Integer Points on A^4+B^4+77618*C^4=4*D^4
[2026.05.13]A^4+B^4+77618*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(r,s,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=197とする。
Pari/GPで簡単なプログラムを作成して、小さい整数解を調べると、
515^4+3897^4+77618*573^4=4*6809^4
773^4+3775^4+77618*253^4=4*3379^4
が見つかった。
■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)766個のuが抽出される。
[pari/gpによる計算]
> PP(197,1,200);
** u= -199/187 ; C1 -65594*x^2 + 74570*y^2 + 69794*z^2
(7373/10243 : -7098/10243 : 1) C2b (733052/978767 : 7033/978767 : 1)
** u= -198/91 ; C1 -8537*x^2 - 47485*y^2 + 5113*z^2
(8249/10743 : 440/10743 : 1) C2a (-283898/3799 : 9381/3799 : 1)
** u= -198/125 ; C1 -18329*x^2 - 54829*y^2 + 25921*z^2
(13041/11125 : -1288/11125 : 1) C2a (101498/14973 : -43/93 : 1)
** u= -198/145 ; C1 -29489*x^2 - 60229*y^2 + 39241*z^2
(46630/45819 : 17413/45819 : 1) C2a (442184/59565 : -35647/59565 : 1)
** u= -198/173 ; C1 -51833*x^2 - 69133*y^2 + 59233*z^2
(-10886/14811 : -9955/14811 : 1) C2a (-1575022/505685 : 141837/505685 : 1)
** u= -196/93 ; C1 -8749*x^2 + 47065*y^2 + 6689*z^2
(-28568/68057 : -22507/68057 : 1) C2b (371417/200827 : 9435/200827 : 1)
** u= -196/179 ; C1 -58285*x^2 + 70457*y^2 + 63793*z^2
(8581/19653 : -16994/19653 : 1) C2b (-279291/518543 : 27673/518543 : 1)
** u= -196/183 ; C1 -62389*x^2 + 71905*y^2 + 66809*z^2
(-18437/21637 : 11834/21637 : 1) C2b (521/1501 : -19335/295697 : 1)
** u= -194/119 ; C1 -16097*x^2 - 51797*y^2 + 22697*z^2
(-13779/26095 : -15472/26095 : 1) C2a (-290272/233871 : 1229/233871 : 1)
** u= -194/121 ; C1 -16945*x^2 - 52277*y^2 + 23953*z^2
(-19834/20083 : 7569/20083 : 1) C2a (-283554392/131173249 : -16036033/131173249 : 1)
** u= -194/125 ; C1 -18761*x^2 - 53261*y^2 + 26489*z^2
(3786/3827 : 1495/3827 : 1) C2a (-18899636/2349075 : 1329083/2349075 : 1)
** u= -194/151 ; C1 -34465*x^2 - 60437*y^2 + 43753*z^2
(-38486/60869 : 42867/60869 : 1) C2a (29575958/48089 : 2535553/48089 : 1)
** u= -194/173 ; C1 -53033*x^2 - 67565*y^2 + 59417*z^2
(71843/69389 : -13524/69389 : 1) C2a (-688514/53817 : 64931/53817 : 1)
** u= -194/189 ; C1 -69577*x^2 - 73357*y^2 + 71417*z^2
(13910/20939 : 15599/20939 : 1) C2a (-2664474/2522623 : 192443/2522623 : 1)
** u= -193/109 ; C1 {+/-} -12506*x^2 + 49130*y^2 + 16706*z^2
(173/253 : 2022/4301 : 1) C2a (15639/4619 : -14179/78523 : 1) C2b (-99038/94217 : 5291/94217 : 1)
** u= -192/95 ; C1 -9029*x^2 + 45889*y^2 + 8641*z^2
(-1845/7777 : 3274/7777 : 1) C2b (405131/240731 : -9927/240731 : 1)
** u= -192/103 ; C1 -10805*x^2 + 47473*y^2 + 13297*z^2
(103379/99897 : 19046/99897 : 1) C2b (-215971/1984237 : 166047/1984237 : 1)
** u= -192/119 ; C1 -16277*x^2 + 51025*y^2 + 22993*z^2
(-612/667 : -1423/3335 : 1) C2b (119941/236003 : -17697/236003 : 1)
** u= -192/145 ; C1 -30629*x^2 + 57889*y^2 + 39841*z^2
(6728/6225 : 1649/6225 : 1) C2b (7003/19945 : 1467/19945 : 1)
** u= -192/157 ; C1 -39533*x^2 + 61513*y^2 + 48073*z^2
(-227515/230703 : -91258/230703 : 1) C2b (394953/463571 : -6937/463571 : 1)
** u= -192/179 ; C1 -59597*x^2 + 68905*y^2 + 63913*z^2
(489576/475727 : -51119/475727 : 1) C2b (438201/673393 : 25477/673393 : 1)
** u= -192/191 ; C1 -72581*x^2 + 73345*y^2 + 72961*z^2
(5292/6863 : -4375/6863 : 1) C2b (-8571/108091 : -7673/108091 : 1)
** u= -191/115 ; C1 -14746*x^2 - 49706*y^2 + 20674*z^2
(254/3983 : 2565/3983 : 1) C2a (1082087/163873 : -68993/163873 : 1)
** u= -191/163 ; C1 -44794*x^2 + 63050*y^2 + 52354*z^2
(-562346/523023 : 248911/2615115 : 1) C2b (27542/33339 : -1267/166695 : 1)
** u= -190/91 ; C1 -8345*x^2 - 44381*y^2 + 6761*z^2
(-30117/33563 : 1028/33563 : 1) C2a (101922/10903 : -3901/10903 : 1)
** u= -190/103 ; C1 -10865*x^2 - 46709*y^2 + 13649*z^2
(-31595/31987 : 8172/31987 : 1) C2a (-5192852/154653 : -282541/154653 : 1)
** u= -190/111 ; C1 -13345*x^2 - 48421*y^2 + 18401*z^2
(-34/29 : 1/29 : 1) C2a (-225218/146525 : -6873/146525 : 1)
** u= -190/167 ; C1 -48625*x^2 - 63989*y^2 + 55249*z^2
(478/449 : -21/449 : 1) C2a (-81114916/10657201 : -7551743/10657201 : 1)
** u= -190/187 ; C1 -68825*x^2 - 71069*y^2 + 69929*z^2
(2718/11065 : 2129/2213 : 1) C2a (-332242686/73695211 : -32782343/73695211 : 1)
** u= -189/137 ; C1 {+/-} -25994*x^2 + 54490*y^2 + 34834*z^2
(5278/5673 : -2699/5673 : 1) C2a (-373883/53813 : -29811/53813 : 1) C2b (178764/436439 : -31817/436439 : 1)
** u= -189/185 ; C1 -66986*x^2 + 69946*y^2 + 68434*z^2
(4454/26817 : 26165/26817 : 1) C2b (444256/783145 : 34911/783145 : 1)
** u= -188/83 ; C1 -7373*x^2 + 42233*y^2 + 2753*z^2
(-7872/13963 : -1375/13963 : 1) C2b (1120867/399271 : -17657/399271 : 1)
** u= -188/105 ; C1 -11509*x^2 + 46369*y^2 + 15161*z^2
(-10859/9467 : 190/9467 : 1) C2b (-191917/595965 : -48563/595965 : 1)
** u= -187/151 ; C1 -36026*x^2 - 57770*y^2 + 44306*z^2
(30526/27551 : 1023/27551 : 1) C2a (414339/422899 : -16063/422899 : 1)
** u= -187/175 ; C1 {+/-} -57194*x^2 + 65594*y^2 + 61106*z^2
(-11709/12235 : -4462/12235 : 1) C2a (29489/39021 : -19/39021 : 1) C2b (1849762/3710783 : 204971/3710783 : 1)
** u= -186/95 ; C1 -9041*x^2 - 43621*y^2 + 9769*z^2
(9030/20129 : 8593/20129 : 1) C2a (2706152/1303323 : -67897/1303323 : 1)
** u= -186/143 ; C1 -30449*x^2 - 55045*y^2 + 39049*z^2
(24978/29833 : 16919/29833 : 1) C2a (2127118/2285763 : -11827/2285763 : 1)
** u= -186/179 ; C1 -61625*x^2 - 66637*y^2 + 64033*z^2
(-5866/7041 : -3977/7041 : 1) C2a (354586/366225 : -22807/366225 : 1)
** u= -186/185 ; C1 -68081*x^2 - 68821*y^2 + 68449*z^2
(23801/23937 : 3080/23937 : 1) C2a (1885372/1923415 : 130431/1923415 : 1)
** u= -186/199 ; C1 -84545*x^2 - 74197*y^2 + 79033*z^2
(-217326/224857 : -6199/224857 : 1) C2a (836542/132149 : -86517/132149 : 1)
** u= -185/133 ; C1 -24250*x^2 + 51914*y^2 + 32674*z^2
(899/1405 : 186/281 : 1) C2b (-24146/56079 : -131/1809 : 1)
** u= -184/85 ; C1 -7421*x^2 + 41081*y^2 + 4649*z^2
(-11152/21205 : 5331/21205 : 1) C2b (-41441/17335 : -421/17335 : 1)
** u= -184/99 ; C1 -9997*x^2 + 43657*y^2 + 12377*z^2
(-956/112511 : 59905/112511 : 1) C2b (1336567/897081 : -22763/897081 : 1)
** u= -184/103 ; C1 -11093*x^2 + 44465*y^2 + 14657*z^2
(-21852/35051 : -16907/35051 : 1) C2b (-4183/21749 : -1801/21749 : 1)
** u= -184/147 ; C1 -33709*x^2 + 55465*y^2 + 41849*z^2
(28148/66323 : 53267/66323 : 1) C2b (-30139/220311 : -16963/220311 : 1)
** u= -184/175 ; C1 -58181*x^2 + 64481*y^2 + 61169*z^2
(-3207/19325 : -18574/19325 : 1) C2b (326479/832885 : 51641/832885 : 1)
** u= -182/109 ; C1 -13177*x^2 - 45005*y^2 + 18433*z^2
(-3907/3329 : -264/3329 : 1) C2a (7628896/131047 : -491819/131047 : 1)
** u= -182/183 ; C1 -67345*x^2 - 66613*y^2 + 66977*z^2
(1318/101389 : 101657/101389 : 1) C2a (2262764/2499815 : -143937/2499815 : 1)
** u= -181/113 ; C1 {+/-} -14794*x^2 + 45530*y^2 + 20914*z^2
(-11789/12781 : 5466/12781 : 1) C2a (347489/280519 : 5369/280519 : 1) C2b (2465474/2050779 : 14417/2050779 : 1)
** u= -181/121 ; C1 -18362*x^2 - 47402*y^2 + 25682*z^2
(-10386/13181 : 7235/13181 : 1) C2a (-114873/67735 : 6493/67735 : 1)
** u= -180/91 ; C1 -8285*x^2 + 40681*y^2 + 8641*z^2
(-97127/96921 : 8606/96921 : 1) C2b (197799/182039 : 12281/182039 : 1)
** u= -180/101 ; C1 -10685*x^2 + 42601*y^2 + 14161*z^2
(-7140/32993 : -18683/32993 : 1) C2b (20471/19159 : -9/161 : 1)
** u= -180/149 ; C1 -36125*x^2 + 54601*y^2 + 43441*z^2
(-24197/22083 : -46/1299 : 1) C2b (-1905831/2225099 : 6811/2225099 : 1)
** u= -180/199 ; C1 -87125*x^2 + 72001*y^2 + 78841*z^2
(3192/3431 : 749/3431 : 1) C2b (1548609/4464299 : 36107/637757 : 1)
** u= -178/147 ; C1 -35065*x^2 - 53293*y^2 + 42257*z^2
(-3797/13127 : 11276/13127 : 1) C2a (-552702/613595 : -14869/613595 : 1)
** u= -178/155 ; C1 -41449*x^2 - 55709*y^2 + 47521*z^2
(-46331/80103 : -62260/80103 : 1) C2a (356596/68369 : -32779/68369 : 1)
** u= -178/193 ; C1 -80513*x^2 - 68933*y^2 + 74273*z^2
(-102/907 : 935/907 : 1) C2a (-1163456/1340025 : 4727/78825 : 1)
** u= -176/73 ; C1 -6229*x^2 + 36305*y^2 + 49*z^2
(-8519/173451 : -5306/173451 : 1) C2b (-6396577/340587 : -16495/340587 : 1)
** u= -176/81 ; C1 -6757*x^2 + 37537*y^2 + 4097*z^2
(-5417/9403 : -2090/9403 : 1) C2b (-640687/253271 : 2067/253271 : 1)
** u= -176/111 ; C1 -14437*x^2 + 43297*y^2 + 20417*z^2
(-80/23747 : 16307/23747 : 1) C2b (-222367/240345 : 12419/240345 : 1)
** u= -176/125 ; C1 -21101*x^2 + 46601*y^2 + 28649*z^2
(12172/24725 : -17571/24725 : 1) C2b (7105573/14438227 : -1016161/14438227 : 1)
** u= -175/83 ; C1 {+/-} -6970*x^2 + 37514*y^2 + 5314*z^2
(36770/42791 : -2859/42791 : 1) C2a (-75257/21667 : 2189/21667 : 1) C2b (98526/44351 : 299/44351 : 1)
** u= -175/187 ; C1 {+/-} -74570*x^2 + 65594*y^2 + 69794*z^2
(25497/27067 : -6362/27067 : 1) C2a (669317/511755 : -60007/511755 : 1) C2b (-1467076/3313061 : 169279/3313061 : 1)
** u= -174/85 ; C1 -7241*x^2 - 37501*y^2 + 6529*z^2
(5946/6667 : -955/6667 : 1) C2a (-1208932/522313 : 25293/522313 : 1)
** u= -174/95 ; C1 -9281*x^2 - 39301*y^2 + 11809*z^2
(65849/67695 : 18788/67695 : 1) C2a (173512288/17890117 : 1352211/2555731 : 1)
** u= -174/97 ; C1 -9809*x^2 - 39685*y^2 + 12889*z^2
(10542/13687 : 5777/13687 : 1) C2a (-483968/200457 : 22171/200457 : 1)
** u= -174/191 ; C1 -79745*x^2 - 66757*y^2 + 72673*z^2
(53709/74683 : 51244/74683 : 1) C2a (6107684/123 : -642091/123 : 1)
** u= -172/79 ; C1 -6437*x^2 + 35825*y^2 + 3833*z^2
(-396/1355 : -2051/6775 : 1) C2b (14747/5749 : 19/5749 : 1)
** u= -172/93 ; C1 -8845*x^2 + 38233*y^2 + 11057*z^2
(-3680/18337 : -9701/18337 : 1) C2b (-634651/465935 : 18519/465935 : 1)
** u= -172/121 ; C1 -19541*x^2 + 44225*y^2 + 26681*z^2
(-3037/3347 : 1638/3347 : 1) C2b (267965/302579 : 62177/1512895 : 1)
** u= -172/127 ; C1 -22853*x^2 + 45713*y^2 + 30233*z^2
(-14728/28615 : -20811/28615 : 1) C2b (23659/431893 : -4907/61699 : 1)
** u= -172/135 ; C1 -27829*x^2 + 47809*y^2 + 35081*z^2
(5084/4627 : -815/4627 : 1) C2b (74377/1207067 : 94341/1207067 : 1)
** u= -172/177 ; C1 -64453*x^2 + 60913*y^2 + 62633*z^2
(-43765/95531 : 85774/95531 : 1) C2b (-53767/333271 : 22743/333271 : 1)
** u= -172/179 ; C1 -66637*x^2 + 61625*y^2 + 64033*z^2
(6559/9273 : -32722/46365 : 1) C2b (-655671/2010613 : -615449/10053065 : 1)
** u= -170/79 ; C1 -6385*x^2 - 35141*y^2 + 4201*z^2
(-1630/5881 : 1911/5881 : 1) C2a (2522536/206719 : 86123/206719 : 1)
** u= -170/91 ; C1 -8425*x^2 - 37181*y^2 + 10321*z^2
(2629/4255 : -372/851 : 1) C2a (-560666/161909 : 26483/161909 : 1)
** u= -170/93 ; C1 -8905*x^2 - 37549*y^2 + 11369*z^2
(-26875/29429 : -9536/29429 : 1) C2a (6483692/132757 : 359301/132757 : 1)
** u= -169/133 ; C1 -27098*x^2 - 46250*y^2 + 34082*z^2
(-94/877 : 3747/4385 : 1) C2a (12499/183 : -1081/183 : 1)
** u= -168/79 ; C1 -6341*x^2 + 34465*y^2 + 4561*z^2
(-13932/27223 : -7897/27223 : 1) C2b (-14753/7367 : -309/7367 : 1)
** u= -168/85 ; C1 -7229*x^2 + 35449*y^2 + 7561*z^2
(-6477/7855 : 2146/7855 : 1) C2b (1389503/791293 : 16209/791293 : 1)
** u= -168/101 ; C1 -11357*x^2 + 38425*y^2 + 15913*z^2
(-3409/4203 : 1970/4203 : 1) C2b (-4005/28271 : 11639/141355 : 1)
** u= -167/123 ; C1 {+/-} -21370*x^2 + 43018*y^2 + 28322*z^2
(-238/17747 : -14399/17747 : 1) C2a (-582797/114359 : -393/961 : 1) C2b (-64366/837165 : -559/7035 : 1)
** u= -166/81 ; C1 -6577*x^2 - 34117*y^2 + 5897*z^2
(-51599/199325 : 79712/199325 : 1) C2a (4799358/259075 : -199853/259075 : 1)
** u= -166/105 ; C1 -12961*x^2 - 38581*y^2 + 18329*z^2
(11702/11575 : 4201/11575 : 1) C2a (17614764/12533869 : -659009/12533869 : 1)
** u= -166/123 ; C1 -21529*x^2 - 42685*y^2 + 28409*z^2
(39641/50551 : 30136/50551 : 1) C2a (1544186/34211 : 126903/34211 : 1)
** u= -166/151 ; C1 -41297*x^2 - 50357*y^2 + 45377*z^2
(165186/161341 : 32855/161341 : 1) C2a (791138/1016925 : 2063/1016925 : 1)
** u= -166/163 ; C1 -52169*x^2 - 54125*y^2 + 53129*z^2
(20067/31067 : -118244/155335 : 1) C2a (488154/586279 : 122311/2931395 : 1)
** u= -166/189 ; C1 -80665*x^2 - 63277*y^2 + 70913*z^2
(-5090/6311 : 3407/6311 : 1) C2a (-414478/342049 : -37977/342049 : 1)
** u= -165/73 ; C1 {+/-} -5690*x^2 + 32554*y^2 + 2194*z^2
(-1991/3957 : 602/3957 : 1) C2a (162233/9357 : 4169/9357 : 1) C2b (311102/194743 : 14343/194743 : 1)
** u= -165/113 ; C1 {+/-} -16490*x^2 + 39994*y^2 + 22834*z^2
(12467/10869 : 1834/10869 : 1) C2a (197059/139195 : -1413/19885 : 1) C2b (4273534/4022431 : -2883/574633 : 1)
** u= -164/73 ; C1 -5653*x^2 + 32225*y^2 + 2377*z^2
(-421/1443 : 350/1443 : 1) C2b (843/503 : -179/2515 : 1)
** u= -164/117 ; C1 -18589*x^2 + 40585*y^2 + 25169*z^2
(152132/132377 : -16333/132377 : 1) C2b (644381/1033761 : 65425/1033761 : 1)
** u= -164/119 ; C1 -19637*x^2 + 41057*y^2 + 26297*z^2
(39320/44819 : -23391/44819 : 1) C2b (-229501/515987 : -36899/515987 : 1)
** u= -164/147 ; C1 -38509*x^2 + 48505*y^2 + 42929*z^2
(-34408/33307 : 6473/33307 : 1) C2b (-864647/3914373 : 281203/3914373 : 1)
** u= -164/157 ; C1 -47149*x^2 + 51545*y^2 + 49249*z^2
(-4151/5759 : -51882/74867 : 1) C2b (-96069/269021 : 222719/3497273 : 1)
** u= -163/71 ; C1 -5482*x^2 + 31610*y^2 + 1618*z^2
(-1522/20511 : 4597/20511 : 1) C2b (-2472/74041 : 6271/74041 : 1)
** u= -163/135 ; C1 {+/-} -29674*x^2 + 44794*y^2 + 35666*z^2
(11678/11215 : -3131/11215 : 1) C2a (844731/69191 : -75761/69191 : 1) C2b (147308/457423 : -32649/457423 : 1)
** u= -162/71 ; C1 -5441*x^2 - 31285*y^2 + 1801*z^2
(-14293/41607 : 8008/41607 : 1) C2a (972464/162879 : -19037/162879 : 1)
** u= -162/97 ; C1 -10433*x^2 - 35653*y^2 + 14593*z^2
(8730/29803 : 18473/29803 : 1) C2a (380494/288093 : 5593/288093 : 1)
