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Integer Points on A^4+B^4+C^4=114242*D^4

[2026.01.06]A^4+B^4+C^4=114242*D^4の整点

■整点を求める方法は、 "A^4+B^4+C^4=3362*D^4の整点" と同様なので、詳細はそちらを参照すること。ただし、参照する数式のみ記載する。

自然数nを固定したとき、不定方程式
       A^4+B^4+C^4=2*n^2*D^4 ----------(1)
を満たす自明でない整数の組(A,B,C,D) (ただし C!=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])の方法およびTom Womackの文書(参考文献[5])を参考にして、(1)を満たす整数の組(A,B,C,D)を探す。
ここで、整数A,B,C,Dは0以上として良い。


■x=A/C,y=B/C.t=D/Cとすると、
       x^4+y^4+1=2*n^2*t^4 ----------(2)
つまり、(2)を満たす有理数の組(x,y,t)を見つければ良い。

そのためには、nある有理数uに対して、
       ±(u^2-2)*y^2=(-u^2+4*u-2)*x^2-2*(u^2-2*u+2)*x+(-u^2+4*u-2) ----------(3a±)
       ±n*(u^2-2)*t^2=(u^2-2*u+2)*x^2+(-u^2+4*u-2)*x+(u^2-2*u+2) ----------(3b±)
の両方を満たす有理数の組(x,y,t)を見つければ良い。


■任意の有理数uについて、２次曲線(3b+)および(3b-)は、non-singularである。
また、u^2 > 2のとき、(3b+)のみ、u^2 < 2のとき、(3b-)のみが成立する。

■２次曲線(3a)がsingularであるのは、u=0,1,2のときであり。そのときに限る。
u=1のとき、(3a+)はsingularであるが、有理点を持たない。
u-0,2のとき、(3a+)はsingularであり、
       x^2 - x + 1=n*t^2　--------(**)
が有理点をもつかどうかを議論する必要がある。

114242=2*239^2であるので、以下では、n=239とする。

■n=239のとき、２次曲線(**)は、有理点を持たないことが確認できる。

{MAGMAでの計算]
> P2 := ProjectiveSpace(Rationals(), 2);
> N:=239;
> C := Conic(P2,-N*y^2+x^2+x*z+z^2);
> HasRationalPoint(C);
false
>


■有理数u(u!=0,1,2)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400以下の範囲で、２次曲線(3a+)と２つの２次曲線の和集合(3b±)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390個のuが抽出される。
これらのuについて、(3a+),(3b±)を共に満たす有理数の組(x,y,t)を見つければ良い。

[MAGMAによる計算]
> PP(239,1,400);
** u= 1/293 ; tau(u)= 585/292 ; -170527*x^2 + 171697*y^2 + 342226*x*z - 170527*z^2
  (85301/103855 : -16776/103855 : 1)  C1b (16198319/707470 : 1024001/707470 : 1)
** u= 3/61 ; tau(u)= 119/58 ; -6719*x^2 + 7433*y^2 + 14170*x*z - 6719*z^2
  (-49/279 : 314/279 : 1)  C1b (22933/47966 : 2667/47966 : 1)
** u= 4/17 ; tau(u)= 30/13 ; -322*x^2 + 562*y^2 + 916*x*z - 322*z^2
  (9/22 : -1/22 : 1)  C1b (731/414 : -41/414 : 1)
** u= -4/25 ; tau(u)= 54/29 ; -1666*x^2 + 1234*y^2 + 2932*x*z - 1666*z^2
  (-61/4 : -75/4 : 1)  C2b (-62119/8395 : 4741/8395 : 1)
** u= -4/81 ; tau(u)= 166/85 ; -14434*x^2 + 13106*y^2 + 27572*x*z - 14434*z^2
  (112/157 : 63/157 : 1)  C2b (18948338/648905 : 1235069/648905 : 1)
** u= -4/117 ; tau(u)= 238/121 ; -29266*x^2 + 27362*y^2 + 56660*x*z - 29266*z^2
  (17717/15866 : 4785/15866 : 1)  C2b (-7477/75081 : -5213/75081 : 1)
** u= -4/145 ; tau(u)= 294/149 ; -44386*x^2 + 42034*y^2 + 86452*x*z - 44386*z^2
  (100312/80239 : -29491/80239 : 1)  C2b (689569/531355 : 40521/531355 : 1)
** u= -4/373 ; tau(u)= 750/377 ; -284242*x^2 + 278242*y^2 + 562516*x*z - 284242*z^2
  (9482/8433 : 1685/8433 : 1)  C2b (5865098/3956197 : -335423/3956197 : 1)
** u= 7/9 ; tau(u)= 11/2 ; 41*x^2 + 113*y^2 + 170*x*z + 41*z^2
  (-137/187 : -138/187 : 1)  C1b (5649/6397 : -533/6397 : 1)
** u= -7/13 ; tau(u)= 33/20 ; -751*x^2 + 289*y^2 + 1138*x*z - 751*z^2
  (5/3 : 92/51 : 1)  C2b (106/189 : -13/189 : 1)
** u= -7/153 ; tau(u)= 313/160 ; -51151*x^2 + 46769*y^2 + 98018*x*z - 51151*z^2
  (5491/19333 : 14808/19333 : 1)  C2b (-69838/40985 : 6469/40985 : 1)
** u= 7/233 ; tau(u)= 459/226 ; -102103*x^2 + 108529*y^2 + 210730*x*z - 102103*z^2
  (33393/49753 : 12326/49753 : 1)  C1b (891189/478678 : 49777/478678 : 1)
** u= -8/29 ; tau(u)= 66/37 ; -2674*x^2 + 1618*y^2 + 4420*x*z - 2674*z^2
  (19/27 : 20/27 : 1)  C2b (-8297/4645 : 177/929 : 1)
** u= -8/41 ; tau(u)= 90/49 ; -4738*x^2 + 3298*y^2 + 8164*x*z - 4738*z^2
  (1123/1460 : -903/1460 : 1)  C2b (3710/4401 : -271/4401 : 1)
** u= -8/101 ; tau(u)= 210/109 ; -23698*x^2 + 20338*y^2 + 44164*x*z - 23698*z^2
  (401/2841 : 2668/2841 : 1)  C2b (41885/222926 : 13719/222926 : 1)
