773*y^2 + 16433*z^2
(86942/305287 : 63755/305287 : 1) C2a (271598/16125 : -21757/16125 : 1)
** u= 38/191 ; C1 -212881*x^2 - 37925*y^2 + 20521*z^2
(-73/1771 : 6456/8855 : 1) C2a (271428/51043 : 23011/51043 : 1)
** u= 41/99 ; C1 -66922*x^2 - 11482*y^2 + 2*z^2
(106/29135 : 287/29135 : 1) C2a (145771/1637 : 267/1637 : 1)
** u= 42/109 ; C1 -79481*x^2 - 13645*y^2 + 961*z^2
(3658/53163 : -11005/53163 : 1) C2a (-6984298/1124587 : -7575/36277 : 1)
** u= 42/143 ; C1 -128033*x^2 - 22213*y^2 + 6673*z^2
(4023/26375 : 10756/26375 : 1) C2a (-299364/105515 : 20999/105515 : 1)
** u= 42/167 ; C1 -169265*x^2 - 29653*y^2 + 12097*z^2
(10945/45663 : -12916/45663 : 1) C2a (-18276/677 : 1319/677 : 1)
** u= 42/169 ; C1 -172961*x^2 - 30325*y^2 + 12601*z^2
(9434/35127 : 11299/175635 : 1) C2a (-11714/11623 : 6873/58115 : 1)
** u= 42/179 ; C1 -192041*x^2 - 33805*y^2 + 15241*z^2
(-7321/27471 : -5980/27471 : 1) C2a (461778/38173 : 35173/38173 : 1)
** u= 43/161 ; C1 -159146*x^2 - 27770*y^2 + 10226*z^2
(-7918/32197 : -4737/32197 : 1) C2a (9569/16249 : 1651/16249 : 1)
** u= 46/125 ; C1 -103241*x^2 - 17741*y^2 + 2009*z^2
(-987/15965 : 4816/15965 : 1) C2a (928/455 : -1249/10205 : 1)
** u= 47/189 ; C1 -216346*x^2 - 37930*y^2 + 15746*z^2
(-62/14633 : -9427/14633 : 1) C2a (-659551/137909 : 49641/137909 : 1)
** u= 49/171 ; C1 -182122*x^2 - 31642*y^2 + 10082*z^2
(-70858/308863 : 38695/308863 : 1) C2a (-298027/65391 : 281/921 : 1)
** u= 50/147 ; C1 -139945*x^2 - 24109*y^2 + 4409*z^2
(-36193/302143 : 95348/302143 : 1) C2a (5537782/6401095 : 661383/6401095 : 1)
** u= 50/167 ; C1 -175345*x^2 - 30389*y^2 + 8689*z^2
(4774/32589 : -13121/32589 : 1) C2a (1539806/1057311 : 136007/1057311 : 1)
** u= 50/169 ; C1 -179105*x^2 - 31061*y^2 + 9161*z^2
(3657/37901 : 18616/37901 : 1) C2a (17624086/855349 : 1083257/855349 : 1)
** u= 50/183 ; C1 -206545*x^2 - 35989*y^2 + 12689*z^2
(1601/66071 : -39044/66071 : 1) C2a (-7062952/288315 : -474113/288315 : 1)
** u= 54/143 ; C1 -136049*x^2 - 23365*y^2 + 2089*z^2
(-8781/103519 : 22564/103519 : 1) C2a (175644/1319 : 5929/1319 : 1)
** u= 54/169 ; C1 -182225*x^2 - 31477*y^2 + 7393*z^2
(21754/127935 : 6647/25587 : 1) C2a (-135794/51227 : -8859/51227 : 1)
** u= 54/173 ; C1 -189929*x^2 - 32845*y^2 + 8329*z^2
(-34109/195501 : 54448/195501 : 1) C2a (-40255436/10027099 : 2475039/10027099 : 1)
** u= 55/141 ; C1 -133450*x^2 - 22906*y^2 + 1346*z^2
(-538/85705 : -4147/17141 : 1) C2a (-42791/2305 : 1191/2305 : 1)
** u= 57/139 ; C1 -131546*x^2 - 22570*y^2 + 226*z^2
(86/73011 : 7303/73011 : 1) C2a (446393/25853 : 5607/25853 : 1)
** u= 57/155 ; C1 -158714*x^2 - 27274*y^2 + 3106*z^2
(-786/6875 : 1337/6875 : 1) C2a (133033/23 : 5067/23 : 1)
** u= 58/175 ; C1 -197089*x^2 - 33989*y^2 + 6961*z^2
(-2425/45327 : 19664/45327 : 1) C2a (-38376954/375409 : 1960529/375409 : 1)
** u= 58/177 ; C1 -201073*x^2 - 34693*y^2 + 7433*z^2
(-10630/134263 : -56633/134263 : 1) C2a (613126/246993 : 39613/246993 : 1)
** u= 58/191 ; C1 -230081*x^2 - 39845*y^2 + 10961*z^2
(-4717/21683 : 924/21683 : 1) C2a (39566/2161 : 2351/2161 : 1)
** u= 58/195 ; C1 -238729*x^2 - 41389*y^2 + 12041*z^2
(6149/63763 : 31060/63763 : 1) C2a (-1015154/171421 : 63861/171421 : 1)
** u= 58/197 ; C1 -243113*x^2 - 42173*y^2 + 12593*z^2
(-4515/64073 : 33292/64073 : 1) C2a (-711038/75289 : -44419/75289 : 1)
** u= 62/153 ; C1 -158833*x^2 - 27253*y^2 + 593*z^2
(-4334/73175 : -2653/73175 : 1) C2a (126416/73797 : -7313/73797 : 1)
** u= 62/175 ; C1 -200369*x^2 - 34469*y^2 + 5081*z^2
(5986/159905 : 59673/159905 : 1) C2a (90202/19853 : 4337/19853 : 1)
** u= 62/177 ; C1 -204385*x^2 - 35173*y^2 + 5537*z^2
(2590/29899 : 10087/29899 : 1) C2a (-497156/9373 : -3183/1339 : 1)
** u= 62/197 ; C1 -246745*x^2 - 42653*y^2 + 10537*z^2
(-5735/146641 : 71568/146641 : 1) C2a (619132/1121721 : 111203/1121721 : 1)