** u= -162/103 ; C1 -12545*x^2 - 36853*y^2 + 17737*z^2
(-3474/2933 : 179/2933 : 1) C2a (96392/7325 : 6711/7325 : 1)
** u= -161/85 ; C1 -7306*x^2 + 33146*y^2 + 8674*z^2
(67538/130885 : 58971/130885 : 1) C2b (202388/177993 : 10709/177993 : 1)
** u= -160/99 ; C1 -11245*x^2 + 35401*y^2 + 15881*z^2
(35339/40369 : -18286/40369 : 1) C2b (-28871/128821 : -10449/128821 : 1)
** u= -160/143 ; C1 -36325*x^2 + 46049*y^2 + 40609*z^2
(-21976/20895 : 403/4179 : 1) C2b (689171/2562135 : 180523/2562135 : 1)
** u= -160/171 ; C1 -62365*x^2 + 54841*y^2 + 58361*z^2
(-10253/10633 : 878/10633 : 1) C2b (-5854789/8853519 : 15971/8853519 : 1)
** u= -159/163 ; C1 -54458*x^2 - 51850*y^2 + 53122*z^2
(16239/18151 : -38914/90755 : 1) C2a (-249607/272913 : -83587/1364565 : 1)
** u= -158/69 ; C1 -5161*x^2 - 29725*y^2 + 1601*z^2
(2557/4865 : 1868/24325 : 1) C2a (4170/1151 : 11/5755 : 1)
** u= -158/77 ; C1 -5945*x^2 - 30893*y^2 + 5297*z^2
(-1585/4877 : 1896/4877 : 1) C2a (219582/29395 : 8819/29395 : 1)
** u= -158/157 ; C1 -48985*x^2 - 49613*y^2 + 49297*z^2
(-2033/2541 : -1528/2541 : 1) C2a (234322/171995 : 20069/171995 : 1)
** u= -158/165 ; C1 -56809*x^2 - 52189*y^2 + 54401*z^2
(-6310/20827 : -20219/20827 : 1) C2a (-1616824/1261981 : 141201/1261981 : 1)
** u= -158/171 ; C1 -63097*x^2 - 54205*y^2 + 58313*z^2
(-97498/101729 : -8237/101729 : 1) C2a (-134442/102269 : 12193/102269 : 1)
** u= -157/81 ; C1 -6586*x^2 - 31210*y^2 + 7346*z^2
(-34/469 : -227/469 : 1) C2a (-62433/33317 : -1207/33317 : 1)
** u= -156/85 ; C1 -7421*x^2 + 31561*y^2 + 9409*z^2
(-59267/53379 : 4850/53379 : 1) C2b (18969/922955 : 797/9515 : 1)
** u= -156/175 ; C1 -68261*x^2 + 54961*y^2 + 60889*z^2
(-20816/130995 : 135913/130995 : 1) C2b (35367/184777 : 11759/184777 : 1)
** u= -154/65 ; C1 -4801*x^2 - 27941*y^2 + 529*z^2
(-2254/6955 : -207/6955 : 1) C2a (795218/45563 : 449/1981 : 1)
** u= -154/69 ; C1 -5017*x^2 - 28477*y^2 + 2297*z^2
(-1502/2263 : -125/2263 : 1) C2a (-1632468/489349 : 21589/489349 : 1)
** u= -154/83 ; C1 -7033*x^2 - 30605*y^2 + 8737*z^2
(-11822/23461 : 11181/23461 : 1) C2a (18538292/3673759 : 949283/3673759 : 1)
** u= -154/95 ; C1 -10321*x^2 - 32741*y^2 + 14569*z^2
(-8594/8793 : 3335/8793 : 1) C2a (1082254/172061 : -71341/172061 : 1)
** u= -154/109 ; C1 -15977*x^2 - 35597*y^2 + 21737*z^2
(718/623 : -75/623 : 1) C2a (8642558/45885 : 680473/45885 : 1)
** u= -154/169 ; C1 -62417*x^2 - 52277*y^2 + 56897*z^2
(79418/101395 : 60489/101395 : 1) C2a (-219515162/36150579 : 22944511/36150579 : 1)
** u= -154/171 ; C1 -64585*x^2 - 52957*y^2 + 58193*z^2
(41683/88999 : -81148/88999 : 1) C2a (3851046/1249675 : 397987/1249675 : 1)
** u= -154/183 ; C1 -78433*x^2 - 57205*y^2 + 66137*z^2
(7621/17423 : -16472/17423 : 1) C2a (1285612/1765309 : 80721/1765309 : 1)
** u= -153/77 ; C1 {+/-} -5930*x^2 + 29338*y^2 + 6082*z^2
(270/457 : -169/457 : 1) C2a (10573/4911 : -253/4911 : 1) C2b (-23812/13265 : 237/13265 : 1)
** u= -153/133 ; C1 {+/-} -30458*x^2 + 41098*y^2 + 34978*z^2
(2126/7869 : -7025/7869 : 1) C2a (-218753/4621 : -20331/4621 : 1) C2b (1278288/1626749 : 32453/1626749 : 1)
** u= -153/149 ; C1 -43226*x^2 - 45610*y^2 + 44386*z^2
(5347/5397 : 1118/5397 : 1) C2a (1363/1647 : 65/1647 : 1)
** u= -152/65 ; C1 -4709*x^2 + 27329*y^2 + 881*z^2
(-8852/24041 : 2265/24041 : 1) C2b (-5367763/1229345 : -37637/1229345 : 1)
** u= -152/163 ; C1 -56845*x^2 + 49673*y^2 + 53017*z^2
(-745/11021 : 11358/11021 : 1) C2b (-950223/1602371 : -48049/1602371 : 1)
** u= -152/173 ; C1 -67565*x^2 + 53033*y^2 + 59417*z^2
(-9807/17131 : -14362/17131 : 1) C2b (143731/1037695 : -66949/1037695 : 1)
** u= -152/187 ; C1 -84253*x^2 + 58073*y^2 + 68713*z^2
(2755/15633 : 16678/15633 : 1) C2b (68093/559911 : 34307/559911 : 1)
** u= -150/77 ; C1 -5945*x^2 - 28429*y^2 + 6529*z^2
(-17046/16699 : -1811/16699 : 1) C2a (-192494/88135 : -5601/88135 : 1)
** u= -150/127 ; C1 -26945*x^2 - 38629*y^2 + 31729*z^2
(-88830/129541 : 90991/129541 : 1) C2a (679738/342575 : -56277/342575 : 1)
** u= -150/133 ; C1 -31145*x^2 - 40189*y^2 + 35089*z^2
(6297/9469 : -6896/9469 : 1) C2a (613456/10125 : 57751/10125 : 1)
** u= -150/179 ; C1 -75305*x^2 - 54541*y^2 + 63241*z^2
(1019/129027 : 138932/129027 : 1) C2a (37285684/13501739 : 3951717/13501739 : 1)
** u= -149/145 ; C1 {+/-} -40906*x^2 + 43226*y^2 + 42034*z^2
(16255/33089 : -28542/33089 : 1) C2a (-3212629/855215 : -313177/855215 : 1) C2b (69406/156531 : -8953/156531 : 1)
** u= -148/127 ; C1 -27365*x^2 + 38033*y^2 + 31817*z^2
(-3688/47627 : -43449/47627 : 1) C2b (131369/190903 : -8023/190903 : 1)
** u= -147/79 ; C1 -6362*x^2 - 27850*y^2 + 7858*z^2
(-123/959 : -506/959 : 1) C2a (97051/33651 : 21803/168255 : 1)
** u= -146/63 ; C1 -4369*x^2 - 25285*y^2 + 1049*z^2
(-28454/101141 : -16867/101141 : 1) C2a (19193934/3744509 : 233573/3744509 : 1)
** u= -146/65 ; C1 -4481*x^2 - 25541*y^2 + 1889*z^2
(6098/14279 : 2925/14279 : 1) C2a (9014742/822065 : -237011/822065 : 1)
** u= -146/87 ; C1 -8353*x^2 - 28885*y^2 + 11657*z^2
(1487/1259 : 16/1259 : 1) C2a (-24962/19261 : 21/19261 : 1)
** u= -146/89 ; C1 -8945*x^2 - 29237*y^2 + 12593*z^2
(1995/1717 : 2968/22321 : 1) C2a (-25506/13993 : -2279/25987 : 1)
** u= -146/91 ; C1 -9577*x^2 - 29597*y^2 + 13537*z^2
(-4714/17485 : 11517/17485 : 1) C2a (24646/17303 : 887/17303 : 1)
** u= -146/93 ; C1 -10249*x^2 - 29965*y^2 + 14489*z^2
(-3829/3221 : 44/3221 : 1) C2a (1221656/522941 : -74037/522941 : 1)
** u= -146/121 ; C1 -23857*x^2 - 35957*y^2 + 28657*z^2
(-17651/17749 : 6660/17749 : 1) C2a (41402/8141 : -3671/8141 : 1)
** u= -146/125 ; C1 -26441*x^2 - 36941*y^2 + 30809*z^2
(-17555/53189 : 46248/53189 : 1) C2a (-410824/491919 : -5111/491919 : 1)
** u= -146/155 ; C1 -50921*x^2 - 45341*y^2 + 47969*z^2
(-173697/183259 : 40580/183259 : 1) C2a (921796/984639 : 67141/984639 : 1)
** u= -146/189 ; C1 -89545*x^2 - 57037*y^2 + 69593*z^2
(51823/108361 : -100552/108361 : 1) C2a (249876/450677 : -6019/450677 : 1)
** u= -145/149 ; C1 {+/-} -45610*x^2 + 43226*y^2 + 44386*z^2
(-4406/16853 : 16467/16853 : 1) C2a (448721/308681 : 40357/308681 : 1) C2b (356826/757331 : -38779/757331 : 1)
** u= -144/65 ; C1 -4421*x^2 + 24961*y^2 + 2209*z^2
(5499/11087 : 2350/11087 : 1) C2b (102949/50525 : -63/1075 : 1)
** u= -144/101 ; C1 -13565*x^2 + 30937*y^2 + 18553*z^2
(-4064/3477 : -91/3477 : 1) C2b (-1368921/1386133 : 32897/1386133 : 1)
** u= -144/151 ; C1 -47765*x^2 + 43537*y^2 + 45553*z^2
(456/19127 : -19559/19127 : 1) C2b (-1767/3779 : -37277/744463 : 1)
** u= -144/169 ; C1 -66197*x^2 + 49297*y^2 + 56497*z^2
(-57925/72159 : 38234/72159 : 1) C2b (137673/566531 : 4801/80933 : 1)
** u= -143/75 ; C1 -5674*x^2 + 26074*y^2 + 6626*z^2
(2411/2855 : -898/2855 : 1) C2b (17078/13545 : -737/13545 : 1)
** u= -142/61 ; C1 -4121*x^2 - 23885*y^2 + 881*z^2
(-8402/31523 : 4947/31523 : 1) C2a (-201826/45639 : 553/45639 : 1)
** u= -142/73 ; C1 -5345*x^2 - 25493*y^2 + 5897*z^2
(1323/4337 : -1996/4337 : 1) C2a (210116/16167 : -10091/16167 : 1)
** u= -142/129 ; C1 -30097*x^2 - 36805*y^2 + 33113*z^2
(27202/48779 : 39187/48779 : 1) C2a (-218606/273113 : -4833/273113 : 1)
** u= -142/141 ; C1 -39481*x^2 - 40045*y^2 + 39761*z^2
(-2782/2803 : 413/2803 : 1) C2a (-13720196/19200589 : -113967/19200589 : 1)
** u= -142/149 ; C1 -46537*x^2 - 42365*y^2 + 44353*z^2
(163/561 : -548/561 : 1) C2a (-5696/1013 : 583/1013 : 1)
** u= -142/151 ; C1 -48401*x^2 - 42965*y^2 + 45521*z^2
(1589/2371 : -1764/2371 : 1) C2a (-12649404/13628699 : 130765/1946957 : 1)
** u= -142/153 ; C1 -50305*x^2 - 43573*y^2 + 46697*z^2
(3094/4619 : -3437/4619 : 1) C2a (47586968/1761809 : -708891/251687 : 1)
** u= -141/113 ; C1 {+/-} -19994*x^2 + 32650*y^2 + 24754*z^2
(413/2697 : -2326/2697 : 1) C2a (635189/62915 : -277557/314575 : 1) C2b (-116760/165749 : 39227/828745 : 1)
** u= -141/193 ; C1 -97274*x^2 + 57130*y^2 + 71794*z^2
(258/3157 : 3523/3157 : 1) C2b (-6/79 : -883/15563 : 1)
** u= -140/109 ; C1 -17965*x^2 + 31481*y^2 + 22801*z^2
(9664/9093 : 2567/9093 : 1) C2b (-164071/351075 : 157/2325 : 1)
** u= -140/151 ; C1 -49045*x^2 + 42401*y^2 + 45481*z^2
(-316/4967 : -5133/4967 : 1) C2b (929079/2100925 : -106067/2100925 : 1)
** u= -140/159 ; C1 -56965*x^2 + 44881*y^2 + 50201*z^2
(-2224/6791 : 6731/6791 : 1) C2b (-2228923/6497415 : -359209/6497415 : 1)
** u= -139/87 ; C1 -8794*x^2 + 26890*y^2 + 12434*z^2
(5869/7279 : -3638/7279 : 1) C2b (-33122/32253 : 1381/32253 : 1)
** u= -138/137 ; C1 -37265*x^2 - 37813*y^2 + 37537*z^2
(-7641/29201 : -28088/29201 : 1) C2a (-1616404/350047 : 160329/350047 : 1)
** u= -138/149 ; C1 -47801*x^2 - 41245*y^2 + 44281*z^2
(3473/14097 : 14120/14097 : 1) C2a (-273392/349693 : 15597/349693 : 1)
** u= -138/163 ; C1 -61913*x^2 - 45613*y^2 + 52513*z^2
(-24954/149621 : 157885/149621 : 1) C2a (454036/91827 : -48727/91827 : 1)
** u= -137/61 ; C1 {+/-} -3946*x^2 + 22490*y^2 + 1666*z^2
(742/2697 : 665/2697 : 1) C2a (-226957/73507 : 7/10501 : 1) C2b (-6054/2849 : -25/407 : 1)
** u= -137/189 ; C1 {+/-} -93802*x^2 + 54490*y^2 + 68738*z^2
(-18551/24853 : 13666/24853 : 1) C2a (249731/477373 : 7695/477373 : 1) C2b (287356/879127 : 38085/879127 : 1)
** u= -136/63 ; C1 -4069*x^2 + 22465*y^2 + 2609*z^2
(-10361/44669 : -14570/44669 : 1) C2b (360293/148493 : -2169/148493 : 1)
** u= -136/73 ; C1 -5429*x^2 + 23825*y^2 + 6689*z^2
(-1992/2881 : -5971/14405 : 1) C2b (1243/1721 : -641/8605 : 1)
** u= -136/89 ; C1 -9685*x^2 + 26417*y^2 + 13633*z^2
(74392/70241 : 22743/70241 : 1) C2b (539769/600665 : 29749/600665 : 1)
** u= -136/103 ; C1 -15509*x^2 + 29105*y^2 + 20129*z^2
(-11783/23917 : -17934/23917 : 1) C2b (-1418777/1592963 : -41905/1592963 : 1)
** u= -136/131 ; C1 -33037*x^2 + 35657*y^2 + 34297*z^2
(8335/10117 : -5838/10117 : 1) C2b (6913/9861 : -41821/1942617 : 1)
** u= -135/107 ; C1 {+/-} -17690*x^2 + 29674*y^2 + 22114*z^2
(650170/2224371 : -1853449/2224371 : 1) C2a (-9821543/2944987 : 822741/2944987 : 1) C2b (268932/300515 : 1949/300515
: 1)
** u= -135/163 ; C1 {+/-} -63050*x^2 + 44794*y^2 + 52354*z^2
(-1323/1559 : -614/1559 : 1) C2a (-1366703/59305 : 148827/59305 : 1) C2b (-87912/153743 : 1957/153743 : 1)
** u= -135/187 ; C1 -92090*x^2 - 53194*y^2 + 67234*z^2
(-27075/80227 : 82862/80227 : 1) C2a (-347093/303575 : -35343/303575 : 1)
** u= -134/61 ; C1 -3865*x^2 - 21677*y^2 + 2113*z^2
(-17639/38877 : -9584/38877 : 1) C2a (-13322/3371 : 307/3371 : 1)
** u= -134/69 ; C1 -4777*x^2 - 22717*y^2 + 5297*z^2
(-9335/33157 : -15428/33157 : 1) C2a (-667172/248891 : -24801/248891 : 1)
** u= -134/133 ; C1 -35113*x^2 - 35645*y^2 + 35377*z^2
(-32174/32187 : -2915/32187 : 1) C2a (252338/277141 : 15773/277141 : 1)
** u= -134/143 ; C1 -43553*x^2 - 38405*y^2 + 40817*z^2
(-3087/53519 : -55076/53519 : 1) C2a (-536672/589029 : 781/12021 : 1)
** u= -134/173 ; C1 -74873*x^2 - 47885*y^2 + 58337*z^2
(-3566/4123 : 909/4123 : 1) C2a (43418/69741 : 2363/69741 : 1)
** u= -133/97 ; C1 {+/-} -13130*x^2 + 27098*y^2 + 17522*z^2
(581/2389 : 1878/2389 : 1) C2a (-493053/4091 : 39947/4091 : 1) C2b (-26308/128221 : 10021/128221 : 1)
** u= -133/113 ; C1 {+/-} -21418*x^2 + 30458*y^2 + 25138*z^2
(5050/6249 : 3781/6249 : 1) C2a (-342883/162169 : 28841/162169 : 1) C2b (178342/355629 : -21697/355629 : 1)
** u= -133/121 ; C1 -26522*x^2 - 32330*y^2 + 29138*z^2
(375471/436037 : -236018/436037 : 1) C2a (30941/35487 : -1339/35487 : 1)
** u= -133/153 ; C1 {+/-} -53338*x^2 + 41098*y^2 + 46418*z^2
(767/8293 : 8770/8293 : 1) C2a (-894169/1200803 : -54207/1200803 : 1) C2b (22528/82589 : 4863/82589 : 1)
** u= -132/101 ; C1 -15101*x^2 + 27625*y^2 + 19441*z^2
(3704/3309 : 2269/16545 : 1) C2b (-13927/16213 : 501/16213 : 1)
** u= -132/155 ; C1 -55709*x^2 + 41449*y^2 + 47521*z^2
(-41800/77067 : -66791/77067 : 1) C2b (96041/430189 : 25893/430189 : 1)
** u= -130/77 ; C1 -6505*x^2 - 22829*y^2 + 9049*z^2
(-18863/21953 : 9468/21953 : 1) C2a (74216/21011 : 4373/21011 : 1)
** u= -130/89 ; C1 -10225*x^2 - 24821*y^2 + 14161*z^2
(46529/43825 : 2856/8765 : 1) C2a (700444/497539 : 293/4181 : 1)
** u= -130/123 ; C1 -28585*x^2 - 32029*y^2 + 30209*z^2
(-1282/6437 : 6133/6437 : 1) C2a (-2241648/1719953 : 179701/1719953 : 1)
** u= -130/179 ; C1 -84025*x^2 - 48941*y^2 + 61681*z^2
(-7003/17775 : -3544/3555 : 1) C2a (-15196/5209 : -1693/5209 : 1)
** u= -128/113 ; C1 -22373*x^2 + 29153*y^2 + 25313*z^2
(511872/555617 : -258785/555617 : 1) C2b (-112067/573169 : -41843/573169 : 1)
** u= -128/149 ; C1 -51101*x^2 + 38585*y^2 + 43961*z^2
(8436/31181 : 31835/31181 : 1) C2b (146741/494959 : -28157/494959 : 1)
** u= -127/75 ; C1 -6154*x^2 - 21754*y^2 + 8546*z^2
(44539/39727 : 7670/39727 : 1) C2a (367943/205363 : -15783/205363 : 1)
** u= -127/179 ; C1 -85402*x^2 + 48170*y^2 + 61378*z^2
(-14962/28619 : 25431/28619 : 1) C2b (-35796/115193 : -4975/115193 : 1)
** u= -126/163 ; C1 -66569*x^2 - 42445*y^2 + 51769*z^2
(1251/9491 : -10364/9491 : 1) C2a (-464426/214569 : -50035/214569 : 1)
** u= -124/55 ; C1 -3221*x^2 + 18401*y^2 + 1289*z^2
(2859/4925 : 518/4925 : 1) C2b (932819/298391 : 4423/298391 : 1)
** u= -124/65 ; C1 -4261*x^2 + 19601*y^2 + 4969*z^2
(143/591 : 290/591 : 1) C2b (-22509/14549 : 437/14549 : 1)
** u= -124/83 ; C1 -8653*x^2 + 22265*y^2 + 12097*z^2
(15397/33789 : -22982/33789 : 1) C2b (-3312913/13903389 : 1104829/13903389 : 1)
** u= -124/131 ; C1 -36205*x^2 + 32537*y^2 + 34273*z^2
(104729/189393 : 159934/189393 : 1) C2b (465903/696499 : 1549/696499 : 1)
** u= -124/149 ; C1 -52477*x^2 + 37577*y^2 + 43777*z^2
(49009/101535 : -93038/101535 : 1) C2b (-1299/2797 : -109/2797 : 1)