** u= -8/197 ; tau(u)= 402/205 ; -83986*x^2 + 77554*y^2 + 161668*x*z - 83986*z^2
  (327/784 : 71/112 : 1)  C2b (549298/86187 : 33671/86187 : 1)
** u= 11/2 ; tau(u)= 7/9 ; -41*x^2 - 113*y^2 + 170*x*z - 41*z^2
  (17/43 : 18/43 : 1)  C1a (2987/7254 : 401/7254 : 1)
** u= -11/9 ; tau(u)= 29/20 ; -679*x^2 + 41*y^2 + 962*x*z - 679*z^2
  (149/8615 : 34632/8615 : 1)  C2b (187630/40999 : 35743/40999 : 1)
** u= 11/61 ; tau(u)= 111/50 ; -4879*x^2 + 7321*y^2 + 12442*x*z - 4879*z^2
  (-230291/336901 : -492790/336901 : 1)  C1b (-4543290/1562417 : -319159/1562417 : 1)
** u= -11/245 ; tau(u)= 501/256 ; -130951*x^2 + 119929*y^2 + 251122*x*z - 130951*z^2
  (2595/1181 : 1568/1181 : 1)  C2b (-190397/2413023 : -166627/2413023 : 1)
** u= -12/113 ; tau(u)= 238/125 ; -31106*x^2 + 25394*y^2 + 56788*x*z - 31106*z^2
  (-1103/1008 : 2285/1008 : 1)  C2b (3504146/947509 : 211257/947509 : 1)
** u= -12/185 ; tau(u)= 382/197 ; -77474*x^2 + 68306*y^2 + 146068*x*z - 77474*z^2
  (311/402 : -1121/2814 : 1)  C2b (-266855/30554 : -133083/213878 : 1)
** u= -12/257 ; tau(u)= 526/269 ; -144578*x^2 + 131954*y^2 + 276820*x*z - 144578*z^2
  (520899/1357262 : 912425/1357262 : 1)  C2b (68969179/5522177 : 4389111/5522177 : 1)
** u= 12/337 ; tau(u)= 662/325 ; -211106*x^2 + 226994*y^2 + 438388*x*z - 211106*z^2
  (29586/19789 : -985/2827 : 1)  C1b (1095601154/1219981 : 69602997/1219981 : 1)
** u= 13/53 ; tau(u)= 93/40 ; -3031*x^2 + 5449*y^2 + 8818*x*z - 3031*z^2
  (-1707/4423 : -4972/4423 : 1)  C1b (232201/561274 : -30753/561274 : 1)
** u= -13/229 ; tau(u)= 471/242 ; -116959*x^2 + 104713*y^2 + 222010*x*z - 116959*z^2
  (5499/5479 : -12958/38353 : 1)  C2b (-314891827/136662249 : -188320457/956635743 : 1)
** u= -13/261 ; tau(u)= 535/274 ; -149983*x^2 + 136073*y^2 + 286394*x*z - 149983*z^2
  (-102601/7540199 : -56133894/52781393 : 1)  C2b (1299787470/601702997 : 515639651/4211920979 : 1)
** u= 16/65 ; tau(u)= 114/49 ; -4546*x^2 + 8194*y^2 + 13252*x*z - 4546*z^2
  (3429/1247 : 686/1247 : 1)  C1b (1706255/292306 : 94771/292306 : 1)
** u= -16/97 ; tau(u)= 210/113 ; -25282*x^2 + 18562*y^2 + 44356*x*z - 25282*z^2
  (-1115/271 : -1586/271 : 1)  C2b (54063/132365 : -7837/132365 : 1)
** u= -16/181 ; tau(u)= 378/197 ; -77362*x^2 + 65266*y^2 + 143140*x*z - 77362*z^2
  (241/35271 : 38158/35271 : 1)  C2b (-13715762/10494629 : 1443043/10494629 : 1)
** u= 16/245 ; tau(u)= 474/229 ; -104626*x^2 + 119794*y^2 + 224932*x*z - 104626*z^2
  (681/1262 : -427/1262 : 1)  C1b (-23034/39401 : 3391/39401 : 1)
** u= 17/25 ; tau(u)= 33/8 ; 161*x^2 + 961*y^2 + 1378*x*z + 161*z^2
  (-3/7 : 20/31 : 1)  C1b (-1958/1345 : 3807/41695 : 1)
** u= -17/233 ; tau(u)= 483/250 ; -124711*x^2 + 108289*y^2 + 233578*x*z - 124711*z^2
  (21313/38577 : -21530/38577 : 1)  C2b (-54356825/17446347 : -4390459/17446347 : 1)
** u= -17/281 ; tau(u)= 579/298 ; -177319*x^2 + 157633*y^2 + 335530*x*z - 177319*z^2
  (39683/134111 : 723250/938777 : 1)  C2b (9468037/502214 : -4303321/3515498 : 1)
** u= 19/29 ; tau(u)= 39/10 ; 161*x^2 + 1321*y^2 + 1882*x*z + 161*z^2
  (-1097/2523 : -1738/2523 : 1)  C1b (-6893370/119861 : -375833/119861 : 1)
** u= -19/61 ; tau(u)= 141/80 ; -12439*x^2 + 7081*y^2 + 20242*x*z - 12439*z^2
  (-46883/215739 : -338432/215739 : 1)  C2b (-184495/19658 : 15249/19658 : 1)
** u= -19/117 ; tau(u)= 253/136 ; -36631*x^2 + 27017*y^2 + 64370*x*z - 36631*z^2
  (12073/4219 : -10020/4219 : 1)  C2b (-2663403/1071194 : 239297/1071194 : 1)
** u= -19/225 ; tau(u)= 469/244 ; -118711*x^2 + 100889*y^2 + 220322*x*z - 118711*z^2
  (40943/14993 : 29940/14993 : 1)  C2b (205493/2442210 : 158023/2442210 : 1)