** u= 63/197 ; C1 -247658*x^2 - 42778*y^2 + 10018*z^2
(3298/36645 : -15859/36645 : 1) C2a (17121/51973 : -4987/51973 : 1)
** u= 66/175 ; C1 -203681*x^2 - 34981*y^2 + 3169*z^2
(11503/145671 : -33940/145671 : 1) C2a (-6588/520195 : 49321/520195 : 1)
** u= 66/179 ; C1 -211817*x^2 - 36397*y^2 + 4057*z^2
(5422/157077 : -50785/157077 : 1) C2a (-377568/187295 : -22747/187295 : 1)
** u= 66/193 ; C1 -241553*x^2 - 41605*y^2 + 7417*z^2
(1509/14873 : 5120/14873 : 1) C2a (-12 : -91/157 : 1)
** u= 67/185 ; C1 -225194*x^2 - 38714*y^2 + 4946*z^2
(-114/86585 : 30947/86585 : 1) C2a (-167767/341407 : 33037/341407 : 1)
** u= 70/171 ; C1 -198985*x^2 - 34141*y^2 + 401*z^2
(2443/61343 : 3068/61343 : 1) C2a (-3357656/120479 : 42633/120479 : 1)
** u= 70/193 ; C1 -245185*x^2 - 42149*y^2 + 5329*z^2
(9490/101619 : -27959/101619 : 1) C2a (12862146/1419485 : -7307/19445 : 1)
** u= 74/193 ; C1 -248849*x^2 - 42725*y^2 + 3209*z^2
(-2782/57235 : 70881/286175 : 1) C2a (40240/21431 : -11917/107155 : 1)
** u= 77/191 ; C1 -247162*x^2 - 42410*y^2 + 1138*z^2
(946/101367 : -16447/101367 : 1) C2a (-1864473/160669 : -37693/160669 : 1)
** u= 78/199 ; C1 -266177*x^2 - 45685*y^2 + 2473*z^2
(-1079/18123 : 3316/18123 : 1) C2a (-2111692/47461 : 55635/47461 : 1)
935
>
■これらのuについて、(3),(5a),(5b)を満たす有理数解(x,y,t)を持たないものもあれば、有理数解(x,y,t)を持つものもある。
これらのuを順に調べれば良い。
ここからは、A^4+B^4+578*C^4=4*D^4(n=17のとき)と同様なので、最終的に得られた整点のみ記述する。
ここで、対応する整点が見つかった各有理数uについて、0 <= A <= B, 0 < C, 0 < Dを満たすように、A,B,C,Dの符号を変更したり、A,Bを交換して、Dの小さい順に並び替えると、以下のようになる。
- u=-15/11のとき
2515^4+2519^4+49298*121^4=4*2183^4
27778979^4+36344935^4+49298*1466729^4=4*28307863^4
7188589463^4+9434796355^4+49298*379772833^4=4*7341466559^4
12780860355307209235015^4+21697310177826857078963^4+49298*666104073190133606897^4=4*15936634278288139380079^4
857425589717205356835561107^4+1459851323149123864121778055^4+49298*44639315416249749622760993^4=4*1071777166270606652564099071^4
34047299760034547600088233103895^4+34210010422737855135126676026563^4+49298*1640648417359437381583483013537^4=4*29600014708325336154647427554239^4
1455540490740360319953608288754295^4+1898410644426557130736693504630259^4+49298*76807773996140926230590254122329^4=4*1480025693230950672404873375918503^4
25223567480278925894561070678596554817395^4+33209020402912125729607439191655316943847^4+49298*1333297926029495650207411563893801242177^4=4*25816446748622271256392651042376144239071^4
2583216586791921896134430851515092380138963555^4+4372585892645370536977637042024360650589753639^4+49298*134769743752346655124394847406806306750798121^4=4*3213112565474982471695586412778601818388419543^4
252450014843422996386334999206147056471872350115^4+537487774852321941494492108193941541285100724567^4+49298*10586737101469962846867858377517298749293433937^4=4*385281744530777369954401322655686168503799339471^4
4392647624318253862471600710257555301336593533230721255^4+9373729398766196640275611503662830246451396384389033091^4+49298*183365405168847796034723139553702003968215684441776121^4=4*6718247173061178087370758675998344715468099775088299847^4
779955638521924467087133116318046853920515259635768549062951^4+1331823101850079217295779699984965008103220162458082037975235^4+49298*40561932623167269154942611002213687939850995215253177086009^4=4*977348866504096611507574045988134035419176275041770026400007^4
196727299605088821207607390954728733201001028472274558248512127841063^4+417888356128092243897660271925973820842447941309584780381761602681875^4+49298*8287416982440266259347138362186332472159435444491158081762712208273^4=4*299596953439847688966188664925381764784124676799930659111599318926799^4