** u= -124/185 ; C1 -94741*x^2 + 49601*y^2 + 64729*z^2
(77420/94533 : 14609/94533 : 1) C2b (-107717/565593 : 3863/80799 : 1)
** u= -124/195 ; C1 -108781*x^2 + 53401*y^2 + 71009*z^2
(295228/367091 : 40495/367091 : 1) C2b (422059/992121 : 937/992121 : 1)
** u= -123/79 ; C1 {+/-} -7466*x^2 + 21370*y^2 + 10546*z^2
(-341/1299 : -890/1299 : 1) C2a (-1667071/138211 : -117453/138211 : 1) C2b (17136/689309 : 56525/689309 : 1)
** u= -123/167 ; C1 {+/-} -72410*x^2 + 43018*y^2 + 53842*z^2
(-64698/84059 : -42403/84059 : 1) C2a (359023/657329 : -13923/657329 : 1) C2b (-30702/96875 : -4403/96875 : 1)
** u= -122/77 ; C1 -6953*x^2 - 20813*y^2 + 9833*z^2
(38102/34015 : -7851/34015 : 1) C2a (-1088882/861615 : 25763/861615 : 1)
** u= -122/81 ; C1 -8161*x^2 - 21445*y^2 + 11441*z^2
(-3623/3673 : -1484/3673 : 1) C2a (-62628/40577 : 3209/40577 : 1)
** u= -122/117 ; C1 -26233*x^2 - 28573*y^2 + 27353*z^2
(24739/24341 : -2300/24341 : 1) C2a (9851772/12637805 : 315203/12637805 : 1)
** u= -122/151 ; C1 -55201*x^2 - 37685*y^2 + 44761*z^2
(96074/106749 : -3821/106749 : 1) C2a (461824/810899 : -3119/810899 : 1)
** u= -122/185 ; C1 -95729*x^2 - 49109*y^2 + 64481*z^2
(-44775/100193 : -96296/100193 : 1) C2a (2651318/1213053 : 299633/1213053 : 1)
** u= -121/109 ; C1 {+/-} -21290*x^2 + 26522*y^2 + 23618*z^2
(15694/15913 : 5271/15913 : 1) C2a (-39643/9429 : -529/1347 : 1) C2b (-83656/208565 : 1913/29795 : 1)
** u= -120/71 ; C1 -5525*x^2 + 19441*y^2 + 7681*z^2
(3097/2685 : 70/537 : 1) C2b (-85049/83689 : -4389/83689 : 1)
** u= -120/139 ; C1 -44285*x^2 + 33721*y^2 + 38281*z^2
(-46852/75351 : -59689/75351 : 1) C2b (-11211841/22206545 : -813837/22206545 : 1)
** u= -120/199 ; C1 -116885*x^2 + 54001*y^2 + 72961*z^2
(31780/176523 : -199787/176523 : 1) C2b (-3641/10129 : 27/1447 : 1)
** u= -119/59 ; C1 -3482*x^2 - 17642*y^2 + 3362*z^2
(-3567/4375 : 1066/4375 : 1) C2a (40513/3075 : 43/75 : 1)
** u= -119/83 ; C1 {+/-} -9098*x^2 + 21050*y^2 + 12482*z^2
(-3318/3131 : 1027/3131 : 1) C2a (9175/6399 : -31/405 : 1) C2b (1790/4819 : 23/305 : 1)
** u= -119/179 ; C1 -89162*x^2 + 46202*y^2 + 60482*z^2
(2995/15071 : -16734/15071 : 1) C2b (-92836/311267 : 12191/311267 : 1)
** u= -118/55 ; C1 -3089*x^2 - 16949*y^2 + 2081*z^2
(-8733/13955 : 3164/13955 : 1) C2a (-322008/26657 : 11143/26657 : 1)
** u= -118/63 ; C1 -4033*x^2 - 17893*y^2 + 4913*z^2
(28577/31855 : 9724/31855 : 1) C2a (-5765504/361505 : 17817/21265 : 1)
** u= -118/111 ; C1 -23137*x^2 - 26245*y^2 + 24593*z^2
(56741/85387 : -63196/85387 : 1) C2a (94872/104579 : -5179/104579 : 1)
** u= -118/123 ; C1 -31513*x^2 - 29053*y^2 + 30233*z^2
(-9590/16853 : 13993/16853 : 1) C2a (360176/526855 : 657/75265 : 1)
** u= -118/149 ; C1 -54601*x^2 - 36125*y^2 + 43441*z^2
(-634/711 : 1621/60435 : 1) C2a (-304/541 : 403/45985 : 1)
** u= -117/89 ; C1 {+/-} -11642*x^2 + 21610*y^2 + 15058*z^2
(-20654/18177 : 641/18177 : 1) C2a (-49271/34173 : -3143/34173 : 1) C2b (16688/24931 : -1383/24931 : 1)
** u= -116/95 ; C1 -14501*x^2 + 22481*y^2 + 17609*z^2
(-12/3079 : -2725/3079 : 1) C2b (134129/241069 : 14293/241069 : 1)
** u= -116/107 ; C1 -21053*x^2 + 24905*y^2 + 22817*z^2
(16684/16423 : 3435/16423 : 1) C2b (-955769/1331567 : -34639/1331567 : 1)
** u= -116/143 ; C1 -49349*x^2 + 33905*y^2 + 40169*z^2
(-3517/10717 : 10866/10717 : 1) C2b (-1461853/2830507 : 75515/2830507 : 1)
** u= -116/147 ; C1 -53293*x^2 + 35065*y^2 + 42257*z^2
(-2248/15979 : -17321/15979 : 1) C2b (-755237/1468361 : 33489/1468361 : 1)
** u= -116/191 ; C1 -107237*x^2 + 49937*y^2 + 67337*z^2
(-22168/46615 : 43299/46615 : 1) C2b (83353/1195661 : 3221/70333 : 1)
** u= -115/63 ; C1 -4090*x^2 - 17194*y^2 + 5234*z^2
(4642/7243 : 3293/7243 : 1) C2a (2965797/243443 : 163609/243443 : 1)
** u= -114/101 ; C1 -17945*x^2 - 23197*y^2 + 20233*z^2
(33878/32151 : -3707/32151 : 1) C2a (-131738/50259 : 11807/50259 : 1)
** u= -114/131 ; C1 -39065*x^2 - 30157*y^2 + 34033*z^2
(562/609 : 97/609 : 1) C2a (-359084/61953 : 38219/61953 : 1)
** u= -114/173 ; C1 -83753*x^2 - 42925*y^2 + 56377*z^2
(2022/5335 : 27113/26675 : 1) C2a (13244/19275 : -5809/96375 : 1)
** u= -114/191 ; C1 -108305*x^2 - 49477*y^2 + 67033*z^2
(-85786/121881 : -63377/121881 : 1) C2a (-1088134/897435 : -120947/897435 : 1)
** u= -113/69 ; C1 {+/-} -5386*x^2 + 17530*y^2 + 7586*z^2
(754/5689 : 3719/5689 : 1) C2a (205909/103739 : -10617/103739 : 1) C2b (55838/66983 : -4119/66983 : 1)
** u= -113/77 ; C1 -7610*x^2 - 18698*y^2 + 10562*z^2
(-1878/5557 : 4001/5557 : 1) C2a (-112233/61051 : 6907/61051 : 1)
** u= -113/133 ; C1 {+/-} -41098*x^2 + 30458*y^2 + 34978*z^2
(11122/33645 : -33661/33645 : 1) C2a (-8311/8993 : 683/8993 : 1) C2b (-37378/63909 : 907/63909 : 1)
** u= -113/141 ; C1 {+/-} -48442*x^2 + 32650*y^2 + 38978*z^2
(-2807/3137 : 1202/15685 : 1) C2a (483597/53837 : -265673/269185 : 1) C2b (-5566/50599 : -15393/252995 : 1)
** u= -113/165 ; C1 {+/-} -74314*x^2 + 39994*y^2 + 51746*z^2
(4190/31013 : -34811/31013 : 1) C2a (719257/337325 : -80409/337325 : 1) C2b (-29732/96917 : 3951/96917 : 1)
** u= -113/181 ; C1 {+/-} -94762*x^2 + 45530*y^2 + 60898*z^2
(86/453 : -509/453 : 1) C2a (-83801/133267 : -7345/133267 : 1) C2b (204572/731649 : 26075/731649 : 1)
** u= -112/59 ; C1 -3517*x^2 + 16025*y^2 + 4153*z^2
(2228/2051 : -27/2051 : 1) C2b (65781/40231 : -967/201155 : 1)
** u= -112/95 ; C1 -15109*x^2 + 21569*y^2 + 17761*z^2
(63763/59881 : -10230/59881 : 1) C2b (828781/2446329 : -170837/2446329 : 1)
** u= -112/109 ; C1 -23117*x^2 + 24425*y^2 + 23753*z^2
(-2759/2747 : -366/2747 : 1) C2b (-68189/94145 : 2689/470725 : 1)
** u= -112/123 ; C1 -33085*x^2 + 27673*y^2 + 30137*z^2
(-8036/9943 : 5519/9943 : 1) C2b (787817/1504431 : -59189/1504431 : 1)
** u= -112/125 ; C1 -34669*x^2 + 28169*y^2 + 31081*z^2
(2951/29307 : 30610/29307 : 1) C2b (-87313/160305 : 5477/160305 : 1)
** u= -112/145 ; C1 -52709*x^2 + 33569*y^2 + 40961*z^2
(-38357/47759 : -21750/47759 : 1) C2b (-317539/811639 : 33787/811639 : 1)
** u= -112/183 ; C1 -98005*x^2 + 46033*y^2 + 61937*z^2
(-6049/7997 : 2854/7997 : 1) C2b (916649/3399523 : -118617/3399523 : 1)
** u= -111/107 ; C1 -22058*x^2 - 23770*y^2 + 22882*z^2
(-35318/34779 : 2621/34779 : 1) C2a (31403/19679 : -2757/19679 : 1)
** u= -110/61 ; C1 -3865*x^2 - 15821*y^2 + 5041*z^2
(20377/20997 : -6248/20997 : 1) C2a (280418/160673 : 121/2263 : 1)
** u= -110/109 ; C1 -23545*x^2 - 23981*y^2 + 23761*z^2
(-6577/15901 : 14424/15901 : 1) C2a (364312/363853 : 25631/363853 : 1)
** u= -110/117 ; C1 -29065*x^2 - 25789*y^2 + 27329*z^2
(-8681/26533 : -25712/26533 : 1) C2a (-185522/236635 : 10203/236635 : 1)
** u= -110/137 ; C1 -45665*x^2 - 30869*y^2 + 36809*z^2
(48422/59339 : -27021/59339 : 1) C2a (6482/10065 : -343/10065 : 1)
** u= -110/147 ; C1 -55465*x^2 - 33709*y^2 + 41849*z^2
(-7799/134647 : 149692/134647 : 1) C2a (-196554/339095 : 9571/339095 : 1)
** u= -110/157 ; C1 -66265*x^2 - 36749*y^2 + 47089*z^2
(5425/15229 : 15624/15229 : 1) C2a (-13457918/27309667 : 1387/125851 : 1)
** u= -109/65 ; C1 -4666*x^2 + 16106*y^2 + 6514*z^2
(398/5349 : 3395/5349 : 1) C2b (-3162/5417 : -401/5417 : 1)
** u= -109/121 ; C1 {+/-} -32330*x^2 + 26522*y^2 + 29138*z^2
(-4572086/7391881 : 5877723/7391881 : 1) C2a (-900893/163491 : -94507/163491 : 1) C2b (-129002/204095 : -1637/204095
: 1)
** u= -109/193 ; C1 {+/-} -113978*x^2 + 49130*y^2 + 67442*z^2
(-142/1121 : -22023/19057 : 1) C2a (-153431/28083 : -307279/477411 : 1) C2b (16/547 : 385/9299 : 1)
** u= -108/67 ; C1 -5165*x^2 + 16153*y^2 + 7297*z^2
(7947/8189 : -3178/8189 : 1) C2b (374519/390367 : -19833/390367 : 1)
** u= -108/77 ; C1 -8045*x^2 + 17593*y^2 + 10897*z^2
(15137/13743 : 3494/13743 : 1) C2b (-3709/4235 : -171/4235 : 1)
** u= -108/91 ; C1 -13757*x^2 + 19945*y^2 + 16273*z^2
(-5184/5563 : -2591/5563 : 1) C2b (10769/14987 : -597/14987 : 1)
** u= -108/103 ; C1 -20213*x^2 + 22273*y^2 + 21193*z^2
(-4716/5635 : 3167/5635 : 1) C2b (15959/1121525 : 81717/1121525 : 1)
** u= -108/115 ; C1 -28109*x^2 + 24889*y^2 + 26401*z^2
(-8411/14205 : -11582/14205 : 1) C2b (301983/541267 : 20221/541267 : 1)
** u= -108/145 ; C1 -54149*x^2 + 32689*y^2 + 40681*z^2
(-10817/23391 : -22070/23391 : 1) C2b (111933/248593 : 7241/248593 : 1)
** u= -107/63 ; C1 -4330*x^2 + 15418*y^2 + 6002*z^2
(-7369/6271 : -242/6271 : 1) C2b (3544/3087 : 127/3087 : 1)
** u= -107/135 ; C1 {+/-} -44794*x^2 + 29674*y^2 + 35666*z^2
(-104029/121063 : 35770/121063 : 1) C2a (136971/5195 : -15127/5195 : 1) C2b (876884/1667115 : -33631/1667115 : 1)
** u= -106/83 ; C1 -10489*x^2 - 18125*y^2 + 13249*z^2
(883/1455 : -26176/36375 : 1) C2a (-90034/205 : -193901/5125 : 1)
** u= -106/105 ; C1 -21841*x^2 - 22261*y^2 + 22049*z^2
(20378/20759 : 4405/20759 : 1) C2a (708/985 : 1637/194045 : 1)
** u= -106/139 ; C1 -48905*x^2 - 30557*y^2 + 37553*z^2
(-33135/37859 : 2068/37859 : 1) C2a (3886966/486873 : -9217/10359 : 1)
** u= -106/157 ; C1 -67913*x^2 - 35885*y^2 + 46697*z^2
(7966/34943 : -38325/34943 : 1) C2a (-402838/19089 : 6613/2727 : 1)
** u= -106/161 ; C1 -72577*x^2 - 37157*y^2 + 48817*z^2
(57718/191655 : 204331/191655 : 1) C2a (20548/17405 : -2197/17405 : 1)
** u= -105/181 ; C1 -98810*x^2 + 43786*y^2 + 59746*z^2
(-6010/9693 : -6833/9693 : 1) C2b (94494/294289 : -6301/294289 : 1)
** u= -104/49 ; C1 -2437*x^2 + 13217*y^2 + 1777*z^2
(-5317/7047 : -1210/7047 : 1) C2b (-93117/61901 : 3943/61901 : 1)
** u= -104/71 ; C1 -6485*x^2 + 15857*y^2 + 8993*z^2
(7452/6367 : -529/6367 : 1) C2b (-66977/649405 : 2279/28235 : 1)
** u= -104/101 ; C1 -19805*x^2 + 21017*y^2 + 20393*z^2
(24736/82709 : -77853/82709 : 1) C2b (49681/88835 : 4111/88835 : 1)
** u= -104/125 ; C1 -36941*x^2 + 26441*y^2 + 30809*z^2
(-72323/139135 : 123486/139135 : 1) C2b (-1463089/2906639 : -95123/2906639 : 1)
** u= -104/153 ; C1 -64213*x^2 + 34225*y^2 + 44417*z^2
(64/101 : 13787/18685 : 1) C2b (97/2249 : -4425/83213 : 1)
** u= -104/189 ; C1 -110797*x^2 + 46537*y^2 + 64217*z^2
(16991/93995 : -107258/93995 : 1) C2b (-43217/164255 : -4029/164255 : 1)
** u= -104/199 ; C1 -126037*x^2 + 50417*y^2 + 70177*z^2
(-57929/94461 : -63490/94461 : 1) C2b (389643/1889041 : 48827/1889041 : 1)
** u= -103/43 ; C1 -2138*x^2 + 12458*y^2 + 98*z^2
(-1099/5155 : -42/5155 : 1) C2b (25876/2933 : 13/419 : 1)
** u= -103/83 ; C1 -10858*x^2 + 17498*y^2 + 13378*z^2
(698/5463 : -4745/5463 : 1) C2b (1766/17883 : 1381/17883 : 1)
** u= -103/123 ; C1 -35578*x^2 - 25738*y^2 + 29858*z^2
(-25438/131023 : 137915/131023 : 1) C2a (-9363/4015 : 983/4015 : 1)
** u= -102/53 ; C1 -2825*x^2 - 13213*y^2 + 3217*z^2
(-26/75 : 7/15 : 1) C2a (-62144/29853 : 1801/29853 : 1)
** u= -102/67 ; C1 -5513*x^2 - 14893*y^2 + 7753*z^2
(11854/16581 : 9545/16581 : 1) C2a (-1098938/235145 : 77547/235145 : 1)
** u= -102/181 ; C1 -100361*x^2 - 43165*y^2 + 59281*z^2
(90681/119501 : -22208/119501 : 1) C2a (223276/183631 : -25245/183631 : 1)
** u= -100/47 ; C1 -2245*x^2 + 12209*y^2 + 1609*z^2
(16/27 : 7/27 : 1) C2b (242857/110727 : -2953/110727 : 1)
** u= -100/77 ; C1 -8845*x^2 + 15929*y^2 + 11329*z^2
(13633/23591 : 17106/23591 : 1) C2b (-412497/853457 : 57367/853457 : 1)
** u= -100/79 ; C1 -9605*x^2 + 16241*y^2 + 12041*z^2
(-9375/12721 : 8246/12721 : 1) C2b (37219/105695 : 7607/105695 : 1)
** u= -100/91 ; C1 -15005*x^2 + 18281*y^2 + 16481*z^2
(-10800/13207 : 7843/13207 : 1) C2b (56353/270625 : -19391/270625 : 1)
** u= -99/47 ; C1 -2234*x^2 - 12010*y^2 + 1714*z^2
(-1803/2327 : -410/2327 : 1) C2a (-1483133/37527 : -56365/37527 : 1)
** u= -99/71 ; C1 {+/-} -6890*x^2 + 14842*y^2 + 9298*z^2
(-5610/4867 : -479/4867 : 1) C2a (512063/99 : -40837/99 : 1) C2b (-88464/189683 : -13483/189683 : 1)
** u= -98/43 ; C1 -1993*x^2 - 11453*y^2 + 673*z^2
(758/2493 : 515/2493 : 1) C2a (757292/73061 : -17431/73061 : 1)
** u= -98/89 ; C1 -14321*x^2 - 17525*y^2 + 15761*z^2
(2425/2417 : -3348/12085 : 1) C2a (89330/112917 : -7451/564585 : 1)
** u= -98/103 ; C1 -22273*x^2 - 20213*y^2 + 21193*z^2
(19843/69567 : 68120/69567 : 1) C2a (363958/185699 : 35269/185699 : 1)
** u= -98/143 ; C1 -55793*x^2 - 30053*y^2 + 38873*z^2
(24375/36043 : 24028/36043 : 1) C2a (-518744/654387 : -47863/654387 : 1)
** u= -98/157 ; C1 -71305*x^2 - 34253*y^2 + 45817*z^2
(-8329/10833 : -3544/10833 : 1) C2a (281722/507961 : -21827/507961 : 1)
** u= -98/167 ; C1 -83585*x^2 - 37493*y^2 + 51017*z^2
(-5334/7001 : -1807/7001 : 1) C2a (114884/58917 : -13249/58917 : 1)
** u= -97/93 ; C1 -16570*x^2 - 18058*y^2 + 17282*z^2
(-1655/3521 : -3058/3521 : 1) C2a (-281/85 : 27/85 : 1)
** u= -97/133 ; C1 {+/-} -46250*x^2 + 27098*y^2 + 34082*z^2
(-5702/11425 : -417/457 : 1) C2a (394857/168715 : -43559/168715 : 1) C2b (-91058/367255 : 18353/367255 : 1)
** u= -97/189 ; C1 -114682*x^2 - 45130*y^2 + 62978*z^2
(-2306/17813 : 20719/17813 : 1) C2a (-150907/139561 : -17319/139561 : 1)
** u= -96/55 ; C1 -3221*x^2 + 12241*y^2 + 4369*z^2
(2064/9367 : 5495/9367 : 1) C2b (-44027/32375 : 507/32375 : 1)
** u= -96/77 ; C1 -9293*x^2 + 15145*y^2 + 11497*z^2
(4859/4623 : 1318/4623 : 1) C2b (229/104503 : 8133/104503 : 1)
** u= -96/121 ; C1 -35957*x^2 + 23857*y^2 + 28657*z^2
(-19476/23149 : 8485/23149 : 1) C2b (131217/361699 : 16903/361699 : 1)
** u= -95/91 ; C1 -15850*x^2 - 17306*y^2 + 16546*z^2
(650/683 : -243/683 : 1) C2a (-1769293/845 : 174313/845 : 1)
** u= -94/43 ; C1 -1913*x^2 - 10685*y^2 + 1097*z^2
(-5899/21707 : 6492/21707 : 1) C2a (-16966902/3348731 : -468791/3348731 : 1)
** u= -94/63 ; C1 -4993*x^2 - 12805*y^2 + 6977*z^2
(-5519/23207 : -16780/23207 : 1) C2a (138/59 : 1787/11623 : 1)