** u= 21/37 ; tau(u)= 53/16 ; -71*x^2 + 2297*y^2 + 3250*x*z - 71*z^2
  (9/431 : 16/431 : 1)  C1b (-234914/362075 : 4743/72415 : 1)
** u= 21/157 ; tau(u)= 293/136 ; -36551*x^2 + 48857*y^2 + 86290*x*z - 36551*z^2
  (78457/165587 : 46612/165587 : 1)  C1b (6997403/915310 : 80985/183062 : 1)
** u= 21/313 ; tau(u)= 605/292 ; -170087*x^2 + 195497*y^2 + 366466*x*z - 170087*z^2
  (-6499/26823 : 31456/26823 : 1)  C1b (57781006/60795479 : 3847071/60795479 : 1)
** u= 24/89 ; tau(u)= 154/65 ; -7874*x^2 + 15266*y^2 + 24292*x*z - 7874*z^2
  (91/326 : -109/326 : 1)  C1b (-749758/202303 : -48321/202303 : 1)
** u= 24/125 ; tau(u)= 226/101 ; -19826*x^2 + 30674*y^2 + 51652*x*z - 19826*z^2
  (-696/1915 : -15539/13405 : 1)  C1b (-233069/13505 : -2679/2555 : 1)
** u= -25/289 ; tau(u)= 603/314 ; -196567*x^2 + 166417*y^2 + 364234*x*z - 196567*z^2
  (1847/487 : -1530/487 : 1)  C2b (-114444962/6001385 : -613127/461645 : 1)
** u= -28/25 ; tau(u)= 78/53 ; -4834*x^2 + 466*y^2 + 6868*x*z - 4834*z^2
  (-21/1924 : 6245/1924 : 1)  C2b (669130/1829 : -117269/1829 : 1)
** u= -28/109 ; tau(u)= 246/137 ; -36754*x^2 + 22978*y^2 + 61300*x*z - 36754*z^2
  (8634/13901 : 10399/13901 : 1)  C2b (6349525/561738 : -450445/561738 : 1)
** u= 28/221 ; tau(u)= 414/193 ; -73714*x^2 + 96898*y^2 + 172180*x*z - 73714*z^2
  (-32748/21277 : 48973/21277 : 1)  C1b (1729058/99129 : 102979/99129 : 1)
** u= -28/289 ; tau(u)= 606/317 ; -200194*x^2 + 166258*y^2 + 368020*x*z - 200194*z^2
  (62263/68604 : -29665/68604 : 1)  C2b (-6058698/4010251 : -605701/4010251 : 1)
** u= -28/373 ; tau(u)= 774/401 ; -320818*x^2 + 277474*y^2 + 599860*x*z - 320818*z^2
  (-14596/357243 : -398845/357243 : 1)  C2b (-1580414/52577 : 108217/52577 : 1)
** u= 29/20 ; tau(u)= -11/9 ; 679*x^2 - 41*y^2 + 962*x*z + 679*z^2
  (-101/107 : -324/107 : 1)  C1a (-6230/2447 : -1069/2447 : 1)
** u= 30/13 ; tau(u)= 4/17 ; 322*x^2 - 562*y^2 + 916*x*z + 322*z^2
  (-324/107 : 101/107 : 1)  C1a (-18199/1150 : -1041/1150 : 1)
** u= -31/37 ; tau(u)= 105/68 ; -8287*x^2 + 1777*y^2 + 11986*x*z - 8287*z^2
  (59/17 : 104/17 : 1)  C2b (256334/39855 : 27391/39855 : 1)
** u= 31/305 ; tau(u)= 579/274 ; -149191*x^2 + 185089*y^2 + 336202*x*z - 149191*z^2
  (-853029/19255939 : -18146606/19255939 : 1)  C1b (25181482/9631735 : -1394343/9631735 : 1)
** u= -31/361 ; tau(u)= 753/392 ; -306367*x^2 + 259681*y^2 + 567970*x*z - 306367*z^2
  (6174737/22747107 : -18660964/22747107 : 1)  C2b (-162532231/1389970 : 2209063/277994 : 1)
** u= 32/49 ; tau(u)= 66/17 ; 446*x^2 + 3778*y^2 + 5380*x*z + 446*z^2
  (-178/291 : -245/291 : 1)  C1b (-1077917/6281 : 58807/6281 : 1)
** u= -32/53 ; tau(u)= 138/85 ; -13426*x^2 + 4594*y^2 + 20068*x*z - 13426*z^2
  (-6585/28567 : -8248/4081 : 1)  C2b (-1674230/347647 : 183951/347647 : 1)
** u= -32/137 ; tau(u)= 306/169 ; -56098*x^2 + 36514*y^2 + 94660*x*z - 56098*z^2
  (4799/10879 : -9048/10879 : 1)  C2b (7828754/3051915 : -95777/610383 : 1)
** u= 32/289 ; tau(u)= 546/257 ; -131074*x^2 + 166018*y^2 + 299140*x*z - 131074*z^2
  (75249/24521 : -40256/24521 : 1)  C1b (20619194/377295 : -251195/75459 : 1)
** u= -32/317 ; tau(u)= 666/349 ; -242578*x^2 + 199954*y^2 + 444580*x*z - 242578*z^2
  (146903/16903 : -144936/16903 : 1)  C2b (-538404622/141908079 : 42776987/141908079 : 1)
** u= 32/369 ; tau(u)= 706/337 ; -226114*x^2 + 271298*y^2 + 499460*x*z - 226114*z^2
  (189637/451597 : -205632/451597 : 1)  C1b (16594282/6104215 : -14191/93911 : 1)
** u= 33/8 ; tau(u)= 17/25 ; -161*x^2 - 961*y^2 + 1378*x*z - 161*z^2
  (9/61 : 380/1891 : 1)  C1a (-11126/275 : 18951/8525 : 1)