225210960596322851720839436936390457790159932915834386205626383447114706819403619031^4+555361155276479827438585531271070453300285528445045287634320621172663955704406420275^4+49298*4326244775863802641452005411936167961860918942571687782736721483834787115056032649^4=4*395345551546933657313182783468117288916185925453661229643610271869003633918452559287^4
1034112304605449970055609759020406936383213688775976637331011786473163168476200897315635^4+1344532547200488826944517835472599881946455518248141425840796946347984565850826310264263^4+49298*54536820530350698732332928586892997036708026367766686226768147997113868842268216362993^4=4*1049226715790567191331412222741412936543084874864042433131724690879903991545972347211119^4
6249743948762157742597793068948282529241254735878709990596524817817329262611374837406787^4+6299601885161138449088692681308846836497589212720317892349170402625149083284276009302135^4+49298*301630900667110274302703608048367445441185527756239171000440510191539621660004968229553^4=4*5442122446536763657998685795359284381438126081862711236407628911118856022876547505199471^4
1036376529502863049704133992069460984064475002154810195813810901565276020469146728701379731^4+2216622503717346472217844660916964993191833155471713786040064423291773595152390861895639415^4+49298*43061057672686372514794109903423443574195157350118649682315824412872005661767577025943881^4=4*1588437109083797345120540230626055252307129927508028470363425924156555834179815027238431607^4
1017065968201151925605557988841101493244701791200904213482327524391451756181264774827029822195^4+2510636906532090838569400675494901119572544503480612625895475177896653884529080759944806212951^4+49298*19199402354206601669619702773737174281558445864684215942313812993912371710021277948569984489^4=4*1787195676939952471278748078955394697433992383621880814389342620414155645152895309392717596887^4
7079435111149635553654073124691216087113253099728323354009427114290210746385679338210344760368199^4+11948296166917595528088819676093442571294585112014777494440628844861707879861999746985984836598275^4+49298*369716247746707649795780727354714876075141136474708214964966056831632432156501339189623434854921^4=4*8784003735645802596278474207921105711253312424089418458562363026600068558639987606667819834712823^4
1200065022815553910259805461601310599304342406202058505953092359334558087499999478566417077810104215^4+1584946116837302786210226134655257344700488793193441646636524683861505948381616500235576650804378611^4+49298*63468726573428454878002926927528278676505450008700562894101250552523364258129448885611328529061961^4=4*1230971527117832279486328045438854608479077309853660624260788168664530907500222609918820298858155767^4
676197365101156298297116216180119737780166557204399107013904319882068518171694774321053362181804280227^4+1665723088461446018811908710625180010134676049049780398745343046742832802625183904695217333366179519575^4+49298*13213609242256883857321837886970043315027158566134846138142536115688293764386084078070711151351150033^4=4*1185816948999352797785344976890855603728532008838888823053212802026483343085287623720610871883875400271^4
2078710516647665269525830174097607456401397727463874530912235402271865503043174893987953134663977033159209495268820499^4+4405421304123783927662989545509515557896704001087747359891974884582248457852889847225015680492177382619251675624420375^4+49298*87960745835121452580815919923866880096640211577151625809025082299877865970130284139017569936808690584571320742374329^4=4*3158878112151213615722303733928938611518728184612033572805540076299105160907820886774132249832726532025494284530961223^4
9620120277213176006160978703915307407703203289393467653158553604107790687443934054072530546528366084952247176738646835235^4+16474780980427329011784887573903029403274113045059174533496350705622039963798444087889795732830293170893227590893532903111^4+49298*499741431919300041786097466176940413917947757103633588258451418094254456385752475330632438931230800094950098440974454649^4=4*12084590465830403204626601502948760977989445442343683425635666536562405043778504441551355400104165985341726845774252224327^4