** u= -94/73 ; C1 -8033*x^2 - 14165*y^2 + 10217*z^2
(6774/6007 : -65/6007 : 1) C2a (161066/113517 : -10507/113517 : 1)
** u= -94/119 ; C1 -34897*x^2 - 22997*y^2 + 27697*z^2
(-1319/1615 : -708/1615 : 1) C2a (633134/208373 : -68833/208373 : 1)
** u= -94/161 ; C1 -77905*x^2 - 34757*y^2 + 47353*z^2
(13474/19651 : -10917/19651 : 1) C2a (904826/268297 : 105761/268297 : 1)
** u= -94/185 ; C1 -110401*x^2 - 43061*y^2 + 60169*z^2
(-1183/6645 : 129592/112965 : 1) C2a (3944/4351 : 7597/73967 : 1)
** u= -93/49 ; C1 {+/-} -2426*x^2 + 11050*y^2 + 2866*z^2
(174/173 : 167/865 : 1) C2a (-14419/597 : 3691/2985 : 1) C2b (2766/2933 : 1007/14665 : 1)
** u= -93/65 ; C1 -5594*x^2 - 12874*y^2 + 7666*z^2
(-8913/8605 : 3094/8605 : 1) C2a (-187093/180115 : -609/180115 : 1)
** u= -93/121 ; C1 -36842*x^2 + 23290*y^2 + 28498*z^2
(-10137/11609 : 118/893 : 1) C2b (145254/557873 : -29293/557873 : 1)
** u= -93/169 ; C1 -88586*x^2 + 37210*y^2 + 51346*z^2
(3049/24609 : 1739878/1501149 : 1) C2b (5552/16577 : -621/1011197 : 1)
** u= -92/41 ; C1 -1781*x^2 + 10145*y^2 + 761*z^2
(5088/7973 : 473/7973 : 1) C2b (84883/31693 : -1309/31693 : 1)
** u= -92/49 ; C1 -2437*x^2 + 10865*y^2 + 2953*z^2
(-1432/1301 : 9/1301 : 1) C2b (-386913/249689 : -5113/249689 : 1)
** u= -92/91 ; C1 -16381*x^2 + 16745*y^2 + 16561*z^2
(-14732/14743 : -1629/14743 : 1) C2b (-219/329 : 1693/64813 : 1)
** u= -92/97 ; C1 -19813*x^2 + 17873*y^2 + 18793*z^2
(-625/3663 : -3698/3663 : 1) C2b (-31631/81405 : -4597/81405 : 1)
** u= -92/99 ; C1 -21037*x^2 + 18265*y^2 + 19553*z^2
(2923/19469 : 19898/19469 : 1) C2b (613/1461 : -77/1461 : 1)
** u= -92/113 ; C1 -30725*x^2 + 21233*y^2 + 25097*z^2
(-75256/150805 : -27339/30161 : 1) C2b (140497/248891 : 2701/248891 : 1)
** u= -92/123 ; C1 -38845*x^2 + 23593*y^2 + 29297*z^2
(-2719/37897 : 42086/37897 : 1) C2b (273097/525791 : -3081/525791 : 1)
** u= -92/169 ; C1 -89077*x^2 + 37025*y^2 + 51193*z^2
(-392/3237 : -18787/16185 : 1) C2b (53783/164853 : -3071/824265 : 1)
** u= -92/191 ; C1 -120581*x^2 + 44945*y^2 + 63161*z^2
(924/1279 : 91/1279 : 1) C2b (734791/9256289 : -35359/1322327 : 1)
** u= -91/87 ; C1 {+/-} -14458*x^2 + 15850*y^2 + 15122*z^2
(-199/971 : -4646/4855 : 1) C2a (22407/30227 : 733/151135 : 1) C2b (3728/5043 : -61/25215 : 1)
** u= -91/135 ; C1 -50266*x^2 - 26506*y^2 + 34514*z^2
(-17930/31859 : 26683/31859 : 1) C2a (-1249/2665 : 27/2665 : 1)
** u= -91/199 ; C1 -133850*x^2 + 47882*y^2 + 67538*z^2
(9039/112715 : 26602/22543 : 1) C2b (-901276/16667207 : -364163/16667207 : 1)
** u= -90/43 ; C1 -1865*x^2 - 9949*y^2 + 1489*z^2
(-3522/4081 : -409/4081 : 1) C2a (-156086/51449 : 4257/51449 : 1)
** u= -90/59 ; C1 -4265*x^2 - 11581*y^2 + 6001*z^2
(1431/1211 : 76/1211 : 1) C2a (824306/561615 : -38311/561615 : 1)
** u= -90/181 ; C1 -106745*x^2 - 40861*y^2 + 57241*z^2
(10866/38107 : -41543/38107 : 1) C2a (-30638/115863 : 379/115863 : 1)
** u= -89/61 ; C1 {+/-} -4810*x^2 + 11642*y^2 + 6658*z^2
(-1031/1149 : 562/1149 : 1) C2a (-55379/43955 : -2263/43955 : 1) C2b (-181308/170515 : -193/170515 : 1)
** u= -89/117 ; C1 {+/-} -34714*x^2 + 21610*y^2 + 26594*z^2
(-539/12781 : -14162/12781 : 1) C2a (10534183/1824733 : -1172451/1824733 : 1) C2b (44882/84657 : -427/84657 : 1)
** u= -89/125 ; C1 -41546*x^2 + 23546*y^2 + 29954*z^2
(8373/10745 : -4814/10745 : 1) C2b (-1606/3725 : 101/3725 : 1)
** u= -89/173 ; C1 -95978*x^2 - 37850*y^2 + 52802*z^2
(1631/2573 : 1578/2573 : 1) C2a (-13917/44533 : -3187/222665 : 1)
** u= -88/41 ; C1 -1717*x^2 + 9425*y^2 + 1153*z^2
(-5/7 : -6/35 : 1) C2b (5145/3121 : 959/15605 : 1)
** u= -88/65 ; C1 -5989*x^2 + 11969*y^2 + 7921*z^2
(-27145/28019 : 12282/28019 : 1) C2b (-86757/110983 : -59/1247 : 1)
** u= -88/87 ; C1 -14965*x^2 + 15313*y^2 + 15137*z^2
(2588/11411 : -11053/11411 : 1) C2b (-12689/17747 : -33/17747 : 1)
** u= -88/101 ; C1 -23197*x^2 + 17945*y^2 + 20233*z^2
(-3707/32151 : 33878/32151 : 1) C2b (-10263/18829 : 575/18829 : 1)
** u= -88/129 ; C1 -45541*x^2 + 24385*y^2 + 31601*z^2
(-1679/20411 : -23122/20411 : 1) C2b (125627/1141147 : -59457/1141147 : 1)
** u= -88/149 ; C1 -66301*x^2 + 29945*y^2 + 40681*z^2
(-716/1389 : 1219/1389 : 1) C2b (753621/2054111 : -24149/2054111 : 1)
** u= -88/163 ; C1 -83213*x^2 + 34313*y^2 + 47513*z^2
(-15000/67739 : -76211/67739 : 1) C2b (17711/225937 : -8371/225937 : 1)
** u= -88/193 ; C1 -126053*x^2 + 44993*y^2 + 63473*z^2
(-9408/48605 : -55541/48605 : 1) C2b (-68021/1495217 : -32549/1495217 : 1)
** u= -87/91 ; C1 {+/-} -17306*x^2 + 15850*y^2 + 16546*z^2
(-393/815 : -3622/4075 : 1) C2a (180235/168981 : -71761/844905 : 1) C2b (5040/13507 : 3919/67535 : 1)
** u= -86/39 ; C1 -1585*x^2 - 8917*y^2 + 833*z^2
(7154/10813 : 1351/10813 : 1) C2a (-4013196/187915 : 17509/26845 : 1)
** u= -86/87 ; C1 -15313*x^2 - 14965*y^2 + 15137*z^2
(-54229/55667 : 11192/55667 : 1) C2a (-7499676/622363 : 758707/622363 : 1)
** u= -86/101 ; C1 -23657*x^2 - 17597*y^2 + 20177*z^2
(-7250/18611 : -18069/18611 : 1) C2a (49576/77925 : 1759/77925 : 1)
** u= -86/159 ; C1 -79105*x^2 - 32677*y^2 + 45233*z^2
(4006/5333 : -721/5333 : 1) C2a (131124/242083 : -12469/242083 : 1)
** u= -86/175 ; C1 -100321*x^2 - 38021*y^2 + 53329*z^2
(11290/121357 : 142551/121357 : 1) C2a (50284/100381 : -1019113/19775057 : 1)
** u= -86/177 ; C1 -103153*x^2 - 38725*y^2 + 54377*z^2
(-1379/2249 : -7136/11245 : 1) C2a (20142/5761 : -2399/5761 : 1)
** u= -86/191 ; C1 -124097*x^2 - 43877*y^2 + 61937*z^2
(-495174/1611865 : -1724533/1611865 : 1) C2a (-15656568/2274601 : 1873681/2274601 : 1)
** u= -84/65 ; C1 -6341*x^2 + 11281*y^2 + 8089*z^2
(208/3129 : -2645/3129 : 1) C2b (-193491/242465 : -9551/242465 : 1)
** u= -84/67 ; C1 -6989*x^2 + 11545*y^2 + 8689*z^2
(-2281/3129 : -2054/3129 : 1) C2b (11001/24641 : 1663/24641 : 1)
** u= -84/89 ; C1 -16757*x^2 + 14977*y^2 + 15817*z^2
(-21060/26257 : 15227/26257 : 1) C2b (5091/8425 : 247/8425 : 1)
** u= -84/107 ; C1 -28349*x^2 + 18505*y^2 + 22369*z^2
(27457/77457 : 78086/77457 : 1) C2b (202487/393677 : -8619/393677 : 1)
** u= -84/109 ; C1 -29837*x^2 + 18937*y^2 + 23137*z^2
(-4668/26957 : 29215/26957 : 1) C2b (-3373/12935 : 681/12935 : 1)
** u= -84/131 ; C1 -48845*x^2 + 24217*y^2 + 32113*z^2
(10143/13441 : -5662/13441 : 1) C2b (-27129/643315 : 31979/643315 : 1)
** u= -84/151 ; C1 -70325*x^2 + 29857*y^2 + 41113*z^2
(-1071/27025 : -6334/5405 : 1) C2b (463941/1365025 : 6281/1365025 : 1)
** u= -84/167 ; C1 -90389*x^2 + 34945*y^2 + 48889*z^2
(-1848/20747 : 24359/20747 : 1) C2b (19049/74321 : 801/74321 : 1)
** u= -83/119 ; C1 {+/-} -38186*x^2 + 21050*y^2 + 27026*z^2
(-1629/2803 : -11482/14015 : 1) C2a (163609/326847 : 26149/1634235 : 1) C2b (-112496/1519423 : 411827/7597115 : 1)
** u= -83/143 ; C1 -61658*x^2 + 27338*y^2 + 37298*z^2
(-7695/12883 : -9638/12883 : 1) C2b (186838/682769 : 19937/682769 : 1)
** u= -83/175 ; C1 {+/-} -101914*x^2 + 37514*y^2 + 52786*z^2
(-77641/108235 : -10362/108235 : 1) C2a (-117041/423701 : 8161/423701 : 1) C2b (-35834/235455 : 4639/235455 : 1)
** u= -82/35 ; C1 -1369*x^2 - 7949*y^2 + 241*z^2
(974/2553 : 5/69 : 1) C2a (-5084/695 : -67/695 : 1)
** u= -82/89 ; C1 -17137*x^2 - 14645*y^2 + 15793*z^2
(8257/10729 : 6660/10729 : 1) C2a (-58912936/1365173 : 6163547/1365173 : 1)
** u= -82/91 ; C1 -18281*x^2 - 15005*y^2 + 16481*z^2
(-19903/109147 : -112260/109147 : 1) C2a (339914/29601 : -35839/29601 : 1)
** u= -82/117 ; C1 -36793*x^2 - 20413*y^2 + 26153*z^2
(-4133/6445 : 4736/6445 : 1) C2a (29423364/691865 : -3355471/691865 : 1)
** u= -82/127 ; C1 -45713*x^2 - 22853*y^2 + 30233*z^2
(-8302/14513 : 11865/14513 : 1) C2a (584184/1003135 : 6437/143305 : 1)
** u= -82/177 ; C1 -105313*x^2 - 38053*y^2 + 53633*z^2
(-14890/80443 : -92233/80443 : 1) C2a (-28276/136645 : -651/136645 : 1)
** u= -81/149 ; C1 -69290*x^2 + 28762*y^2 + 39778*z^2
(-21121/30693 : -1162/2361 : 1) C2b (2/271 : -2067/53387 : 1)
** u= -80/47 ; C1 -2405*x^2 + 8609*y^2 + 3329*z^2
(435/4457 : -2762/4457 : 1) C2b (-3607/9923 : 793/9923 : 1)
** u= -80/89 ; C1 -17525*x^2 + 14321*y^2 + 15761*z^2
(60952/73165 : 7335/14633 : 1) C2b (-119239/189059 : 1511/189059 : 1)
** u= -80/131 ; C1 -50285*x^2 + 23561*y^2 + 31721*z^2
(-6540/11359 : 9079/11359 : 1) C2b (-8669/23159 : 389/23159 : 1)
** u= -80/171 ; C1 -97885*x^2 + 35641*y^2 + 50201*z^2
(16744/33239 : 28039/33239 : 1) C2b (-1231/27001 : 669/27001 : 1)
** u= -79/35 ; C1 {+/-} -1306*x^2 + 7466*y^2 + 514*z^2
(554/2083 : 495/2083 : 1) C2a (11779/2329 : -241/2329 : 1) C2b (-132344/61551 : -3863/61551 : 1)
** u= -79/43 ; C1 -1898*x^2 + 8090*y^2 + 2402*z^2
(-486/1103 : 553/1103 : 1) C2b (-159934/115517 : 4069/115517 : 1)
** u= -79/123 ; C1 {+/-} -43018*x^2 + 21370*y^2 + 28322*z^2
(-14399/17747 : -238/17747 : 1) C2a (-4191/9707 : -1/571 : 1) C2b (-27878/67081 : 129/9583 : 1)
** u= -78/35 ; C1 -1289*x^2 - 7309*y^2 + 601*z^2
(-1209/1903 : -200/1903 : 1) C2a (-42538/14463 : 107/14463 : 1)
** u= -78/43 ; C1 -1913*x^2 - 7933*y^2 + 2473*z^2
(1986/1801 : 245/1801 : 1) C2a (-209654/18083 : 11697/18083 : 1)
** u= -78/47 ; C1 -2465*x^2 - 8293*y^2 + 3457*z^2
(-578/501 : 73/501 : 1) C2a (1802/1365 : 31/1365 : 1)
** u= -78/83 ; C1 -14633*x^2 - 12973*y^2 + 13753*z^2
(-4770/6121 : 3749/6121 : 1) C2a (42304/11145 : 4321/11145 : 1)
** u= -78/145 ; C1 -65969*x^2 - 27109*y^2 + 37561*z^2
(-10155/19649 : 16852/19649 : 1) C2a (-173662/495105 : 8471/495105 : 1)
** u= -77/153 ; C1 {+/-} -75850*x^2 + 29338*y^2 + 41042*z^2
(-25987/245285 : 57418/49057 : 1) C2a (-248593/125881 : 29343/125881 : 1) C2b (-1209044/4443753 : 4393/4443753 : 1)
** u= -76/43 ; C1 -1949*x^2 + 7625*y^2 + 2609*z^2
(16/131 : 381/655 : 1) C2b (-59723/55157 : -14833/275785 : 1)
** u= -76/145 ; C1 -66821*x^2 + 26801*y^2 + 37289*z^2
(-35469/67523 : -56630/67523 : 1) C2b (-248749/995225 : -2857/142175 : 1)
** u= -76/161 ; C1 -86437*x^2 + 31697*y^2 + 44617*z^2
(761260/1139433 : 497173/1139433 : 1) C2b (-123721/562233 : -551/562233 : 1)
** u= -76/183 ; C1 -117589*x^2 + 39265*y^2 + 55529*z^2
(114608/198403 : 127799/198403 : 1) C2b (-151171/4972269 : -1051/4972269 : 1)
** u= -74/35 ; C1 -1241*x^2 - 6701*y^2 + 929*z^2
(470/1481 : -513/1481 : 1) C2a (-1156/435 : 23/435 : 1)
** u= -74/45 ; C1 -2281*x^2 - 7501*y^2 + 3209*z^2
(-2458/3751 : 2045/3751 : 1) C2a (-367372/127903 : -21777/127903 : 1)
** u= -74/91 ; C1 -19945*x^2 - 13757*y^2 + 16273*z^2
(10634/11813 : -1059/11813 : 1) C2a (249454/418645 : -7597/418645 : 1)
** u= -74/127 ; C1 -48529*x^2 - 21605*y^2 + 29449*z^2
(-31318/57297 : -47663/57297 : 1) C2a (57848/155537 : -155/155537 : 1)
** u= -74/193 ; C1 -134593*x^2 - 42725*y^2 + 60337*z^2
(-3349/6333 : -4616/6333 : 1) C2a (24706/48779 : 15539/243895 : 1)
** u= -73/53 ; C1 -3898*x^2 - 8138*y^2 + 5218*z^2
(-214/185 : 3/185 : 1) C2a (36307/32215 : 1393/32215 : 1)
** u= -73/165 ; C1 {+/-} -93274*x^2 + 32554*y^2 + 45986*z^2
(1081/9457 : 11090/9457 : 1) C2a (-400449/2465515 : 14837/2465515 : 1) C2b (5008/596733 : -11021/596733 : 1)
** u= -72/47 ; C1 -2693*x^2 + 7393*y^2 + 3793*z^2
(1451/1401 : -490/1401 : 1) C2b (-58097/82981 : 5337/82981 : 1)
** u= -72/49 ; C1 -3077*x^2 + 7585*y^2 + 4273*z^2
(-9419/18087 : -12178/18087 : 1) C2b (23663/34939 : 2199/34939 : 1)
** u= -71/51 ; C1 -3562*x^2 - 7642*y^2 + 4802*z^2
(2450/2111 : 49/2111 : 1) C2a (-45749/45437 : 39/6491 : 1)
** u= -71/91 ; C1 -20602*x^2 + 13322*y^2 + 16162*z^2
(6703/7695 : -1534/7695 : 1) C2b (-9027714/26845793 : -1286461/26845793 : 1)
** u= -71/99 ; C1 {+/-} -25930*x^2 + 14842*y^2 + 18818*z^2
(1358/2543 : 2231/2543 : 1) C2a (-17859/33853 : 7/349 : 1) C2b (551648/1376139 : 473/14187 : 1)
** u= -70/33 ; C1 -1105*x^2 - 5989*y^2 + 809*z^2
(70/103 : 23/103 : 1) C2a (-757762/88283 : 27051/88283 : 1)
** u= -70/39 ; C1 -1585*x^2 - 6421*y^2 + 2081*z^2
(-583/1183 : 608/1183 : 1) C2a (817208/41227 : 46749/41227 : 1)
** u= -70/141 ; C1 -64825*x^2 - 24781*y^2 + 34721*z^2
(287/1613 : -1852/1613 : 1) C2a (622692/318625 : 73597/318625 : 1)
** u= -70/163 ; C1 -92105*x^2 - 31469*y^2 + 44489*z^2
(-11178/23933 : 1621/1841 : 1) C2a (-32446/219489 : -2483/219489 : 1)
** u= -70/173 ; C1 -106105*x^2 - 34829*y^2 + 49249*z^2
(-38846/99027 : 96277/99027 : 1) C2a (493252/8902595 : -113303/8902595 : 1)
** u= -70/179 ; C1 -114985*x^2 - 36941*y^2 + 52201*z^2
(70/249 : -269/249 : 1) C2a (254566/245929 : 30773/245929 : 1)
** u= -70/193 ; C1 -137105*x^2 - 42149*y^2 + 59369*z^2
(-16477/77473 : -87012/77473 : 1) C2a (169506/124271 : 20513/124271 : 1)
** u= -69/41 ; C1 {+/-} -1850*x^2 + 6442*y^2 + 2578*z^2
(-853/753 : 134/753 : 1) C2a (-17753/2461 : -1113/2461 : 1) C2b (-9404/22213 : -1743/22213 : 1)
** u= -69/113 ; C1 {+/-} -37418*x^2 + 17530*y^2 + 23602*z^2
(12023/24561 : 22442/24561 : 1) C2a (207997/283029 : 20381/283029 : 1) C2b (-34686/88823 : 941/88823 : 1)
** u= -68/37 ; C1 -1405*x^2 + 5993*y^2 + 1777*z^2
(656/12573 : 6839/12573 : 1) C2b (24263/65955 : 5363/65955 : 1)
** u= -68/55 ; C1 -4789*x^2 + 7649*y^2 + 5881*z^2
(-5480/4963 : 369/4963 : 1) C2b (-210501/309331 : -15187/309331 : 1)
** u= -68/69 ; C1 -9661*x^2 + 9385*y^2 + 9521*z^2
(-193/1847 : -1850/1847 : 1) C2b (-4087/35903 : -2505/35903 : 1)
** u= -68/97 ; C1 -25285*x^2 + 14033*y^2 + 17977*z^2
(20213/24627 : 6386/24627 : 1) C2b (-51363/452549 : -24259/452549 : 1)
** u= -68/139 ; C1 -63421*x^2 + 23945*y^2 + 33601*z^2
(653/42733 : 50610/42733 : 1) C2b (-306409/1235931 : 4979/1235931 : 1)
** u= -67/55 ; C1 -4874*x^2 - 7514*y^2 + 5906*z^2
(-50/83 : -1047/1411 : 1) C2a (-463/423 : -431/7191 : 1)
** u= -67/111 ; C1 -36346*x^2 - 16810*y^2 + 22706*z^2
(-89/131 : 3190/5371 : 1) C2a (-10371/23299 : 23215/955259 : 1)