** u= 33/20 ; tau(u)= -7/13 ; 751*x^2 - 289*y^2 + 1138*x*z + 751*z^2
  (-1/583 : 15956/9911 : 1)  C1a (-814/1171 : -1359/19907 : 1)
** u= 33/245 ; tau(u)= 457/212 ; -88799*x^2 + 118961*y^2 + 209938*x*z - 88799*z^2
  (-174243/112015 : -257824/112015 : 1)  C1b (16553011/761855 : 987099/761855 : 1)
** u= -35/257 ; tau(u)= 549/292 ; -169303*x^2 + 130873*y^2 + 302626*x*z - 169303*z^2
  (79559/343981 : -313008/343981 : 1)  C2b (-37095950/1352873 : 2633921/1352873 : 1)
** u= -37/181 ; tau(u)= 399/218 ; -93679*x^2 + 64153*y^2 + 160570*x*z - 93679*z^2
  (-13631/8029 : 25286/8029 : 1)  C2b (134281615/21746706 : -8891125/21746706 : 1)
** u= 39/10 ; tau(u)= 19/29 ; -161*x^2 - 1321*y^2 + 1882*x*z - 161*z^2
  (3113/23499 : -854/3357 : 1)  C1a (-403699/46226 : 22397/46226 : 1)
** u= 41/81 ; tau(u)= 121/40 ; -1519*x^2 + 11441*y^2 + 16322*x*z - 1519*z^2
  (67/5017 : 1692/5017 : 1)  C1b (3360310/160963 : 182969/160963 : 1)
** u= -43/277 ; tau(u)= 597/320 ; -202951*x^2 + 151609*y^2 + 358258*x*z - 202951*z^2
  (-10993665/615532289 : 723421808/615532289 : 1)  C2b (319297/294413 : 20149/294413 : 1)
** u= -43/313 ; tau(u)= 669/356 ; -251623*x^2 + 194089*y^2 + 449410*x*z - 251623*z^2
  (-73/177 : 1948/1239 : 1)  C2b (534134/477603 : 232501/3343221 : 1)
** u= 44/117 ; tau(u)= 190/73 ; -8722*x^2 + 25442*y^2 + 38036*x*z - 8722*z^2
  (25621/118498 : 22359/118498 : 1)  C1b (1476283350/88627859 : 81567721/88627859 : 1)
** u= 47/49 ; tau(u)= 51/2 ; 2201*x^2 + 2593*y^2 + 4810*x*z + 2201*z^2
  (-7801/9587 : 3010/9587 : 1)  C1b (-103141494/3494767 : 6328601/3494767 : 1)
** u= -47/245 ; tau(u)= 537/292 ; -168319*x^2 + 117841*y^2 + 290578*x*z - 168319*z^2
  (92163/249817 : 210952/249817 : 1)  C2b (7070565903/207233443 : 499361467/207233443 : 1)
** u= -48/305 ; tau(u)= 658/353 ; -246914*x^2 + 183746*y^2 + 435268*x*z - 246914*z^2
  (-3642/9041 : -14341/9041 : 1)  C2b (644975/81946 : -42399/81946 : 1)
** u= 49/89 ; tau(u)= 129/40 ; -799*x^2 + 13441*y^2 + 19042*x*z - 799*z^2
  (-1383/98507 : 27748/98507 : 1)  C1b (-4338581/1658326 : 256377/1658326 : 1)
** u= -49/97 ; tau(u)= 243/146 ; -40231*x^2 + 16417*y^2 + 61450*x*z - 40231*z^2
  (-6233/17987 : -36162/17987 : 1)  C2b (4808950/860829 : -380065/860829 : 1)
** u= -49/193 ; tau(u)= 435/242 ; -114727*x^2 + 72097*y^2 + 191626*x*z - 114727*z^2
  (2557/76225 : -93478/76225 : 1)  C2b (91940182271/73261219 : 6852560579/73261219 : 1)
** u= 51/2 ; tau(u)= 47/49 ; -2201*x^2 - 2593*y^2 + 4810*x*z - 2201*z^2
  (3611/3529 : -1414/3529 : 1)  C1a (-470/741 : 5/57 : 1)
** u= 51/125 ; tau(u)= 199/74 ; -8351*x^2 + 28649*y^2 + 42202*x*z - 8351*z^2
  (-107/1017 : -682/1017 : 1)  C1b (21134330/5247619 : 1151559/5247619 : 1)
** u= -51/157 ; tau(u)= 365/208 ; -83927*x^2 + 46697*y^2 + 135826*x*z - 83927*z^2
  (375/4969 : 43832/34783 : 1)  C2b (88663/326867 : 153369/2288069 : 1)
** u= -51/181 ; tau(u)= 413/232 ; -105047*x^2 + 62921*y^2 + 173170*x*z - 105047*z^2
  (-469/4513 : 6340/4513 : 1)  C2b (152813/276706 : -16731/276706 : 1)
** u= -51/349 ; tau(u)= 749/400 ; -317399*x^2 + 241001*y^2 + 563602*x*z - 317399*z^2
  (12359/433 : 13744/433 : 1)  C2b (142250/355021 : 20913/355021 : 1)
** u= -51/373 ; tau(u)= 797/424 ; -356951*x^2 + 275657*y^2 + 637810*x*z - 356951*z^2
  (-140711/5982891 : -6951604/5982891 : 1)  C2b (63464179/8927582 : -4100283/8927582 : 1)
** u= -52/37 ; tau(u)= 126/89 ; -13138*x^2 + 34*y^2 + 18580*x*z - 13138*z^2
  (-1/2 : 55/2 : 1)  C2b (-2103/2539 : 4589/2539 : 1)
** u= 52/113 ; tau(u)= 174/61 ; -4738*x^2 + 22834*y^2 + 32980*x*z - 4738*z^2
  (-4519/10322 : -67765/72254 : 1)  C1b (26779/16817 : -11353/117719 : 1)