9555552730387995860600304696591142703947196862427862732515237073417801081581881974513228626720884273727346153960565266704419560771^4+24017949653796842344323591331431504969890256969303723003464492235480671763506214986682059581205955411661921486032091967113428329575^4+49298*107917622764003985091091281169915957771025271240610141658285788311508656720741474158893920796559219946343882513409916974711278759^4=4*17088728967025517383942177393682642448058813428083482045374622825549959677638064279181755566714465551824596655345175606388628984167^4
62280530307072814501430609654399488344093937249902179861883566756153872229337192674676306494007705183202799403213250939212238517335^4+153896248697061190880421890659350399380827932465511704033138058008619600934050965137025071315651288600452510030048040819645450521187^4+49298*1154903563492480616890929083300750044140635002466045312314566123717530179585785782004912206730038920787512695984212829415776608753^4=4*109547733529129365035076086174539217637807279862589238716706149486423028490268293066903515664763589771812600738999743930945938065071^4
11204940444570091846496695866835271282074842595051159110610309213927816263164516305126659224035745934963325387442483023952627248214220990210647^4+28146180572829072711921310807735950348532831447415498592347912730964292356671585061269780020360871156982325805882782121860941670760580822533475^4+49298*130510051133448379937134932818226661461213278988130846329922649583975417481099830905074327930391155313333147914310818757858354116292072939663^4=4*20026276069300018790957232683632195812216660578395629790316698731024841125713484003826821113642978218037787284162747561231559661849537974077231^4
110495900108801534074745556659358139871716074465266962819974214054604220256549063013015565144471791808283818315035661839003951237581789779400290295^4+277899735144075878238514587717720195651781949336375745008214170090747295337130204675999098030630671485720638615304481759814909825210810289102690771^4+49298*1208729988822288377261241089884074255297906462783991561328757461732901197673289090695145522883144628046992696618678434291867831502574103100663319^4=4*197722144673496873681132569670101231585745120010755309607594634665714233041337563390664186124262431524929210435663355866547701366131031558698282327^4
27529666308414661126692541360326012022528154000553229081150972256636110737001780119041192729135185009824548456580821051930126083634757761203927418935^4+67743218212838139375610389038873343326216100434596993615044766931717056860908071199901184340173199660587784211521786230686930995913506056938439441763^4+49298*547046354032079917499432505504283420172960539514886686366379882569313225882030758109682949978387515232665120767359899913436628544251402601555030657^4=4*48227472216876257913368312426196428722900530836896492585875547628841969471538093811210485972024831166781236321072947259878254640239417526906340138719^4
3315500160298038894107490119923682247181081756612571268243949483867302786915255189801735653981899055219940951151696660716739106505954648934540718449409927^4+7107331488490570417970320296388983118814601357530323395300376163674960568620282887928272348191665214524636790881831578937050876741154811712501869824013395^4+49298*137108276783761716257191254308611741675929440065603242657077753304261666413376008356672291033435152436944590995074393791291374369247551985991065912465857^4=4*5092377185021643768511565763998534315257064190217939058492906130654189693264378244965476825640523257935675708023000308517024066064816649008466891723186911^4
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...