** u= -67/135 ; C1 -59434*x^2 + 22714*y^2 + 31826*z^2
(201209/414727 : 367510/414727 : 1) C2b (14194/63081 : -1003/63081 : 1)
** u= -66/73 ; C1 -11729*x^2 - 9685*y^2 + 10609*z^2
(-618/947 : -721/947 : 1) C2a (1266028/85593 : -1295/831 : 1)
** u= -66/89 ; C1 -20465*x^2 - 12277*y^2 + 15313*z^2
(-46959/55457 : 12656/55457 : 1) C2a (435932/843345 : -161/843345 : 1)
** u= -66/91 ; C1 -21737*x^2 - 12637*y^2 + 15937*z^2
(-5973/20527 : -21680/20527 : 1) C2a (-2179028/112179 : -246479/112179 : 1)
** u= -66/127 ; C1 -51473*x^2 - 20485*y^2 + 28537*z^2
(4133/9951 : -9748/9951 : 1) C2a (-573178/699039 : 63577/699039 : 1)
** u= -66/185 ; C1 -126641*x^2 - 38581*y^2 + 54289*z^2
(-2097/25345 : -29824/25345 : 1) C2a (-60422/4893 : -31/21 : 1)
** u= -65/37 ; C1 {+/-} -1450*x^2 + 5594*y^2 + 1954*z^2
(578/513 : 73/513 : 1) C2a (-425689/42821 : -25097/42821 : 1) C2b (111776/118989 : 7361/118989 : 1)
** u= -65/157 ; C1 -86650*x^2 - 28874*y^2 + 40834*z^2
(-182/3509 : -4161/3509 : 1) C2a (5599/33961 : -673/33961 : 1)
** u= -64/63 ; C1 -7813*x^2 + 8065*y^2 + 7937*z^2
(1763/1769 : -262/1769 : 1) C2b (-110603/164409 : 4139/164409 : 1)
** u= -64/67 ; C1 -9389*x^2 + 8585*y^2 + 8969*z^2
(-668/3487 : -3495/3487 : 1) C2b (-100891/239399 : 13013/239399 : 1)
** u= -64/97 ; C1 -26309*x^2 + 13505*y^2 + 17729*z^2
(-1991/7291 : 7878/7291 : 1) C2b (4099/91171 : -4687/91171 : 1)
** u= -64/109 ; C1 -35597*x^2 + 15977*y^2 + 21737*z^2
(22712/39425 : -31071/39425 : 1) C2b (26389/404603 : 17639/404603 : 1)
** u= -64/113 ; C1 -39013*x^2 + 16865*y^2 + 23137*z^2
(-10484/32157 : 34123/32157 : 1) C2b (-214181/763893 : -19447/763893 : 1)
** u= -64/123 ; C1 -48253*x^2 + 19225*y^2 + 26777*z^2
(1156/6379 : 36511/31895 : 1) C2b (-1991/19311 : 3193/96555 : 1)
** u= -63/155 ; C1 -85034*x^2 - 27994*y^2 + 39586*z^2
(-4674/12487 : -12415/12487 : 1) C2a (8117/152283 : 1777/152283 : 1)
** u= -63/163 ; C1 -95738*x^2 - 30538*y^2 + 43138*z^2
(-9422/32103 : -34315/32103 : 1) C2a (6533/26249 : -921/26249 : 1)
** u= -62/63 ; C1 -8065*x^2 - 7813*y^2 + 7937*z^2
(2155/2179 : 172/2179 : 1) C2a (253594/193055 : -21843/193055 : 1)
** u= -62/107 ; C1 -34553*x^2 - 15293*y^2 + 20873*z^2
(16415/34631 : -32064/34631 : 1) C2a (33638/46305 : -3413/46305 : 1)
** u= -62/149 ; C1 -77897*x^2 - 26045*y^2 + 36833*z^2
(-7099/11137 : 4968/11137 : 1) C2a (12174/239183 : -895/239183 : 1)
** u= -62/161 ; C1 -93521*x^2 - 29765*y^2 + 42041*z^2
(-2274/4111 : -2761/4111 : 1) C2a (-146974/38631 : -17615/38631 : 1)
** u= -62/163 ; C1 -96265*x^2 - 30413*y^2 + 42937*z^2
(215146/343217 : 140691/343217 : 1) C2a (66316/318167 : -10271/318167 : 1)
** u= -62/191 ; C1 -138881*x^2 - 40325*y^2 + 56321*z^2
(4382/18229 : 99747/91145 : 1) C2a (-7733802/4236763 : -931841/4236763 : 1)
** u= -61/89 ; C1 {+/-} -21610*x^2 + 11642*y^2 + 15058*z^2
(439/1497 : -1594/1497 : 1) C2a (70387/33515 : -7861/33515 : 1) C2b (-29134/94257 : 3827/94257 : 1)
** u= -61/97 ; C1 -27098*x^2 + 13130*y^2 + 17522*z^2
(-3366/14033 : -15473/14033 : 1) C2b (-58676/345173 : 15377/345173 : 1)
** u= -61/113 ; C1 -39994*x^2 + 16490*y^2 + 22834*z^2
(406/669 : -469/669 : 1) C2b (-363352/1204077 : -2297/172011 : 1)
** u= -61/137 ; C1 {+/-} -64138*x^2 + 22490*y^2 + 31762*z^2
(26773/39821 : -13974/39821 : 1) C2a (-24283/141301 : -973/141301 : 1) C2b (41902/275859 : 1855/275859 : 1)
** u= -61/193 ; C1 -142874*x^2 - 40970*y^2 + 57074*z^2
(6534/10349 : 563/10349 : 1) C2a (482429/39489 : 57389/39489 : 1)
** u= -60/37 ; C1 -1565*x^2 + 4969*y^2 + 2209*z^2
(-188/1629 : -1081/1629 : 1) C2b (477521/389959 : 57/8297 : 1)
** u= -60/91 ; C1 -23165*x^2 + 11881*y^2 + 15601*z^2
(-389/477 : -6658/51993 : 1) C2b (-469/2225 : -11043/242525 : 1)
** u= -59/47 ; C1 -3434*x^2 + 5690*y^2 + 4274*z^2
(-1773/1627 : -302/1627 : 1) C2b (20402/54197 : 3833/54197 : 1)
** u= -59/71 ; C1 -11930*x^2 - 8522*y^2 + 9938*z^2
(1601/2011 : -1062/2011 : 1) C2a (20107/6099 : -2153/6099 : 1)
** u= -59/143 ; C1 -71978*x^2 - 23930*y^2 + 33842*z^2
(-362/631 : 411/631 : 1) C2a (59/11763 : 53/11763 : 1)
** u= -58/47 ; C1 -3505*x^2 - 5573*y^2 + 4297*z^2
(-1487/5091 : -4312/5091 : 1) C2a (13054/4415 : -1103/4415 : 1)
** u= -58/51 ; C1 -4537*x^2 - 5965*y^2 + 5153*z^2
(-94/317 : 283/317 : 1) C2a (95468/118571 : 159/118571 : 1)
** u= -58/59 ; C1 -7081*x^2 - 6845*y^2 + 6961*z^2
(2/33 : 1229/1221 : 1) C2a (1922/77 : -7223/2849 : 1)
** u= -58/77 ; C1 -15145*x^2 - 9293*y^2 + 11497*z^2
(1318/4623 : 4859/4623 : 1) C2a (-245102/130841 : -26363/130841 : 1)
** u= -58/79 ; C1 -16241*x^2 - 9605*y^2 + 12041*z^2
(-3843/11623 : 12016/11623 : 1) C2a (-307722/225293 : -32195/225293 : 1)
** u= -58/159 ; C1 -92881*x^2 - 28645*y^2 + 40361*z^2
(-21863/79387 : -85616/79387 : 1) C2a (197486/794231 : 30759/794231 : 1)
** u= -56/37 ; C1 -1693*x^2 + 4505*y^2 + 2377*z^2
(-2384/5437 : 3669/5437 : 1) C2b (827/939 : -47/939 : 1)
** u= -56/83 ; C1 -18989*x^2 + 10025*y^2 + 13049*z^2
(300/487 : 1859/2435 : 1) C2b (-9251/551645 : 146029/2758225 : 1)
** u= -56/107 ; C1 -36413*x^2 + 14585*y^2 + 20297*z^2
(-40668/58939 : -26555/58939 : 1) C2b (-280031/1061843 : -18239/1061843 : 1)
** u= -56/125 ; C1 -53261*x^2 + 18761*y^2 + 26489*z^2
(1495/3827 : 3786/3827 : 1) C2b (147193/873415 : -1147/873415 : 1)
** u= -56/127 ; C1 -55333*x^2 + 19265*y^2 + 27217*z^2
(196/2567 : -3033/2567 : 1) C2b (-21737/2957631 : 53203/2957631 : 1)
** u= -56/131 ; C1 -59597*x^2 + 20297*y^2 + 28697*z^2
(-13744/20795 : 7533/20795 : 1) C2b (6257/138689 : -1597/138689 : 1)
** u= -55/43 ; C1 {+/-} -2810*x^2 + 4874*y^2 + 3554*z^2
(-825/967 : -538/967 : 1) C2a (651111/21019 : -55997/21019 : 1) C2b (-35114/46921 : 2101/46921 : 1)
** u= -54/47 ; C1 -3809*x^2 - 5125*y^2 + 4369*z^2
(1029/1139 : -2824/5695 : 1) C2a (-2566/1571 : 207/1571 : 1)
** u= -54/91 ; C1 -24665*x^2 - 11197*y^2 + 15193*z^2
(10707/14443 : 5524/14443 : 1) C2a (-35102/81579 : -1873/81579 : 1)
** u= -54/191 ; C1 -144065*x^2 - 39397*y^2 + 54193*z^2
(-12914/23121 : -11203/23121 : 1) C2a (360314/29695 : 42597/29695 : 1)
** u= -53/41 ; C1 -2522*x^2 - 4490*y^2 + 3218*z^2
(-7738/6989 : -1173/6989 : 1) C2a (-551/3 : 47/3 : 1)
** u= -53/65 ; C1 -10154*x^2 + 7034*y^2 + 8306*z^2
(-1214/1345 : 93/1345 : 1) C2b (-5248/10015 : -257/10015 : 1)
** u= -53/129 ; C1 -58666*x^2 - 19450*y^2 + 27506*z^2
(-431/5177 : -30554/25885 : 1) C2a (-1467/10471 : -941/52355 : 1)
** u= -52/27 ; C1 -733*x^2 + 3433*y^2 + 833*z^2
(1624/1675 : -343/1675 : 1) C2b (6263/10885 : -123/1555 : 1)
** u= -52/63 ; C1 -9445*x^2 + 6673*y^2 + 7817*z^2
(-6196/7543 : 3509/7543 : 1) C2b (-8057/51825 : 3167/51825 : 1)
** u= -52/73 ; C1 -14165*x^2 + 8033*y^2 + 10217*z^2
(2617/5071 : -4542/5071 : 1) C2b (-1199/106357 : -5957/106357 : 1)
** u= -52/81 ; C1 -18661*x^2 + 9265*y^2 + 12281*z^2
(10529/13159 : -2498/13159 : 1) C2b (-312047/1463953 : 63657/1463953 : 1)
** u= -52/95 ; C1 -28069*x^2 + 11729*y^2 + 16201*z^2
(-7579/10885 : -5118/10885 : 1) C2b (-2423/10233 : 281/10233 : 1)
** u= -52/119 ; C1 -48757*x^2 + 16865*y^2 + 23833*z^2
(-19352/28611 : 8609/28611 : 1) C2b (49737/668989 : 9397/668989 : 1)
** u= -52/125 ; C1 -54829*x^2 + 18329*y^2 + 25921*z^2
(-1288/11125 : 13041/11125 : 1) C2b (993/379477 : 11/2357 : 1)
** u= -51/31 ; C1 {+/-} -1082*x^2 + 3562*y^2 + 1522*z^2
(-242/903 : -575/903 : 1) C2a (-322763/181575 : 15043/181575 : 1) C2b (588/755 : -49/755 : 1)
** u= -50/27 ; C1 -745*x^2 - 3229*y^2 + 929*z^2
(845/959 : -316/959 : 1) C2a (84402/17005 : -4333/17005 : 1)
** u= -50/33 ; C1 -1345*x^2 - 3589*y^2 + 1889*z^2
(1654/3607 : -2413/3607 : 1) C2a (-50632/5963 : -3669/5963 : 1)
** u= -50/89 ; C1 -24305*x^2 - 10421*y^2 + 14321*z^2
(6993/9113 : 268/9113 : 1) C2a (-58034/30741 : 6737/30741 : 1)
** u= -50/113 ; C1 -43745*x^2 - 15269*y^2 + 21569*z^2
(-790/8683 : 10233/8683 : 1) C2a (-288924/392819 : -33827/392819 : 1)
** u= -50/161 ; C1 -99905*x^2 - 28421*y^2 + 39521*z^2
(-3623/47689 : 55824/47689 : 1) C2a (306048/367127 : 38711/367127 : 1)
** u= -50/169 ; C1 -111505*x^2 - 31061*y^2 + 42961*z^2
(-56849/361593 : 411388/361593 : 1) C2a (246938/834617 : 43579/834617 : 1)
** u= -50/189 ; C1 -143305*x^2 - 38221*y^2 + 52121*z^2
(1198/2207 : -1123/2207 : 1) C2a (144/104719 : 4567/104719 : 1)
** u= -49/29 ; C1 -922*x^2 - 3242*y^2 + 1282*z^2
(-1015/921 : -206/921 : 1) C2a (-3797/1909 : -181/1909 : 1)
** u= -49/69 ; C1 -12682*x^2 + 7162*y^2 + 9122*z^2
(65/5053 : -5702/5053 : 1) C2b (-40624/146775 : 6773/146775 : 1)
** u= -49/93 ; C1 {+/-} -27418*x^2 + 11050*y^2 + 15362*z^2
(1034/2065 : -9049/10325 : 1) C2a (75879/35095 : 44621/175475 : 1) C2b (-13528/52695 : 5179/263475 : 1)
** u= -48/43 ; C1 -3293*x^2 + 4153*y^2 + 3673*z^2
(108/1243 : -1165/1243 : 1) C2b (-153367/194191 : 213/194191 : 1)
** u= -48/59 ; C1 -8381*x^2 + 5785*y^2 + 6841*z^2
(1548/2227 : 91/131 : 1) C2b (50577/103127 : 3341/103127 : 1)
** u= -48/113 ; C1 -44453*x^2 + 15073*y^2 + 21313*z^2
(9965/46023 : -51982/46023 : 1) C2b (292991/3865427 : -26361/3865427 : 1)
** u= -47/35 ; C1 {+/-} -1754*x^2 + 3434*y^2 + 2306*z^2
(-390/379 : 137/379 : 1) C2a (-63309/21755 : 4933/21755 : 1) C2b (69484/73261 : -997/73261 : 1)
** u= -46/27 ; C1 -793*x^2 - 2845*y^2 + 1097*z^2
(-1453/1739 : 760/1739 : 1) C2a (-45882/1751 : -2867/1751 : 1)
** u= -46/45 ; C1 -3961*x^2 - 4141*y^2 + 4049*z^2
(7874/8015 : -1873/8015 : 1) C2a (130736/89209 : -11331/89209 : 1)
** u= -46/77 ; C1 -17593*x^2 - 8045*y^2 + 10897*z^2
(11218/23171 : 21261/23171 : 1) C2a (683188/303041 : 78923/303041 : 1)
** u= -46/109 ; C1 -41465*x^2 - 13997*y^2 + 19793*z^2
(22454/82963 : -90771/82963 : 1) C2a (69184/806997 : 2569/806997 : 1)
** u= -46/111 ; C1 -43297*x^2 - 14437*y^2 + 20417*z^2
(-25831/41399 : -20560/41399 : 1) C2a (-13086/317083 : -1487/317083 : 1)
** u= -46/119 ; C1 -51025*x^2 - 16277*y^2 + 22993*z^2
(22922/45165 : 7027/9033 : 1) C2a (6814/118513 : -2339/118513 : 1)
** u= -46/129 ; C1 -61585*x^2 - 18757*y^2 + 26393*z^2
(-4798/8467 : -5029/8467 : 1) C2a (2058/5219 : -283/5219 : 1)
** u= -46/143 ; C1 -78049*x^2 - 22565*y^2 + 31489*z^2
(-33214/77601 : 67733/77601 : 1) C2a (262/2063 : -77/2063 : 1)
** u= -46/165 ; C1 -107881*x^2 - 29341*y^2 + 40289*z^2
(-6437/32345 : 35836/32345 : 1) C2a (-424976/1766755 : 88767/1766755 : 1)
** u= -46/169 ; C1 -113825*x^2 - 30677*y^2 + 41993*z^2
(28266/118775 : 25571/23755 : 1) C2a (-4512/17591 : -131/2513 : 1)
** u= -45/169 ; C1 -114410*x^2 - 30586*y^2 + 41746*z^2
(16131/31181 : 18806/31181 : 1) C2a (73/687 : -31/687 : 1)
** u= -44/45 ; C1 -4141*x^2 + 3961*y^2 + 4049*z^2
(172/941 : -935/941 : 1) C2b (2653/33317 : 2331/33317 : 1)
** u= -44/79 ; C1 -19237*x^2 + 8177*y^2 + 11257*z^2
(2500/3403 : -1113/3403 : 1) C2b (2823/8809 : -127/8809 : 1)
** u= -44/103 ; C1 -36853*x^2 + 12545*y^2 + 17737*z^2
(18716/61167 : 65275/61167 : 1) C2b (4621/68793 : 665/68793 : 1)
** u= -43/55 ; C1 {+/-} -7514*x^2 + 4874*y^2 + 5906*z^2
(-4310/8143 : 423/479 : 1) C2a (-18459/9221 : -1969/9221 : 1) C2b (-1802/9665 : -553/9665 : 1)
** u= -43/119 ; C1 -52186*x^2 - 16010*y^2 + 22546*z^2
(-2641/9019 : -9582/9019 : 1) C2a (-7811/44879 : 1483/44879 : 1)
** u= -42/31 ; C1 -1361*x^2 - 2725*y^2 + 1801*z^2
(26/69 : -53/69 : 1) C2a (56068/52683 : -1865/52683 : 1)
** u= -42/43 ; C1 -3785*x^2 - 3613*y^2 + 3697*z^2
(3102/3181 : 523/3181 : 1) C2a (-16892/13471 : 1437/13471 : 1)
** u= -42/65 ; C1 -11969*x^2 - 5989*y^2 + 7921*z^2
(12282/28019 : -27145/28019 : 1) C2a (-302734/680939 : 81/7651 : 1)
** u= -42/79 ; C1 -19697*x^2 - 8005*y^2 + 11113*z^2
(9294/14393 : 8663/14393 : 1) C2a (43036/33447 : -4957/33447 : 1)
** u= -42/101 ; C1 -35801*x^2 - 11965*y^2 + 16921*z^2
(3813/10093 : 10028/10093 : 1) C2a (-31400038/128246097 : 3718595/128246097 : 1)
** u= -42/131 ; C1 -65561*x^2 - 18925*y^2 + 26401*z^2
(3663/9947 : 9568/9947 : 1) C2a (-30064/88977 : 23521/444885 : 1)
** u= -42/151 ; C1 -90401*x^2 - 24565*y^2 + 33721*z^2
(-1953/6827 : -120140/116059 : 1) C2a (172348/325203 : -415199/5528451 : 1)
** u= -42/173 ; C1 -122345*x^2 - 31693*y^2 + 42697*z^2
(8582/22803 : -20401/22803 : 1) C2a (1302824/60473 : 152391/60473 : 1)
** u= -41/37 ; C1 -2458*x^2 - 3050*y^2 + 2722*z^2
(89/513 : 478/513 : 1) C2a (-1103/599 : 95/599 : 1)
** u= -41/69 ; C1 {+/-} -14170*x^2 + 6442*y^2 + 8738*z^2
(3217/4153 : 794/4153 : 1) C2a (14493/30949 : 973/30949 : 1) C2b (11816/161877 : 7163/161877 : 1)
** u= -41/93 ; C1 -29674*x^2 - 10330*y^2 + 14594*z^2
(-2158/17257 : 20183/17257 : 1) C2a (-5127/1967 : -613/1967 : 1)
** u= -40/17 ; C1 -325*x^2 + 1889*y^2 + 49*z^2
(-329/1555 : 42/311 : 1) C2b (-1167/7357 : 89/1051 : 1)
** u= -40/51 ; C1 -6445*x^2 + 4201*y^2 + 5081*z^2
(-256/5299 : 5819/5299 : 1) C2b (99703/242263 : -9813/242263 : 1)
** u= -40/81 ; C1 -21445*x^2 + 8161*y^2 + 11441*z^2
(3107/4271 : -454/4271 : 1) C2b (-31969/135675 : 1687/135675 : 1)
** u= -39/115 ; C1 -49706*x^2 - 14746*y^2 + 20674*z^2
(-13350/30967 : -27271/30967 : 1) C2a (-4157/1053 : 497/1053 : 1)
** u= -39/139 ; C1 -76442*x^2 - 20842*y^2 + 28642*z^2
(4671/12679 : 11870/12679 : 1) C2a (-1057/1885 : 147/1885 : 1)
** u= -38/71 ; C1 -15857*x^2 - 6485*y^2 + 8993*z^2
(88826/141337 : 91701/141337 : 1) C2a (22296/1357 : 115/59 : 1)
** u= -38/77 ; C1 -19385*x^2 - 7373*y^2 + 10337*z^2
(-393/1333 : 1444/1333 : 1) C2a (-82984/5367 : -9899/5367 : 1)
** u= -38/81 ; C1 -21937*x^2 - 8005*y^2 + 11273*z^2
(-1879/2837 : -1288/2837 : 1) C2a (652/1789 : -63/1789 : 1)