** u= 52/149 ; tau(u)= 246/97 ; -16114*x^2 + 41698*y^2 + 63220*x*z - 16114*z^2
  (34506/9101 : 4001/9101 : 1)  C1b (205105/84362 : 11315/84362 : 1)
** u= -52/193 ; tau(u)= 438/245 ; -117346*x^2 + 71794*y^2 + 194548*x*z - 117346*z^2
  (3519/5042 : -3703/5042 : 1)  C2b (-338093930/1621291 : -25529967/1621291 : 1)
** u= 52/389 ; tau(u)= 726/337 ; -224434*x^2 + 299938*y^2 + 529780*x*z - 224434*z^2
  (67898/123227 : 5797/123227 : 1)  C1b (2442793/543555 : -27557/108711 : 1)
** u= 53/16 ; tau(u)= 21/37 ; 71*x^2 - 2297*y^2 + 3250*x*z + 71*z^2
  (-43/4101 : -520/4101 : 1)  C1a (32957/15119 : 153/1163 : 1)
** u= 54/29 ; tau(u)= -4/25 ; 1666*x^2 - 1234*y^2 + 2932*x*z + 1666*z^2
  (-274/449 : 285/449 : 1)  C1a (20409/28901 : -3091/28901 : 1)
** u= 55/281 ; tau(u)= 507/226 ; -99127*x^2 + 154897*y^2 + 260074*x*z - 99127*z^2
  (-9775471/13664421 : 20122622/13664421 : 1)  C1b (-465935/725734 : -59313/725734 : 1)
** u= -56/81 ; tau(u)= 218/137 ; -34402*x^2 + 9986*y^2 + 50660*x*z - 34402*z^2
  (4811/983759 : 1819368/983759 : 1)  C2b (58985/87339 : 6605/87339 : 1)
** u= 56/85 ; tau(u)= 114/29 ; 1454*x^2 + 11314*y^2 + 16132*x*z + 1454*z^2
  (-57907/340229 : -113068/340229 : 1)  C1b (141716146/3248071 : 7758009/3248071 : 1)
** u= 56/121 ; tau(u)= 186/65 ; -5314*x^2 + 26146*y^2 + 37732*x*z - 5314*z^2
  (-141/1795 : -1012/1795 : 1)  C1b (-767306/12985 : 42267/12985 : 1)
** u= 56/181 ; tau(u)= 306/125 ; -28114*x^2 + 62386*y^2 + 96772*x*z - 28114*z^2
  (1309/4936 : -1315/4936 : 1)  C1b (-537418/619825 : 53029/619825 : 1)
** u= 57/97 ; tau(u)= 137/40 ; 49*x^2 + 15569*y^2 + 22018*x*z + 49*z^2
  (-4611/113023 : 26396/113023 : 1)  C1b (-612005/38783 : -33351/38783 : 1)
** u= 59/61 ; tau(u)= 63/2 ; 3473*x^2 + 3961*y^2 + 7450*x*z + 3473*z^2
  (-141/163 : -50/163 : 1)  C1b (1121250/271627 : -535/1823 : 1)
** u= -59/137 ; tau(u)= 333/196 ; -73351*x^2 + 34057*y^2 + 114370*x*z - 73351*z^2
  (7209/41819 : -53536/41819 : 1)  C2b (300629/371865 : 4895/74373 : 1)
** u= -60/229 ; tau(u)= 518/289 ; -163442*x^2 + 101282*y^2 + 271924*x*z - 163442*z^2
  (2/15 : -17/15 : 1)  C2b (-47823142/14126965 : 4304469/14126965 : 1)
** u= 61/113 ; tau(u)= 165/52 ; -1687*x^2 + 21817*y^2 + 30946*x*z - 1687*z^2
  (-38355/358771 : -24572/51253 : 1)  C1b (-40946030/1480949 : 2236351/1480949 : 1)
** u= 63/2 ; tau(u)= 59/61 ; -3473*x^2 - 3961*y^2 + 7450*x*z - 3473*z^2
  (14551/10157 : 1370/10157 : 1)  C1a (45554/23193 : 2531/23193 : 1)
** u= -64/157 ; tau(u)= 378/221 ; -93586*x^2 + 45202*y^2 + 146980*x*z - 93586*z^2
  (-122/49 : -235/49 : 1)  C2b (-5079414/3153823 : -618017/3153823 : 1)
** u= -64/181 ; tau(u)= 426/245 ; -115954*x^2 + 61426*y^2 + 185572*x*z - 115954*z^2
  (-55487/60261 : 150892/60261 : 1)  C2b (85865/223803 : -14539/223803 : 1)
** u= 66/17 ; tau(u)= 32/49 ; -446*x^2 - 3778*y^2 + 5380*x*z - 446*z^2
  (5951/20649 : -10976/20649 : 1)  C1a (3348178/933445 : -37121/186689 : 1)
** u= 66/37 ; tau(u)= -8/29 ; 2674*x^2 - 1618*y^2 + 4420*x*z + 2674*z^2
  (-172/151 : 125/151 : 1)  C1a (14317/2929 : 1229/2929 : 1)
** u= 68/181 ; tau(u)= 294/113 ; -20914*x^2 + 60898*y^2 + 91060*x*z - 20914*z^2
  (67687/836328 : 396403/836328 : 1)  C1b (-616507/6907826 : 395703/6907826 : 1)
** u= -68/197 ; tau(u)= 462/265 ; -135826*x^2 + 72994*y^2 + 218068*x*z - 135826*z^2
  (98541/71458 : 80833/71458 : 1)  C2b (37699/88121 : 5617/88121 : 1)
** u= 68/265 ; tau(u)= 462/197 ; -72994*x^2 + 135826*y^2 + 218068*x*z - 72994*z^2
  (246538/1422907 : 746677/1422907 : 1)  C1b (-394434/81451 : -24841/81451 : 1)