- u=-16/9のとき
27^4+55^4+49298*3^4=4*43^4
9699943693612005^4+34912734889894681^4+49298*2301606057870171^4=4*29124410196936419^4
14646446810426836571957927673770360527690040325^4+21961018240341812058717113422253010864451774489^4+49298*1059874259472548870194663488918970211217590859^4=4*17085129653567121276799509078850648327867065491^4
114867473395712703771244281684808187856613093906872566242436842450432643170141329221051397^4+5507532716484846474446979292059168458820856013339144656327970520115752605736088382342892535^4+49298*472279680362602043741274141921640114799348450063211010850948494994047186860345866504744787^4=4*5388636773836236191688200138106330639920960895957710157970386919620213107783879448138075067^4
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1529862092648071690332774081526303580241195048446589092295154706196161695643985187457201878306368598094406835038776795486733767255265520607973677875793237376431716358479792993272361698865713290932588437280901508771652535126084951631672981703743305555809993341686850372486507976146811549173829884596136818666431227064890015635524846820501138498791957180810751979633591913337128430940782719225703792176536357819435736375^4+3015298489702982558167400120248513900611162913227704117580895482596414517114295018380045982282523995206869331391835765525989614601463081556242462151634282266532550217891238411148076475607717585655999646475971754291537840639113626356573195438308235879291211753308754564393456682477391153994452643843704645249283805073298782530670811286068820190936387626386183502498039493307070957398892210641005793892899587442174071973^4+49298*368862811816092054572170355224999809249308712988895011231836972438194943198602013148735974054931504507218084160480179983165375213047562443364148862182624570402903160185814666006704718531248466493784842721419834040378524444556726596702908380600794205829191744090065985956177017586148766230911699801171055378751319669572327275462318035077742930212515572637045298364046691224125842907249232341007243290180653381603049763^4=4*3977109186077445983069815777169541368515623752849257423427159833921497384030839730374873564628906019583660258997618166560105302479172077346288191154664673665093154376800572701817567541776074571769183934499431732205139004135398143443126052447996512913190401551337406423060523763619498008865726964850584377632984239815994810614998811976583283344515920886381228142106610185250689217318590459116887089272217208104087842763^4
...
[参考文献]
- [1]Noam Elkies, "On A^4+B^4+C^4=D^4", Math Comp. 51(184), p824-835, 1988.
- [2]StarkExchange MATHEMATICS, "Distribution of Primitive Pytagorean Triples (PPT) and of solutions of A^4+B^4+C^4=D^4", 2016/07/08.
- [3]StarkExchange MATHEMATICS, "More elliptic curves for x^4+y^4+z^4=1?", 2017/07/28.
- [4]Tom Womack, "The quartic surfaces x^4+y^4+z^4=N", 2013/05/17.
- [5]Tom Womack, "elk18.mag", 2013/06/07.
- [6]Tom Womack, "elk18.pts", 2013/06/07.
- [7]Tom Womack, "Integer points on x^4+y^4+z^4=Nt^4", 2013/06/07.
| Last Update: 2026.05.15 |
| H.Nakao |