** u= -38/91 ; C1 -29017*x^2 - 9725*y^2 + 13753*z^2
(1342/2017 : 3081/10085 : 1) C2a (1361252/5590337 : -795541/27951685 : 1)
** u= -38/99 ; C1 -35401*x^2 - 11245*y^2 + 15881*z^2
(-2506/3749 : 281/3749 : 1) C2a (136738/49333 : -16401/49333 : 1)
** u= -38/115 ; C1 -50089*x^2 - 14669*y^2 + 20521*z^2
(1369/9543 : -11000/9543 : 1) C2a (-173426/11141 : 20671/11141 : 1)
** u= -38/199 ; C1 -169201*x^2 - 41045*y^2 + 53281*z^2
(-98/1117 : 1257/1117 : 1) C2a (2733358/2096773 : -333145/2096773 : 1)
** u= -37/65 ; C1 {+/-} -12874*x^2 + 5594*y^2 + 7666*z^2
(238/4965 : -5801/4965 : 1) C2a (121781/89509 : 13861/89509 : 1) C2b (2126/15159 : 587/15159 : 1)
** u= -37/121 ; C1 -56666*x^2 - 16010*y^2 + 22226*z^2
(-6342/15193 : 13345/15193 : 1) C2a (-494883/632777 : -63245/632777 : 1)
** u= -37/145 ; C1 -85034*x^2 - 22394*y^2 + 30386*z^2
(-12951/21937 : 4010/21937 : 1) C2a (-210123/567593 : -35497/567593 : 1)
** u= -35/47 ; C1 {+/-} -5690*x^2 + 3434*y^2 + 4274*z^2
(-63/17083 : 19058/17083 : 1) C2a (-1068669/972661 : -105857/972661 : 1) C2b (-6826/15511 : 481/15511 : 1)
** u= -35/79 ; C1 {+/-} -21370*x^2 + 7466*y^2 + 10546*z^2
(9553/15707 : 9342/15707 : 1) C2a (19531/75359 : 1867/75359 : 1) C2b (-15938/268533 : -4643/268533 : 1)
** u= -35/87 ; C1 -26890*x^2 - 8794*y^2 + 12434*z^2
(9295/14711 : 6466/14711 : 1) C2a (-18471/222551 : -3487/222551 : 1)
** u= -35/199 ; C1 -171370*x^2 - 40826*y^2 + 52306*z^2
(-23518/47643 : -24217/47643 : 1) C2a (-594587/438545 : 71993/438545 : 1)
** u= -34/147 ; C1 -89209*x^2 - 22765*y^2 + 30449*z^2
(86/1289 : -1481/1289 : 1) C2a (-1659516/4352899 : 285617/4352899 : 1)
** u= -34/177 ; C1 -133729*x^2 - 32485*y^2 + 42209*z^2
(-54163/103957 : 44332/103957 : 1) C2a (-14636/46879 : 3009/46879 : 1)
** u= -33/29 ; C1 -1466*x^2 - 1930*y^2 + 1666*z^2
(-1638/1537 : -35/1537 : 1) C2a (-167227/37807 : -2199/5401 : 1)
** u= -33/37 ; C1 -3050*x^2 + 2458*y^2 + 2722*z^2
(-558/625 : -43/125 : 1) C2b (149824/550015 : -33141/550015 : 1)
** u= -33/53 ; C1 -8138*x^2 - 3898*y^2 + 5218*z^2
(1035/1457 : 778/1457 : 1) C2a (45163/88935 : -3067/88935 : 1)
** u= -33/109 ; C1 -46106*x^2 - 12970*y^2 + 17986*z^2
(4002/14273 : -15019/14273 : 1) C2a (-914059/900381 : 4939/39147 : 1)
** u= -32/17 ; C1 -293*x^2 + 1313*y^2 + 353*z^2
(-55/203 : 102/203 : 1) C2b (-131/175 : -13/175 : 1)
** u= -32/37 ; C1 -3133*x^2 + 2393*y^2 + 2713*z^2
(-3028/3837 : -2165/3837 : 1) C2b (-17/261 : -17/261 : 1)
** u= -32/67 ; C1 -14893*x^2 + 5513*y^2 + 7753*z^2
(-15077/130145 : -152334/130145 : 1) C2b (681/3923 : -71/3923 : 1)
** u= -32/77 ; C1 -20813*x^2 + 6953*y^2 + 9833*z^2
(-2328/6805 : 7019/6805 : 1) C2b (-2243/78001 : -173/78001 : 1)
** u= -31/51 ; C1 {+/-} -7642*x^2 + 3562*y^2 + 4802*z^2
(49/2111 : 2450/2111 : 1) C2a (57399/3577 : -137/73 : 1) C2b (-14176/49735 : -33/1015 : 1)
** u= -31/123 ; C1 -61354*x^2 - 16090*y^2 + 21794*z^2
(78842/237047 : 228929/237047 : 1) C2a (94087/132157 : 12561/132157 : 1)
** u= -30/47 ; C1 -6305*x^2 - 3109*y^2 + 4129*z^2
(618/901 : 551/901 : 1) C2a (-16072/7467 : -1829/7467 : 1)
** u= -30/173 ; C1 -129785*x^2 - 30829*y^2 + 39409*z^2
(59301/157721 : -130364/157721 : 1) C2a (-5520652/824277 : 630569/824277 : 1)
** u= -29/25 ; C1 {+/-} -1066*x^2 + 1466*y^2 + 1234*z^2
(-250/693 : -599/693 : 1) C2a (-77/17 : 7/17 : 1) C2b (-5642/14373 : -959/14373 : 1)
** u= -28/33 ; C1 -2533*x^2 + 1873*y^2 + 2153*z^2
(1340/1897 : -1307/1897 : 1) C2b (22507/38931 : -653/38931 : 1)
** u= -28/37 ; C1 -3485*x^2 + 2153*y^2 + 2657*z^2
(-288/361 : 163/361 : 1) C2b (7991/45655 : -2551/45655 : 1)
** u= -28/57 ; C1 -10645*x^2 + 4033*y^2 + 5657*z^2
(-541/1763 : 1894/1763 : 1) C2b (-10849/89595 : 2381/89595 : 1)
** u= -28/59 ; C1 -11581*x^2 + 4265*y^2 + 6001*z^2
(1867/19053 : 22390/19053 : 1) C2b (-1851/45581 : 1205/45581 : 1)
** u= -26/11 ; C1 -137*x^2 - 797*y^2 + 17*z^2
(-25/179 : -24/179 : 1) C2a (16366/1233 : -217/1233 : 1)
** u= -26/19 ; C1 -505*x^2 - 1037*y^2 + 673*z^2
(-481/723 : -476/723 : 1) C2a (19634/19783 : 209/19783 : 1)
** u= -26/37 ; C1 -3673*x^2 - 2045*y^2 + 2617*z^2
(181/2157 : 2428/2157 : 1) C2a (23386/18527 : -2461/18527 : 1)
** u= -26/49 ; C1 -7585*x^2 - 3077*y^2 + 4273*z^2
(-257/6777 : 7976/6777 : 1) C2a (121474/345943 : -6749/345943 : 1)
** u= -26/61 ; C1 -12937*x^2 - 4397*y^2 + 6217*z^2
(-491/3165 : -3668/3165 : 1) C2a (-37532/21751 : 4489/21751 : 1)
** u= -26/67 ; C1 -16153*x^2 - 5165*y^2 + 7297*z^2
(127/539 : 600/539 : 1) C2a (-277964/366907 : -33937/366907 : 1)
** u= -26/139 ; C1 -82825*x^2 - 19997*y^2 + 25873*z^2
(1409/2595 : -140/519 : 1) C2a (-470554/112793 : 54271/112793 : 1)
** u= -26/161 ; C1 -113537*x^2 - 26597*y^2 + 33617*z^2
(35207/82385 : 57336/82385 : 1) C2a (-1146/8125 : -479/8125 : 1)
** u= -26/163 ; C1 -116569*x^2 - 27245*y^2 + 34369*z^2
(-24466/51009 : 26855/51009 : 1) C2a (-139196/753209 : 45707/753209 : 1)
** u= -26/191 ; C1 -163217*x^2 - 37157*y^2 + 45737*z^2
(-6849/27155 : 26488/27155 : 1) C2a (-2968/29535 : 1787/29535 : 1)
** u= -25/29 ; C1 {+/-} -1930*x^2 + 1466*y^2 + 1666*z^2
(-931/1009 : -126/1009 : 1) C2a (7609/7519 : -653/7519 : 1) C2b (-10952/39753 : 331/5679 : 1)
** u= -25/69 ; C1 -17530*x^2 - 5386*y^2 + 7586*z^2
(-1603/4637 : 4682/4637 : 1) C2a (-11607/13373 : 1429/13373 : 1)
** u= -25/157 ; C1 -108170*x^2 - 25274*y^2 + 31874*z^2
(-1026/1909 : -301/1909 : 1) C2a (106673/109527 : -13589/109527 : 1)
** u= -24/17 ; C1 -389*x^2 + 865*y^2 + 529*z^2
(736/969 : 575/969 : 1) C2b (1749/2231 : 5/97 : 1)
** u= -23/75 ; C1 -21754*x^2 - 6154*y^2 + 8546*z^2
(667/3131 : 3470/3131 : 1) C2a (47537/107567 : 6897/107567 : 1)
** u= -23/107 ; C1 -47930*x^2 - 11978*y^2 + 15842*z^2
(-5874/29747 : 32129/29747 : 1) C2a (-551589/444377 : -761/4993 : 1)
** u= -23/155 ; C1 -106394*x^2 - 24554*y^2 + 30626*z^2
(14743/28159 : -6870/28159 : 1) C2a (-132363/70505 : -15449/70505 : 1)
** u= -22/13 ; C1 -185*x^2 - 653*y^2 + 257*z^2
(-162/139 : -13/139 : 1) C2a (-5166/3707 : 109/3707 : 1)
** u= -22/21 ; C1 -841*x^2 - 925*y^2 + 881*z^2
(17/29 : 4/5 : 1) C2a (1434/1787 : -271/8935 : 1)
** u= -22/35 ; C1 -3529*x^2 - 1709*y^2 + 2281*z^2
(-2270/4017 : -3301/4017 : 1) C2a (418276/72035 : -48563/72035 : 1)
** u= -22/41 ; C1 -5281*x^2 - 2165*y^2 + 3001*z^2
(2419/3209 : -24/3209 : 1) C2a (19166/34471 : 1865/34471 : 1)
** u= -22/47 ; C1 -7393*x^2 - 2693*y^2 + 3793*z^2
(3719/7135 : -5808/7135 : 1) C2a (89594/195313 : 9493/195313 : 1)
** u= -22/57 ; C1 -11713*x^2 - 3733*y^2 + 5273*z^2
(-970/1447 : -73/1447 : 1) C2a (-8546/65303 : 1593/65303 : 1)
** u= -22/71 ; C1 -19441*x^2 - 5525*y^2 + 7681*z^2
(-3598/5725 : -579/28625 : 1) C2a (73820/91439 : 46883/457195 : 1)
** u= -22/89 ; C1 -32257*x^2 - 8405*y^2 + 11353*z^2
(614/1783 : -69183/73103 : 1) C2a (2488/301 : 11959/12341 : 1)
** u= -22/91 ; C1 -33881*x^2 - 8765*y^2 + 11801*z^2
(-1326/4261 : -4201/4261 : 1) C2a (-18748/63627 : -3701/63627 : 1)
** u= -22/101 ; C1 -42601*x^2 - 10685*y^2 + 14161*z^2
(-18683/32993 : -7140/32993 : 1) C2a (66628/6307 : 65/53 : 1)
** u= -22/113 ; C1 -54385*x^2 - 13253*y^2 + 17257*z^2
(-22367/41469 : -13648/41469 : 1) C2a (2238284/866267 : 261401/866267 : 1)
** u= -22/145 ; C1 -92849*x^2 - 21509*y^2 + 26921*z^2
(30531/56753 : -2740/56753 : 1) C2a (-4182/23005 : 1411/23005 : 1)
** u= -22/195 ; C1 -173449*x^2 - 38509*y^2 + 46121*z^2
(12914/26657 : 9995/26657 : 1) C2a (-1136306/1545851 : -157551/1545851 : 1)
** u= -21/137 ; C1 -82778*x^2 - 19210*y^2 + 24082*z^2
(11014/21873 : -8777/21873 : 1) C2a (-524933/66789 : -59345/66789 : 1)
** u= -20/21 ; C1 -925*x^2 + 841*y^2 + 881*z^2
(89/95 : -158/551 : 1) C2b (-1093/2103 : -2693/60987 : 1)
** u= -20/27 ; C1 -1885*x^2 + 1129*y^2 + 1409*z^2
(41/73 : 62/73 : 1) C2b (3613/45645 : -2621/45645 : 1)
** u= -20/29 ; C1 -2285*x^2 + 1241*y^2 + 1601*z^2
(456/869 : 769/869 : 1) C2b (-78709/199381 : 5981/199381 : 1)
** u= -19/39 ; C1 -5002*x^2 - 1882*y^2 + 2642*z^2
(1087/1783 : 1150/1783 : 1) C2a (-387/1429 : -19/1429 : 1)
** u= -19/63 ; C1 -15418*x^2 - 4330*y^2 + 6002*z^2
(1042/2879 : 2761/2879 : 1) C2a (627/16129 : 613/16129 : 1)
** u= -19/135 ; C1 -81226*x^2 - 18586*y^2 + 22994*z^2
(-8125/32107 : 31414/32107 : 1) C2a (-2493253/1270805 : -289299/1270805 : 1)
** u= -18/25 ; C1 -1649*x^2 - 949*y^2 + 1201*z^2
(42/1019 : -1145/1019 : 1) C2a (-55976/19005 : -6253/19005 : 1)
** u= -18/101 ; C1 -44057*x^2 - 10525*y^2 + 13513*z^2
(-139/381 : 1624/1905 : 1) C2a (1045486/459231 : -609959/2296155 : 1)
** u= -18/115 ; C1 -58169*x^2 - 13549*y^2 + 17041*z^2
(1210/3273 : 2681/3273 : 1) C2a (228776/574689 : -41861/574689 : 1)
** u= -18/199 ; C1 -184001*x^2 - 39925*y^2 + 46441*z^2
(-5254/24657 : 120413/123285 : 1) C2a (-1840094/4435717 : 1734351/22178585 : 1)
** u= -17/77 ; C1 -24698*x^2 - 6218*y^2 + 8258*z^2
(9355/23437 : 19542/23437 : 1) C2a (-110013/66061 : -13189/66061 : 1)
** u= -17/165 ; C1 -125194*x^2 - 27514*y^2 + 32546*z^2
(20087/39445 : 2126/39445 : 1) C2a (5375833/70625 : 589131/70625 : 1)
** u= -16/7 ; C1 -53*x^2 + 305*y^2 + 17*z^2
(36/67 : 5/67 : 1) C2b (1721/907 : 65/907 : 1)
** u= -16/21 ; C1 -1117*x^2 + 697*y^2 + 857*z^2
(-337/2083 : -2270/2083 : 1) C2b (-5903/49169 : -2853/49169 : 1)
** u= -15/19 ; C1 -890*x^2 - 586*y^2 + 706*z^2
(-9/79 : -86/79 : 1) C2a (-10667/1305 : -1177/1305 : 1)
** u= -15/187 ; C1 -163850*x^2 - 35194*y^2 + 40354*z^2
(-4182/24643 : 24797/24643 : 1) C2a (3781/2819 : 447/2819 : 1)
** u= -14/11 ; C1 -185*x^2 - 317*y^2 + 233*z^2
(49/71 : -48/71 : 1) C2a (319792/25401 : -27553/25401 : 1)
** u= -14/23 ; C1 -1553*x^2 - 725*y^2 + 977*z^2
(-6/49 : -281/245 : 1) C2a (12278/4149 : -1423/4149 : 1)
** u= -14/51 ; C1 -10345*x^2 - 2797*y^2 + 3833*z^2
(1450/5933 : -6361/5933 : 1) C2a (35616/337 : -4201/337 : 1)
** u= -14/55 ; C1 -12241*x^2 - 3221*y^2 + 4369*z^2
(3494/6177 : -2315/6177 : 1) C2a (2516/72679 : 3289/72679 : 1)
** u= -14/75 ; C1 -24121*x^2 - 5821*y^2 + 7529*z^2
(2195/23051 : -25832/23051 : 1) C2a (-22602/2317 : -2593/2317 : 1)
** u= -14/85 ; C1 -31561*x^2 - 7421*y^2 + 9409*z^2
(4850/53379 : -59267/53379 : 1) C2a (81682/56357 : -101/581 : 1)
** u= -14/103 ; C1 -47473*x^2 - 10805*y^2 + 13297*z^2
(-8386/16357 : 4503/16357 : 1) C2a (-2114/12587 : 785/12587 : 1)
** u= -14/121 ; C1 -66625*x^2 - 14837*y^2 + 17833*z^2
(-7358/27415 : 5139/5483 : 1) C2a (17836/355325 : 21943/355325 : 1)
** u= -14/127 ; C1 -73729*x^2 - 16325*y^2 + 19489*z^2
(1442/3761 : 13689/18805 : 1) C2a (56764/464803 : 147521/2324015 : 1)
** u= -14/149 ; C1 -102857*x^2 - 22397*y^2 + 26177*z^2
(-21575/54421 : -36384/54421 : 1) C2a (-64036/51255 : 7699/51255 : 1)
** u= -13/57 ; C1 -13450*x^2 - 3418*y^2 + 4562*z^2
(-6158/14825 : -2401/2965 : 1) C2a (-8777/31091 : -1827/31091 : 1)
** u= -12/19 ; C1 -1037*x^2 + 505*y^2 + 673*z^2
(-352/471 : 203/471 : 1) C2b (-5013/22829 : -955/22829 : 1)
** u= -11/63 ; C1 -17194*x^2 - 4090*y^2 + 5234*z^2
(134/1831 : 2053/1831 : 1) C2a (21952663/124034993 : -7298679/124034993 : 1)
** u= -10/17 ; C1 -865*x^2 - 389*y^2 + 529*z^2
(575/969 : 736/969 : 1) C2a (-3092/7337 : 7/319 : 1)
** u= -10/29 ; C1 -3145*x^2 - 941*y^2 + 1321*z^2
(16693/30597 : -19568/30597 : 1) C2a (-1156/3191 : -167/3191 : 1)
** u= -10/41 ; C1 -6865*x^2 - 1781*y^2 + 2401*z^2
(1519/2761 : -1176/2761 : 1) C2a (1174/5411 : -41/773 : 1)
** u= -10/43 ; C1 -7625*x^2 - 1949*y^2 + 2609*z^2
(1923/13895 : 3124/2779 : 1) C2a (2586/3571 : 347/3571 : 1)
** u= -10/113 ; C1 -59425*x^2 - 12869*y^2 + 14929*z^2
(542/1519 : 1149/1519 : 1) C2a (70072/237127 : 16991/237127 : 1)
** u= -10/123 ; C1 -70825*x^2 - 15229*y^2 + 17489*z^2
(78538/167365 : 11801/33473 : 1) C2a (265256/387685 : 38079/387685 : 1)
** u= -10/143 ; C1 -96625*x^2 - 20549*y^2 + 23209*z^2
(-1346/4065 : 637/813 : 1) C2a (2543152/290435 : -272993/290435 : 1)
** u= -9/37 ; C1 -5594*x^2 - 1450*y^2 + 1954*z^2
(147/341 : 1354/1705 : 1) C2a (-737/651 : 457/3255 : 1)
** u= -9/173 ; C1 -143498*x^2 - 30010*y^2 + 32962*z^2
(11811/35777 : 27182/35777 : 1) C2a (229361/620517 : -48247/620517 : 1)
** u= -8/11 ; C1 -317*x^2 + 185*y^2 + 233*z^2
(-67/641 : -714/641 : 1) C2b (23147/53989 : -1633/53989 : 1)
** u= -7/27 ; C1 -2938*x^2 - 778*y^2 + 1058*z^2
(23/55 : 46/55 : 1) C2a (6247/11615 : -39/505 : 1)
** u= -7/43 ; C1 -8090*x^2 - 1898*y^2 + 2402*z^2
(210/551 : 443/551 : 1) C2a (390519/153235 : -45107/153235 : 1)
** u= -7/139 ; C1 -92762*x^2 - 19370*y^2 + 21218*z^2
(19467/42019 : -10918/42019 : 1) C2a (-3123/19261 : 13/187 : 1)
** u= -7/171 ; C1 -141466*x^2 - 29290*y^2 + 31586*z^2
(-338/827 : -431/827 : 1) C2a (-5087/14743 : 1137/14743 : 1)
** u= -6/5 ; C1 -41*x^2 - 61*y^2 + 49*z^2
(42/199 : -175/199 : 1) C2a (-362/135 : 31/135 : 1)
** u= -6/41 ; C1 -7457*x^2 - 1717*y^2 + 2137*z^2
(550/2019 : 1939/2019 : 1) C2a (12814/4763 : -1467/4763 : 1)
** u= -6/49 ; C1 -10865*x^2 - 2437*y^2 + 2953*z^2
(47/837 : 916/837 : 1) C2a (-42512/40031 : 5307/40031 : 1)
** u= -6/65 ; C1 -19601*x^2 - 4261*y^2 + 4969*z^2
(-4278/9031 : 3305/9031 : 1) C2a (2671436/150189 : -290831/150189 : 1)
** u= -6/115 ; C1 -63401*x^2 - 13261*y^2 + 14569*z^2
(-19219/40587 : 6620/40587 : 1) C2a (-21561106/12168469 : 2419599/12168469 : 1)
** u= -6/181 ; C1 -159497*x^2 - 32797*y^2 + 34897*z^2
(-5789/43689 : 43220/43689 : 1) C2a (1747318/1895419 : -223539/1895419 : 1)
** u= -5/161 ; C1 -126410*x^2 - 25946*y^2 + 27506*z^2
(34890/81589 : 33559/81589 : 1) C2a (48667/87525 : -7867/87525 : 1)
** u= -4/5 ; C1 -61*x^2 + 41*y^2 + 49*z^2
(-175/199 : 42/199 : 1) C2b (207/385 : -1/55 : 1)
** u= -2/3 ; C1 -25*x^2 - 13*y^2 + 17*z^2
(-2/5 : -1 : 1) C2a (-1474/2113 : 129/2113 : 1)