** u= 71/241 ; tau(u)= 411/170 ; -52759*x^2 + 111121*y^2 + 173962*x*z - 52759*z^2
  (20192893/6289345 : -3681874/6289345 : 1)  C1b (-43715/87337 : 6231/87337 : 1)
** u= -71/269 ; tau(u)= 609/340 ; -226159*x^2 + 139681*y^2 + 375922*x*z - 226159*z^2
  (28997/933731 : -50332/40597 : 1)  C2b (26094647/27583918 : 1800431/27583918 : 1)
** u= -76/73 ; tau(u)= 222/149 ; -38626*x^2 + 4882*y^2 + 55060*x*z - 38626*z^2
  (436/231 : 127/33 : 1)  C2b (89209205/13426946 : -12343935/13426946 : 1)
** u= 76/245 ; tau(u)= 414/169 ; -51346*x^2 + 114274*y^2 + 177172*x*z - 51346*z^2
  (52086/215389 : 68341/215389 : 1)  C1b (22317402/8919317 : 1224463/8919317 : 1)
** u= 76/269 ; tau(u)= 462/193 ; -68722*x^2 + 138946*y^2 + 219220*x*z - 68722*z^2
  (150023/483998 : 111499/483998 : 1)  C1b (-131640667/530015 : 1514517/106003 : 1)
** u= -77/333 ; tau(u)= 743/410 ; -330271*x^2 + 215849*y^2 + 557978*x*z - 330271*z^2
  (89449/40453 : 73434/40453 : 1)  C2b (-50488003/6212153 : 4000241/6212153 : 1)
** u= 78/53 ; tau(u)= -28/25 ; 4834*x^2 - 466*y^2 + 6868*x*z + 4834*z^2
  (-1877/1242 : 4265/1242 : 1)  C1a (-451/1345 : -189/1345 : 1)
** u= -80/89 ; tau(u)= 258/169 ; -50722*x^2 + 9442*y^2 + 72964*x*z - 50722*z^2
  (5/8 : -13/8 : 1)  C2b (4999726/216521 : 616883/216521 : 1)
** u= 80/121 ; tau(u)= 162/41 ; 3038*x^2 + 22882*y^2 + 32644*x*z + 3038*z^2
  (-103/535 : 198/535 : 1)  C1b (2395/7986 : 467/7986 : 1)
** u= 80/277 ; tau(u)= 474/197 ; -71218*x^2 + 147058*y^2 + 231076*x*z - 71218*z^2
  (44156/245625 : -114541/245625 : 1)  C1b (74959061/830390 : 4283337/830390 : 1)
** u= -83/113 ; tau(u)= 309/196 ; -69943*x^2 + 18649*y^2 + 102370*x*z - 69943*z^2
  (10511/53693 : 90160/53693 : 1)  C2b (-4609684639/233361157 : 511399657/233361157 : 1)
** u= 84/121 ; tau(u)= 158/37 ; 4318*x^2 + 22226*y^2 + 32020*x*z + 4318*z^2
  (-1068/5543 : -1529/5543 : 1)  C1b (1241545/338954 : 73035/338954 : 1)
** u= 84/313 ; tau(u)= 542/229 ; -97826*x^2 + 188882*y^2 + 300820*x*z - 97826*z^2
  (14111983/105718812 : 59292647/105718812 : 1)  C1b (-7576777/1179661 : -463983/1179661 : 1)
** u= -85/157 ; tau(u)= 399/242 ; -109903*x^2 + 42073*y^2 + 166426*x*z - 109903*z^2
  (132361/79785 : -143594/79785 : 1)  C2b (1169801/19594821 : 1714117/19594821 : 1)
** u= 87/257 ; tau(u)= 427/170 ; -50231*x^2 + 124529*y^2 + 189898*x*z - 50231*z^2
  (36169/9329 : -6946/9329 : 1)  C1b (-5819824166/13623671 : 328920393/13623671 : 1)
** u= -88/229 ; tau(u)= 546/317 ; -193234*x^2 + 97138*y^2 + 305860*x*z - 193234*z^2
  (3837/4681 : 4040/4681 : 1)  C2b (-2210117594/287947945 : -38997153/57589589 : 1)
** u= -88/373 ; tau(u)= 834/461 ; -417298*x^2 + 270514*y^2 + 703300*x*z - 417298*z^2
  (1705186/158618359 : 195225667/158618359 : 1)  C2b (-4976350/8428259 : -889815/8428259 : 1)
** u= 89/205 ; tau(u)= 321/116 ; -18991*x^2 + 76129*y^2 + 110962*x*z - 18991*z^2
  (-8063/2055 : -6436/2055 : 1)  C1b (-296683658/11364055 : -16501923/11364055 : 1)
** u= -89/281 ; tau(u)= 651/370 ; -265879*x^2 + 150001*y^2 + 431722*x*z - 265879*z^2
  (76745/79809 : -64042/79809 : 1)  C2b (-460736454/24185719 : -36936847/24185719 : 1)
** u= -89/377 ; tau(u)= 843/466 ; -426391*x^2 + 276337*y^2 + 718570*x*z - 426391*z^2
  (-24919/31349 : 67126/31349 : 1)  C2b (-3083115/934121 : 273955/934121 : 1)
** u= 90/49 ; tau(u)= -8/41 ; 4738*x^2 - 3298*y^2 + 8164*x*z + 4738*z^2
  (-1613/1789 : 1092/1789 : 1)  C1a (-210530/7819 : 14831/7819 : 1)
** u= 93/40 ; tau(u)= 13/53 ; 3031*x^2 - 5449*y^2 + 8818*x*z + 3031*z^2
  (-203/1185 : -644/1185 : 1)  C1a (223682/331887 : 26741/331887 : 1)