** u= -2/17 ; C1 -1313*x^2 - 293*y^2 + 353*z^2
(291/605 : -248/605 : 1) C2a (-1308/3929 : 281/3929 : 1)
** u= -2/27 ; C1 -3433*x^2 - 733*y^2 + 833*z^2
(-889/2995 : -2548/2995 : 1) C2a (-566/13783 : 129/1969 : 1)
** u= -2/89 ; C1 -38897*x^2 - 7925*y^2 + 8273*z^2
(90/343 : 1441/1715 : 1) C2a (2218834/72855 : -1142393/364275 : 1)
** u= -2/147 ; C1 -106873*x^2 - 21613*y^2 + 22193*z^2
(16603/59015 : 47044/59015 : 1) C2a (109744/676217 : 48813/676217 : 1)
** u= -2/161 ; C1 -128321*x^2 - 25925*y^2 + 26561*z^2
(2746/12251 : 10791/12251 : 1) C2a (3192916/502893 : 1637759/2514465 : 1)
** u= -1/5 ; C1 -106*x^2 - 26*y^2 + 34*z^2
(22/41 : 15/41 : 1) C2a (163/55 : -19/55 : 1)
** u= -1/85 ; C1 -35786*x^2 - 7226*y^2 + 7394*z^2
(-510/3109 : 2933/3109 : 1) C2a (63317/43827 : -7153/43827 : 1)
** u= -1/117 ; C1 -67978*x^2 - 13690*y^2 + 13922*z^2
(1/13 : -478/481 : 1) C2a (-31/97 : -279/3589 : 1)
** u= -1/125 ; C1 -77626*x^2 - 15626*y^2 + 15874*z^2
(545/60857 : -61326/60857 : 1) C2a (-52589/132031 : 10751/132031 : 1)
** u= -1/173 ; C1 -148954*x^2 - 29930*y^2 + 30274*z^2
(-649/3801 : 3538/3801 : 1) C2a (-4777/4433 : -577/4433 : 1)
** u= 1/11 ; C1 -650*x^2 - 122*y^2 + 98*z^2
(21/95 : 14/19 : 1) C2a (-677/609 : 11/87 : 1)
** u= 1/43 ; C1 -9418*x^2 - 1850*y^2 + 1762*z^2
(82/219 : -107/219 : 1) C2a (2669/6191 : -2609/30955 : 1)
** u= 1/91 ; C1 -41770*x^2 - 8282*y^2 + 8098*z^2
(-1469/3839 : -1878/3839 : 1) C2a (-250153/70055 : -25429/70055 : 1)
** u= 2/27 ; C1 -3865*x^2 - 733*y^2 + 617*z^2
(-218/1673 : -1451/1673 : 1) C2a (-10584/8423 : -1169/8423 : 1)
** u= 2/31 ; C1 -5057*x^2 - 965*y^2 + 833*z^2
(1057/3071 : 1512/3071 : 1) C2a (-476/2463 : -191/2463 : 1)
** u= 2/39 ; C1 -7921*x^2 - 1525*y^2 + 1361*z^2
(-478/1157 : -1/13 : 1) C2a (2578/5255 : -2313/26275 : 1)
** u= 2/89 ; C1 -40321*x^2 - 7925*y^2 + 7561*z^2
(-358/911 : -1869/4555 : 1) C2a (184/79 : 19/79 : 1)
** u= 2/93 ; C1 -43993*x^2 - 8653*y^2 + 8273*z^2
(22205/57809 : -26236/57809 : 1) C2a (59808/15629 : -6001/15629 : 1)
** u= 2/95 ; C1 -45889*x^2 - 9029*y^2 + 8641*z^2
(-1655/17847 : -17056/17847 : 1) C2a (-299564/92311 : -30281/92311 : 1)
** u= 2/109 ; C1 -60281*x^2 - 11885*y^2 + 11441*z^2
(-14298/32827 : -683/32827 : 1) C2a (934/102159 : 7409/102159 : 1)
** u= 2/147 ; C1 -109225*x^2 - 21613*y^2 + 21017*z^2
(1387/3299 : -928/3299 : 1) C2a (59412/123295 : -10681/123295 : 1)
** u= 2/151 ; C1 -115217*x^2 - 22805*y^2 + 22193*z^2
(28329/67367 : 656/2323 : 1) C2a (49724/40143 : 5729/40143 : 1)
** u= 3/25 ; C1 -3434*x^2 - 634*y^2 + 466*z^2
(90/977 : -811/977 : 1) C2a (-30629/6269 : 2691/6269 : 1)
** u= 6/41 ; C1 -9425*x^2 - 1717*y^2 + 1153*z^2
(94/5175 : -847/1035 : 1) C2a (-13832/19245 : 1909/19245 : 1)
** u= 6/47 ; C1 -12209*x^2 - 2245*y^2 + 1609*z^2
(-5026/14289 : -2993/14289 : 1) C2a (3286/2091 : -325/2091 : 1)
** u= 6/49 ; C1 -13217*x^2 - 2437*y^2 + 1777*z^2
(-1210/7047 : -5317/7047 : 1) C2a (-568352/251161 : -52719/251161 : 1)
** u= 6/61 ; C1 -20105*x^2 - 3757*y^2 + 2953*z^2
(-174/659 : 7199/11203 : 1) C2a (-274/553 : -837/9401 : 1)
** u= 6/115 ; C1 -68921*x^2 - 13261*y^2 + 11809*z^2
(-35175/85403 : 196/2083 : 1) C2a (-19316/1701 : 263/243 : 1)
** u= 6/127 ; C1 -83729*x^2 - 16165*y^2 + 14569*z^2
(4031/9771 : 1372/9771 : 1) C2a (604804/18471 : 57869/18471 : 1)
** u= 6/181 ; C1 -168185*x^2 - 32797*y^2 + 30553*z^2
(27387/70333 : 27604/70333 : 1) C2a (-2252314/76627 : 219111/76627 : 1)
** u= 7/45 ; C1 -11434*x^2 - 2074*y^2 + 1346*z^2
(-118/1085 : 829/1085 : 1) C2a (12809/8711 : -1251/8711 : 1)
** u= 7/101 ; C1 -53882*x^2 - 10250*y^2 + 8738*z^2
(126/317 : -47/317 : 1) C2a (18837/8339 : -9313/41695 : 1)
** u= 7/109 ; C1 -62506*x^2 - 11930*y^2 + 10306*z^2
(-3221/8929 : 3810/8929 : 1) C2a (-28913/104477 : 8329/104477 : 1)
** u= 9/35 ; C1 -7466*x^2 - 1306*y^2 + 514*z^2
(186/755 : -163/755 : 1) C2a (-3443/1735 : 261/1735 : 1)
** u= 9/187 ; C1 -181658*x^2 - 35050*y^2 + 31522*z^2
(1255/15759 : -73346/78795 : 1) C2a (83455/29431 : 41349/147155 : 1)
** u= 10/39 ; C1 -9265*x^2 - 1621*y^2 + 641*z^2
(-406/2713 : 1403/2713 : 1) C2a (-27318/3773 : 1759/3773 : 1)
** u= 10/41 ; C1 -10145*x^2 - 1781*y^2 + 761*z^2
(-1075/22033 : -14172/22033 : 1) C2a (-186886/114531 : -15533/114531 : 1)
** u= 10/61 ; C1 -21145*x^2 - 3821*y^2 + 2401*z^2
(-4606/25019 : 16611/25019 : 1) C2a (-6718/637 : -11/13 : 1)
** u= 10/63 ; C1 -22465*x^2 - 4069*y^2 + 2609*z^2
(-173/4579 : -3644/4579 : 1) C2a (-440406/1801 : 35533/1801 : 1)
** u= 10/123 ; C1 -80665*x^2 - 15229*y^2 + 12569*z^2
(5066/21317 : 15463/21317 : 1) C2a (-58248/46813 : -6419/46813 : 1)
** u= 10/143 ; C1 -108065*x^2 - 20549*y^2 + 17489*z^2
(-3258/10453 : -6097/10453 : 1) C2a (206184/418189 : -37013/418189 : 1)
** u= 11/73 ; C1 -29978*x^2 - 5450*y^2 + 3602*z^2
(630/3541 : 12353/17705 : 1) C2a (76365/7709 : -31427/38545 : 1)
** u= 11/105 ; C1 -59866*x^2 - 11146*y^2 + 8594*z^2
(-4055/14893 : -9094/14893 : 1) C2a (64433/13277 : -5793/13277 : 1)
** u= 14/51 ; C1 -16057*x^2 - 2797*y^2 + 977*z^2
(-1535/9451 : 4204/9451 : 1) C2a (217148/302369 : 28341/302369 : 1)
** u= 14/55 ; C1 -18401*x^2 - 3221*y^2 + 1289*z^2
(350/18301 : -11547/18301 : 1) C2a (-344946/887801 : 76879/887801 : 1)
** u= 14/75 ; C1 -32521*x^2 - 5821*y^2 + 3329*z^2
(-9970/46369 : -25967/46369 : 1) C2a (-195514/49541 : -15429/49541 : 1)
** u= 14/79 ; C1 -35825*x^2 - 6437*y^2 + 3833*z^2
(702/4501 : -3053/4501 : 1) C2a (-15612342/667345 : 1215079/667345 : 1)
** u= 14/85 ; C1 -41081*x^2 - 7421*y^2 + 4649*z^2
(5331/21205 : -11152/21205 : 1) C2a (1796634/395989 : -146761/395989 : 1)
** u= 14/103 ; C1 -59009*x^2 - 10805*y^2 + 7529*z^2
(-5103/26987 : 19112/26987 : 1) C2a (29806/38211 : -3925/38211 : 1)
** u= 14/121 ; C1 -80177*x^2 - 14837*y^2 + 11057*z^2
(38414/109591 : -31245/109591 : 1) C2a (116522/80541 : 11929/80541 : 1)
** u= 14/127 ; C1 -87953*x^2 - 16325*y^2 + 12377*z^2
(-1521/6707 : -4652/6707 : 1) C2a (512740/37611 : -225397/188055 : 1)
** u= 14/149 ; C1 -119545*x^2 - 22397*y^2 + 17833*z^2
(7867/71061 : 60748/71061 : 1) C2a (42026/14903 : 3949/14903 : 1)
** u= 15/37 ; C1 -9290*x^2 - 1594*y^2 + 34*z^2
(206/4533 : -437/4533 : 1) C2a (96467/753 : -1421/753 : 1)
** u= 17/83 ; C1 -40378*x^2 - 7178*y^2 + 3778*z^2
(1015/8511 : -5686/8511 : 1) C2a (103/22921 : -1871/22921 : 1)
** u= 18/95 ; C1 -52289*x^2 - 9349*y^2 + 5281*z^2
(-6453/61211 : -43400/61211 : 1) C2a (3156004/130575 : -239233/130575 : 1)
** u= 18/101 ; C1 -58601*x^2 - 10525*y^2 + 6241*z^2
(-2607/20045 : 70784/100225 : 1) C2a (38690/10191 : -197/645 : 1)
** u= 18/115 ; C1 -74729*x^2 - 13549*y^2 + 8761*z^2
(12310/36033 : 1939/36033 : 1) C2a (141506/20271 : -11579/20271 : 1)
** u= 18/151 ; C1 -125201*x^2 - 23125*y^2 + 17041*z^2
(1009/6471 : -25172/32355 : 1) C2a (6694/7083 : -20041/177075 : 1)
** u= 18/169 ; C1 -155297*x^2 - 28885*y^2 + 22153*z^2
(523809/1393133 : -115484/1393133 : 1) C2a (-298546/515073 : -47897/515073 : 1)
** u= 18/199 ; C1 -212657*x^2 - 39925*y^2 + 32113*z^2
(-5235/33331 : 136712/166655 : 1) C2a (636106/108123 : 58079/108123 : 1)
** u= 19/73 ; C1 -32554*x^2 - 5690*y^2 + 2194*z^2
(142/733 : -303/733 : 1) C2a (9350467/5019013 : 718501/5019013 : 1)
** u= 21/167 ; C1 -153914*x^2 - 28330*y^2 + 20434*z^2
(-7698/21547 : -3595/21547 : 1) C2a (664679/300359 : 61581/300359 : 1)
** u= 22/57 ; C1 -21745*x^2 - 3733*y^2 + 257*z^2
(-482/4663 : -379/4663 : 1) C2a (230422/44185 : 7149/44185 : 1)
** u= 22/71 ; C1 -31937*x^2 - 5525*y^2 + 1433*z^2
(254/1493 : 453/1493 : 1) C2a (-4696/6057 : -563/6057 : 1)
** u= 22/91 ; C1 -49897*x^2 - 8765*y^2 + 3793*z^2
(1447/6371 : -2376/6371 : 1) C2a (-37054/33587 : 3707/33587 : 1)
** u= 22/101 ; C1 -60377*x^2 - 10685*y^2 + 5273*z^2
(414/8227 : -5695/8227 : 1) C2a (2492574/1893067 : 235025/1893067 : 1)
** u= 22/145 ; C1 -118369*x^2 - 21509*y^2 + 14161*z^2
(-595/2461 : 1428/2461 : 1) C2a (-510662/113645 : -359/955 : 1)
** u= 22/195 ; C1 -207769*x^2 - 38509*y^2 + 28961*z^2
(-298910/1249693 : -832139/1249693 : 1) C2a (-5294906/1989259 : -487971/1989259 : 1)
** u= 23/77 ; C1 -37258*x^2 - 6458*y^2 + 1858*z^2
(554/2845 : -747/2845 : 1) C2a (-2213/2245 : -223/2245 : 1)
** u= 23/189 ; C1 -196522*x^2 - 36250*y^2 + 26498*z^2
(-262/1265 : 22327/31625 : 1) C2a (561/313 : -271/1565 : 1)
** u= 26/73 ; C1 -34913*x^2 - 6005*y^2 + 857*z^2
(3459/23113 : 2584/23113 : 1) C2a (16032/4499 : 719/4499 : 1)
** u= 26/89 ; C1 -49537*x^2 - 8597*y^2 + 2617*z^2
(-1546/37255 : 20217/37255 : 1) C2a (-201248/104231 : -14189/104231 : 1)
** u= 26/101 ; C1 -62185*x^2 - 10877*y^2 + 4273*z^2
(-3322/15243 : -5309/15243 : 1) C2a (-10642/19939 : 1787/19939 : 1)
** u= 26/139 ; C1 -111737*x^2 - 19997*y^2 + 11417*z^2
(9695/50927 : -30912/50927 : 1) C2a (226322/202209 : 3397/28887 : 1)
** u= 26/163 ; C1 -150473*x^2 - 27245*y^2 + 17417*z^2
(-41877/155531 : 76016/155531 : 1) C2a (-31386/6473 : 2581/6473 : 1)
** u= 26/191 ; C1 -202945*x^2 - 37157*y^2 + 25873*z^2
(-74081/291999 : 171452/291999 : 1) C2a (73838054/611447 : -6208381/611447 : 1)
** u= 26/199 ; C1 -219377*x^2 - 40277*y^2 + 28577*z^2
(-28782/110957 : -64985/110957 : 1) C2a (546288/99835 : 1147/2435 : 1)
** u= 29/119 ; C1 -85450*x^2 - 15002*y^2 + 6418*z^2
(-509/2475 : -214/495 : 1) C2a (-5189753/1111631 : -354167/1111631 : 1)
** u= 30/89 ; C1 -51185*x^2 - 8821*y^2 + 1681*z^2
(-1722/10727 : -2173/10727 : 1) C2a (900682/224557 : 1071/5477 : 1)
** u= 30/151 ; C1 -133025*x^2 - 23701*y^2 + 12841*z^2
(-62587/203415 : 4160/40683 : 1) C2a (24608/25573 : -2769/25573 : 1)
** u= 30/173 ; C1 -171305*x^2 - 30829*y^2 + 18649*z^2
(-9638/29499 : 3199/29499 : 1) C2a (-2885968/1213155 : -246373/1213155 : 1)
** u= 31/109 ; C1 -73882*x^2 - 12842*y^2 + 4162*z^2
(-86/405 : -103/405 : 1) C2a (101/47 : 7/47 : 1)
** u= 31/125 ; C1 -94586*x^2 - 16586*y^2 + 6914*z^2
(-4195/17509 : 5238/17509 : 1) C2a (-210519/181589 : 20341/181589 : 1)
** u= 31/149 ; C1 -130442*x^2 - 23162*y^2 + 12002*z^2
(-2025/8053 : 3242/8053 : 1) C2a (357/509 : -49/509 : 1)
** u= 31/157 ; C1 -143674*x^2 - 25610*y^2 + 13954*z^2
(4037/13517 : -2850/13517 : 1) C2a (-61/11 : -911/2167 : 1)
** u= 34/113 ; C1 -80369*x^2 - 13925*y^2 + 3929*z^2
(2254/10883 : -10119/54415 : 1) C2a (-28632/30781 : -15011/153905 : 1)
** u= 34/147 ; C1 -129193*x^2 - 22765*y^2 + 10457*z^2
(-1213/6899 : 3676/6899 : 1) C2a (74276/1063 : 5073/1063 : 1)
** u= 35/121 ; C1 -91370*x^2 - 15866*y^2 + 4946*z^2
(1986/10093 : -3007/10093 : 1) C2a (-248369/283431 : 27527/283431 : 1)
** u= 35/169 ; C1 -167690*x^2 - 29786*y^2 + 15506*z^2
(15249/54761 : -15874/54761 : 1) C2a (1166401/338169 : -89183/338169 : 1)
** u= 37/103 ; C1 -69658*x^2 - 11978*y^2 + 1618*z^2
(-3094/26179 : 6075/26179 : 1) C2a (24841/2107 : -937/2107 : 1)
** u= 38/99 ; C1 -65497*x^2 - 11245*y^2 + 833*z^2
(-1778/33721 : 8113/33721 : 1) C2a (-14536/203 : -57/29 : 1)
** u= 38/115 ; C1 -85049*x^2 - 14669*y^2 + 3041*z^2
(3429/18143 : 260/18143 : 1) C2a (-344/75 : -17/75 : 1)
** u= 38/119 ; C1 -90337*x^2 - 15605*y^2 + 3673*z^2
(229/3527 : -1620/3527 : 1) C2a (156046/178217 : -16823/178217 : 1)
** u= 38/153 ; C1 -141745*x^2 - 24853*y^2 + 10337*z^2
(7133/28781 : -7372/28781 : 1) C2a (-1423356/308593 : 95959/308593 : 1)
** u= 38/167 ; C1 -166273*x^2 - 29333*y^2 + 13753*z^2
(-19594/192849 : -123535/192849 : 1) C2a (410296/492787 : -49457/492787 : 1)
** u= 38/175 ; C1 -181169*x^2 - 32069*y^2 + 15881*z^2
(5339/28855 : 15852/28855 : 1) C2a (15227712/365105 : -1080139/365105 : 1)
** u= 39/109 ; C1 -77930*x^2 - 13402*y^2 + 1858*z^2
(3798/25889 : 3007/25889 : 1) C2a (1688317/33591 : 63403/33591 : 1)
** u= 42/151 ; C1 -141137*x^2 - 24565*y^2 + 8353*z^2
(-2241/11263 : -64244/191471 : 1) C2a (52372/13789 : -55851/234413 : 1)
** u= 42/173 ; C1 -180473*x^2 - 31693*y^2 + 13633*z^2
(-6461/32649 : -14860/32649 : 1) C2a (86728/36225 : 6467/36225 : 1)
** u= 42/181 ; C1 -195977*x^2 - 34525*y^2 + 15793*z^2
(86/5151 : 17389/25755 : 1) C2a (-21746/2079 : 7459/10395 : 1)
** u= 43/113 ; C1 -85130*x^2 - 14618*y^2 + 1202*z^2
(533/8821 : 2178/8821 : 1) C2a (-643249/42417 : 18929/42417 : 1)
** u= 45/199 ; C1 -235850*x^2 - 41626*y^2 + 19666*z^2
(-4726/22215 : 2065/4443 : 1) C2a (925531/214971 : 66493/214971 : 1)
** u= 46/119 ; C1 -94817*x^2 - 16277*y^2 + 1097*z^2
(-243/5975 : -1436/5975 : 1) C2a (86278/16335 : 2647/16335 : 1)
** u= 46/129 ; C1 -109057*x^2 - 18757*y^2 + 2657*z^2
(6934/74491 : -22505/74491 : 1) C2a (949132/70919 : -36489/70919 : 1)
** u= 46/157 ; C1 -154249*x^2 - 26765*y^2 + 8089*z^2
(3626/40591 : 20547/40591 : 1) C2a (-10278874/861961 : -573923/861961 : 1)
** u= 46/165 ; C1 -168601*x^2 - 29341*y^2 + 9929*z^2
(-2246/36427 : -20495/36427 : 1) C2a (109788/43837 : -7403/43837 : 1)
** u= 46/169 ; C1 -176017*x^2 - 30677*y^2 + 10897*z^2
(-5305/45529 : 23976/45529 : 1) C2a (-108416/731377 : 61313/731377 : 1)
** u= 47/117 ; C1 -92650*x^2 - 15898*y^2 + 482*z^2
(86/2665 : -83/533 : 1) C2a (-66541/4223 : 1221/4223 : 1)
** u= 47/125 ; C1 -103834*x^2 - 17834*y^2 + 1666*z^2
(-10241/87265 : 10038/87265 : 1) C2a (-70853/2345 : 313/335 : 1)
** u= 47/133 ; C1 -115658*x^2 - 19898*y^2 + 2978*z^2
(-410/17473 : 6687/17473 : 1) C2a (-594739/6345 : 23189/6345 : 1)
** u= 49/155 ; C1 -152906*x^2 - 26426*y^2 + 6434*z^2
(-1875/19943 : -8746/19943 : 1) C2a (571893/797 : -28433/797 : 1)
** u= 49/171 ; C1 -182122*x^2 - 31642*y^2 + 10082*z^2
(-70858/308863 : 38695/308863 : 1) C2a (-302501/15407 : 243/217 : 1)
** u= 50/161 ; C1 -164305*x^2 - 28421*y^2 + 7321*z^2
(4558/72727 : 35247/72727 : 1) C2a (-749464/653105 : -66931/653105 : 1)
** u= 50/169 ; C1 -179105*x^2 - 31061*y^2 + 9161*z^2
(3657/37901 : 18616/37901 : 1) C2a (412372/274497 : -32221/274497 : 1)
** u= 50/189 ; C1 -218905*x^2 - 38221*y^2 + 14321*z^2
(1178/19307 : 11477/19307 : 1) C2a (-617222/273185 : 44337/273185 : 1)
** u= 51/137 ; C1 -124394*x^2 - 21370*y^2 + 2194*z^2
(-218/2337 : 13/57 : 1) C2a (7487/5267 : 507/5267 : 1)
** u= 54/185 ; C1 -214001*x^2 - 37141*y^2 + 11329*z^2
(24501/107213 : -6880/107213 : 1) C2a (-507296/12979 : -28251/12979 : 1)
** u= 54/191 ; C1 -226577*x^2 - 39397*y^2 + 12937*z^2
(2286/20465 : -10367/20465 : 1) C2a (-3769688/1073055 : -235403/1073055 : 1)
** u= 55/141 ; C1 -133450*x^2 - 22906*y^2 + 1346*z^2
(-538/85705 : -4147/17141 : 1) C2a (2513739/217415 : -64099/217415 : 1)
** u= 55/181 ; C1 -206650*x^2 - 35786*y^2 + 9826*z^2
(-34/225 : 17/45 : 1) C2a (82981/10625 : -263/625 : 1)
** u= 58/163 ; C1 -174025*x^2 - 29933*y^2 + 4297*z^2
(715/4907 : -696/4907 : 1) C2a (1291258/160235 : 51121/160235 : 1)
** u= 62/161 ; C1 -173377*x^2 - 29765*y^2 + 2113*z^2
(-3386/52203 : 11255/52203 : 1) C2a (634148/118681 : -19769/118681 : 1)
** u= 62/187 ; C1 -225065*x^2 - 38813*y^2 + 7937*z^2
(-4998/60917 : -24779/60917 : 1) C2a (3186/6085 : 533/6085 : 1)
** u= 63/173 ; C1 -197210*x^2 - 33898*y^2 + 4162*z^2
(5451/38101 : 2318/38101 : 1) C2a (-8447/8561 : 783/8561 : 1)
** u= 66/167 ; C1 -187889*x^2 - 32245*y^2 + 1489*z^2
(7/87 : 8/87 : 1) C2a (1136078/1032963 : -90889/1032963 : 1)
** u= 66/185 ; C1 -224321*x^2 - 38581*y^2 + 5449*z^2
(-4198/105579 : 38365/105579 : 1) C2a (12190094/422109 : -462971/422109 : 1)
** u= 70/173 ; C1 -202985*x^2 - 34829*y^2 + 809*z^2
(-307/7469 : 864/7469 : 1) C2a (496866/53459 : -8873/53459 : 1)
** u= 70/179 ; C1 -215225*x^2 - 36941*y^2 + 2081*z^2
(126/3673 : 817/3673 : 1) C2a (-52612/30207 : -2851/30207 : 1)
** u= 70/193 ; C1 -245185*x^2 - 42149*y^2 + 5329*z^2
(9490/101619 : -27959/101619 : 1) C2a (1952812/346385 : -1039/4745 : 1)
** u= 73/195 ; C1 -252394*x^2 - 43354*y^2 + 4226*z^2
(1742/13775 : 911/13775 : 1) C2a (-258207/114547 : -12647/114547 : 1)
** u= 74/183 ; C1 -227089*x^2 - 38965*y^2 + 929*z^2
(11027/182107 : 9056/182107 : 1) C2a (-401026/66439 : -8403/66439 : 1)
** u= 74/193 ; C1 -248849*x^2 - 42725*y^2 + 3209*z^2
(-2782/57235 : 70881/286175 : 1) C2a (-522440/135699 : -92213/678495 : 1)
** u= 78/191 ; C1 -248081*x^2 - 42565*y^2 + 601*z^2
(-3301/128439 : 13016/128439 : 1) C2a (2158778/277303 : 34929/277303 : 1)
** u= 82/199 ; C1 -270001*x^2 - 46325*y^2 + 241*z^2
(-358/14377 : 573/14377 : 1) C2a (104692/17251 : 8239/86255 : 1)
766
>
■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=10/63のとき
515^4+3897^4+77618*573^4=4*6809^4
71681371645220789679006543923756237415^4+137296450935572598739374907028900810707^4+77618*13238517707011716489562121309301710373^4=4*162158832840738449791708981737307085761^4
71089361057474529174587820624711379688283790851993952502142186820263681309915515854919635864130893589206253^4+73151021475137603723217818890681619934652297295126320926260375637147198186859965998534513398816550459661945^4+77618*7209028753189185516748672937649012599311726930588431931258910011971322333035480336059403819718378856268213^4=4*90117360397101778121925911304355718698100553732288134220861436823100062673512552314548895752353073736789201^4
567721729744540602017272376072389701750373237857294881349732968617474057979719041550581121062471697820416868196795799659437872495355379898733007503156730388438348144066433973136751506105835249694993799534861955^4+990074272305209638755829825477771142555373834379449804102684587494677920405647868499010142818122148021282896752207594512918565497997669596999472151104932343653164322747369344125434572209353992583100873849208423^4+77618*93815934686131965493222975720279618995844155181304393233595242745124288835724918756414099576119408074407869714917672344108342425484715747129705318708896010911224465881920495066717520365341809405964907160533613^4=4*1153331951118424754135494561880523710421848138412698759385488622942759498369982838925354365294559319528197832011638314538345176703968910038864063482647100138738935035361596689199554739101505373137886299937833289^4
4924644465529725982018058126671069450132284076111387659699920327938503135758664356287174200068348422522086156907110226420535289407084499570814103023152450630280306017955456013823453567979485556009125617992948142967871717511997023448421840753912332735794322324867462123419241544286527729606620086789468384019741591890750064961198975616789868568743^4+212053637839200387349465926210654215480021490066606229352882211239854248966037090113771837990623828269785460285707371734013803294974118718735755518028146222279063019257195581141159858897871022285752098307348174688560247016482534099811296107573898865576964597231074645376687479689084128520795723460313268066899065800068457734577951956706712361564925^4+77618*28846306826447287555786848455046437847614244413898717000220374983541469642225239295948690422110590809521916641049368982604669617024163911439724187492083589627691852560509319621435488061605613853427452809057079406966899627957474865511709251352877949537207237725655688195282671156258166646979258176010927276560264302486493188166755149201393389482893^4=4*343617906255247308015793667848981941749847772266332315716754665876558203232761619393129515124539222778595524999773384621261219686966242339753838187301052622078688282550147388998224078735338484936973053950620670011047458495378750302744978901601424522399825939111818626197059281754722314703369739330626501827566440649191455802611754031828329374952809^4
...
- u=7/101のとき
673327255213428529776076932288895^4+918860253578255007820616602242013^4+77618*70150168986811813604946483484223^4=4*914531515228281342839090599887953^4
279453333507368182478983250973087945675552128035050860353371864544645188691682027094197392703937184170774157797225189309154053648402979720131828393580228809582296163754390292046683547830902833502861126891442703137702213796574364367322883115152364453453595699815334638605564031810966244773236640913645^4+2048070715781860788045027179962422624244747096492115761517077519053309684068301550919365179364016979895576175303823697843471167809492617822827021733885872193817657509452702686800410289017536583687684123464343838990185077343419658508219932000820716264892776757958255751481179827116542019277672242840543^4+77618*208538689371592690450822209887322937555109946908658332363796051989337835609303041431902503442584416098527880891347162924836284132709331269411248156987333748534708272620361461466056164504458425895516439488221353478814826056656931560458896008485454653456949257131150159909494051131650861201293567769703^4=4*2531961639424503323484756206727197021877399636269429379077110485375494029441073682028352955225235921743330056167535579347788501461534469513779181551157232082219821076913131338080923701440187120062394465631431299422534897231872049073723265640380783213301350777020959918777575017590352051586597120505417^4
3765712642858941403086183166461716760117583470166133851526180829298763891370742674172862717763322006828375715679534332911807637661691517441266966901424680265438806610452514307125958358633757147837980453511967622334670749018047556094560304561708697506414694158150459301406864003206257024314407077466895042937881126051603259218652841133205704050879675271101990696982035480378543921910992741271358050295916590512441043319013440245934505503460476228914967690948683090891391342596760554653769030374002461426366329757038346044805337272529537769282358048312333688224017601465092259761013964829173572650781345191261079747093017086244509057467977645602233753155488260743777714344378433666512640869706753971409060014431050661202167864171547650293243265217662535917099848789501541435940945585876227914044281881047687118948468654224274962048358445^4+12411407099009336504960165872652310197538819445080884111097021940263016343671579386100013974481770525629592585019576467025878157154909052848419047086266810505894624786989255580444181553301434748299055071096435059980781166742890675076293121888656700815571691247045491195867136402468900953231236871416675144711871498741184592054435944027971684781518965790914667648393874098325334587565147156224734825340403251926571976657671132357278837470425967733403943199819096981695816009212876146444186564892565836892451373512881669715905438221663352662354631797742567458204057383082324262522388719753228834516933315886601220888675136754179663462511418769367897796466950553675169969632549224970250301856361487197224723442259205134339221896059650537015770352897340262119829188812104840567871545534109766450231993943209205444958366178224476899824917697^4+77618*1732805709958744855427291512373469602360269928929090302288192646326924041831704703110164405772369983684520311249552367792284499286737873500047568744196825112533988415292258638206819655972931669561860415880723143239616673468265511046920451769108600400438359596524848082072192544543724578073658346268386931834558038448387836100870963643680348773603733592041336595668792695602713417800118543004882390185370744215840602970126981047705157793941051496924157826429533228886399505500149885897704798333395122696142514967552125235531168928287118860567083765668139196573431501599722506705267213013251197912304214526509212934365365971298413383252417188580081131445190105917887819199735543716971780200377652677570188399394195650942477955836455558142168641625466098673032068645798443095751434604886011269706824570978247015385961229369697600713577463^4=4*20624161203655383879628769743281513356760035381524206082567687536740184430245343693512201144530819150357605970984553056670061050363708502308838443269865966790543093526676390081830389345799227169933714051172185082676767403986793266139126326988213606573765971479458802396566807095093157909292407436888391807014418166021450564598261904383666488274968833544869338330458975154383167485840486278151555224859023026312079147477571335939023861347011647582239308572637079329274912367894186626814956809212950720331254676146504133918192891875627390891479923285213772687242107086906001676989480045003152124729144918519683027197639803538783401628650327901551654387904685058096216004370597287410006577294942764054883844192366968718265702157166635203983697997545154250166478656993861217755411249864853246019888527114205857188641047299804603844460587257^4
...
- u=-35/199のとき
773^4+3775^4+77618*253^4=4*3379^4
2269712151003133132858045855997046755^4+2374073423633974403486522357810928361^4+77618*113369502436963214875588537469803661^4=4*2053499892813242761608655886228453507^4
33071011624096199296553754282300192974859362662692426371018391240056452679888558136276094725533945831^4+492478674592111411272467290630395099360415486902239010424740890940966172827394467220952233159367924845^4+77618*37088537867808138218680082957179974730388603274221428501143257600588216928995071827587941114365144749^4=4*476199119468840006245628343505004569410887017829911508600477643626069638288402127834182934139147660323^4
27069109077246983378423026421258268694172587295145469293097759769398799963960414475109755949865515780995381480144856031963956046886853650552923663059778906801630774102331406260958286857245755268947695^4+84470649685914976086536035452237940224903272915484333973908539688517057264641498850433069497606356273216456635433662621104474061167964619062879109141169901219222733575933644902283282124838620173524917^4+77618*5127987200901353661436043234379499883134405597599967897399493621314808978141563229207386098609103237491652719638051505363041882969767707508150558439126074839824116855319865206987421905907834494082397^4=4*71599166096798650996338090730225785315268352061815642630071708585615072468543832530597889144050981162333628056320183233009459407048790041260555908801451871348593897802541946829633401282617017834885651^4
6361317228322587726246687900093002925052205217752658968463262789953619934851888608909309959337484814387078988976944502871607621055709687490286349666996062758348169443589026153232651353364482538026023652885271880689472777056630845109484692109578651718954493774447737331948869294230698767063420966418099507323432809205844943449637745^4+7290393465744683088825983758037807003046933586965075866717975448606030915373357487733082095012191477360975111070046074778144560835325544654786876102928606386710987861091174352036727019357108549131525705478001241323997484387867857840126592025547646814895273968096057778630659195460336680843053741961062606831277139233418839880818603^4+77618*339841078861264840085480452729878289986980362253730262916687642200673127246360122478087665403328730825060715306014695212743262163271074017616054441989197424524860045946093607792347598379660721050545876789664937556513945151431273905970260664742017247918426325809244237155742583263895636195012122048574031953320717607862806475372957^4=4*6088788167282699225025089727291624851390472200320306254708172327859538671085035047391276075197192387555137350197297844738409489992223881083937052108497334161580229847376269301947262414235697981199008556999008144581060410716580946507012283965740694567927875106807280724735786696061008454422498054760343893421456791582365704676524371^4
...
[2026.05.14追記]u=7/101のときの整数解を追加した。
[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: 2026.05.14 |
| H.Nakao |