** u= 93/337 ; tau(u)= 581/244 ; -110423*x^2 + 218489*y^2 + 346210*x*z - 110423*z^2
  (2413/9863 : 276968/719999 : 1)  C1b (-431218/4339 : -1818327/316747 : 1)
** u= -96/145 ; tau(u)= 386/241 ; -106946*x^2 + 32834*y^2 + 158212*x*z - 106946*z^2
  (-3763/33211 : 65122/33211 : 1)  C2b (-3627905/508589 : -400539/508589 : 1)
** u= 96/293 ; tau(u)= 490/197 ; -68402*x^2 + 162482*y^2 + 249316*x*z - 68402*z^2
  (-211019/336725 : 418936/336725 : 1)  C1b (56620223/37616365 : -3328923/37616365 : 1)
** u= -97/153 ; tau(u)= 403/250 ; -115591*x^2 + 37409*y^2 + 171818*x*z - 115591*z^2
  (-86399/4872529 : -8678490/4872529 : 1)  C2b (23545/58126 : 4483/58126 : 1)
** u= -97/265 ; tau(u)= 627/362 ; -252679*x^2 + 131041*y^2 + 402538*x*z - 252679*z^2
  (609/545 : -518/545 : 1)  C2b (10892353/9998350 : 725427/9998350 : 1)
** u= -97/361 ; tau(u)= 819/458 ; -410119*x^2 + 251233*y^2 + 680170*x*z - 410119*z^2
  (1092607/807227 : -790362/807227 : 1)  C2b (23412710/63406549 : -233345/3729797 : 1)
** u= -101/117 ; tau(u)= 335/218 ; -84847*x^2 + 17177*y^2 + 122426*x*z - 84847*z^2
  (26171/37907 : 58398/37907 : 1)  C2b (3870726/2187689 : 346049/2187689 : 1)
** u= 101/313 ; tau(u)= 525/212 ; -79687*x^2 + 185737*y^2 + 285826*x*z - 79687*z^2
  (151413/1714747 : -933700/1714747 : 1)  C1b (-4444349810/158799503 : -254830433/158799503 : 1)
** u= -103/169 ; tau(u)= 441/272 ; -137359*x^2 + 46513*y^2 + 205090*x*z - 137359*z^2
  (-2400547/422041419 : 728349440/422041419 : 1)  C2b (-7297789/1362502 : 794519/1362502 : 1)
** u= -103/225 ; tau(u)= 553/328 ; -204559*x^2 + 90641*y^2 + 316418*x*z - 204559*z^2
  (253/7 : -372/7 : 1)  C2b (-7343835/2313386 : -770311/2313386 : 1)
** u= 103/377 ; tau(u)= 651/274 ; -139543*x^2 + 273649*y^2 + 434410*x*z - 139543*z^2
  (314479/66859 : -139042/66859 : 1)  C1b (3798698/2135071 : 213911/2135071 : 1)
** u= -103/397 ; tau(u)= 897/500 ; -489391*x^2 + 304609*y^2 + 815218*x*z - 489391*z^2
  (485017/42547423 : 53418980/42547423 : 1)  C2b (-13075/1041 : -1027/1041 : 1)
** u= -104/101 ; tau(u)= 306/205 ; -73234*x^2 + 9586*y^2 + 104452*x*z - 73234*z^2
  (608/3991 : -9903/3991 : 1)  C2b (-41066/70661 : 15653/70661 : 1)
** u= -104/305 ; tau(u)= 714/409 ; -323746*x^2 + 175234*y^2 + 520612*x*z - 323746*z^2
  (-71141/104962 : 227791/104962 : 1)  C2b (147322645/4095022 : 11416617/4095022 : 1)
** u= 105/68 ; tau(u)= -31/37 ; 8287*x^2 - 1777*y^2 + 11986*x*z + 8287*z^2
  (-887/617 : -1324/617 : 1)  C1a (566467/17890 : -68777/17890 : 1)
** u= 105/137 ; tau(u)= 169/32 ; 8977*x^2 + 26513*y^2 + 39586*x*z + 8977*z^2
  (-123991/510351 : 32968/510351 : 1)  C1b (1683430/873347 : 115401/873347 : 1)
** u= 105/377 ; tau(u)= 649/272 ; -136943*x^2 + 273233*y^2 + 432226*x*z - 136943*z^2
  (68977/490479 : 263512/490479 : 1)  C1b (-47210323/3412585 : 2784321/3412585 : 1)
** u= 111/50 ; tau(u)= 11/61 ; 4879*x^2 - 7321*y^2 + 12442*x*z + 4879*z^2
  (11 : 10 : 1)  C1a (4542127/418245 : -281551/418245 : 1)
** u= -111/377 ; tau(u)= 865/488 ; -463967*x^2 + 271937*y^2 + 760546*x*z - 463967*z^2
  (23335/21261 : 17684/21261 : 1)  C2b (10244662/22121363 : 1363623/22121363 : 1)
** u= -112/81 ; tau(u)= 274/193 ; -61954*x^2 + 578*y^2 + 87620*x*z - 61954*z^2
  (19 : 3222/17 : 1)  C2b (1217/1659 : -11239/28203 : 1)
** u= 112/113 ; tau(u)= 114 ; 12542*x^2 + 12994*y^2 + 25540*x*z + 12542*z^2
  (-106117/122901 : 13630/122901 : 1)  C1b (-282114/406877 : -23333/406877 : 1)
** u= -112/121 ; tau(u)= 354/233 ; -96034*x^2 + 16738*y^2 + 137860*x*z - 96034*z^2
  (18002/4593 : 36047/4593 : 1)  C2b (159370/163871 : -16535/163871 : 1)
** u= 112/153 ; tau(u)= 194/41 ; 9182*x^2 + 34274*y^2 + 50180*x*z + 9182*z^2
  (-48007/111323 : -62346/111323 : 1)  C1b (-194846/168487 : -12901/168487 : 1)
** u= 112/221 ; tau(u)= 330/109 ; -11218*x^2 + 85138*y^2 + 121444*x*z - 11218*z^2
  (-17351/209467 : 104906/209467 : 1)  C1b (5879178/3786395 : 3769/39035 : 1)
** u= 112/225 ; tau(u)= 338/113 ; -12994*x^2 + 88706*y^2 + 126788*x*z - 12994*z^2
  (2521/146836 : 51285/146836 : 1)  C1b (-1774534003/124094462 : -97964293/124094462 : 1)
** u= -112/337 ; tau(u)= 786/449 ; -390658*x^2 + 214594*y^2 + 630340*x*z - 390658*z^2
  (33212/270587 : -329999/270587 : 1)  C2b (13362865/1568931 : 976085/1568931 : 1)
** u= 114 ; tau(u)= 112/113 ; -12542*x^2 - 12994*y^2 + 25540*x*z - 12542*z^2
  (7/8 : 1/8 : 1)  C1a (269511/260998 : -17167/260998 : 1)
** u= 114/29 ; tau(u)= 56/85 ; -1454*x^2 - 11314*y^2 + 16132*x*z - 1454*z^2
  (219/2320 : 163/2320 : 1)  C1a (162456667/2346278 : 8862147/2346278 : 1)
** u= 114/49 ; tau(u)= 16/65 ; 4546*x^2 - 8194*y^2 + 13252*x*z + 4546*z^2
  (-487/150 : -161/150 : 1)  C1a (435402/74753 : -27127/74753 : 1)
** u= -115/157 ; tau(u)= 429/272 ; -134743*x^2 + 36073*y^2 + 197266*x*z - 134743*z^2
  (5097/191 : 9584/191 : 1)  C2b (-3756898/2417867 : 608541/2417867 : 1)
** u= -115/289 ; tau(u)= 693/404 ; -313207*x^2 + 153817*y^2 + 493474*x*z - 313207*z^2
  (-2121/7433 : -13124/7433 : 1)  C2b (185837/442282 : 29059/442282 : 1)
** u= 119/58 ; tau(u)= 3/61 ; 6719*x^2 - 7433*y^2 + 14170*x*z + 6719*z^2
  (3389/10719 : -13546/10719 : 1)  C1a (-399298994/24058267 : 24532707/24058267 : 1)
** u= 119/369 ; tau(u)= 619/250 ; -110839*x^2 + 258161*y^2 + 397322*x*z - 110839*z^2
  (362423/2239247 : -979890/2239247 : 1)  C1b (40915798/23709537 : 2336129/23709537 : 1)
** u= 121/40 ; tau(u)= 41/81 ; 1519*x^2 - 11441*y^2 + 16322*x*z + 1519*z^2
  (-125/1943 : -396/1943 : 1)  C1a (2395/7986 : 467/7986 : 1)
** u= 121/225 ; tau(u)= 329/104 ; -6991*x^2 + 86609*y^2 + 122882*x*z - 6991*z^2
  (-19157/108553 : -62700/108553 : 1)  C1b (-11331098/3730227 : 660817/3730227 : 1)
** u= -124/117 ; tau(u)= 358/241 ; -100786*x^2 + 12002*y^2 + 143540*x*z - 100786*z^2
  (172/169 : 375/169 : 1)  C2b (-243391098/12314999 : -39890957/12314999 : 1)
** u= 124/197 ; tau(u)= 270/73 ; 4718*x^2 + 62242*y^2 + 88276*x*z + 4718*z^2
  (-21613/148402 : 53331/148402 : 1)  C1b (42786577/3469803 : -2348327/3469803 : 1)
** u= 125/193 ; tau(u)= 261/68 ; 6377*x^2 + 58873*y^2 + 83746*x*z + 6377*z^2
  (-8077/14913 : 11840/14913 : 1)  C1b (12237379/33113295 : 1972907/33113295 : 1)
** u= 125/241 ; tau(u)= 357/116 ; -11287*x^2 + 100537*y^2 + 143074*x*z - 11287*z^2
  (-4239/303571 : 110360/303571 : 1)  C1b (-16921949/443526 : 925547/443526 : 1)
** u= 126/89 ; tau(u)= -52/37 ; 13138*x^2 - 34*y^2 + 18580*x*z + 13138*z^2
  (-211/1076 : 18453/1076 : 1)  C1a (-129/218 : -167/218 : 1)
** u= -128/101 ; tau(u)= 330/229 ; -88498*x^2 + 4018*y^2 + 125284*x*z - 88498*z^2
  (2661/2885 : 69968/20195 : 1)  C2b (-13466/7181 : 34367/50267 : 1)
** u= 128/169 ; tau(u)= 210/41 ; 13022*x^2 + 40738*y^2 + 60484*x*z + 13022*z^2
  (-785/1087 : -832/1087 : 1)  C1b (-222126/1366691 : 74491/1366691 : 1)
** u= -128/365 ; tau(u)= 858/493 ; -469714*x^2 + 250066*y^2 + 752548*x*z - 469714*z^2
  (781/735 : 94/105 : 1)  C2b (4128674/958115 : -286371/958115 : 1)
** u= 129/40 ; tau(u)= 49/89 ; 799*x^2 - 13441*y^2 + 19042*x*z + 799*z^2
  (-349/27159 : -5516/27159 : 1)  C1a (-43451495/266462 : -2364981/266462 : 1)
** u= 132/197 ; tau(u)= 262/65 ; 8974*x^2 + 60194*y^2 + 86068*x*z + 8974*z^2
  (-213/100 : 149/100 : 1)  C1b (-6632761/142006 : -362037/142006 : 1)
** u= -132/349 ; tau(u)= 830/481 ; -445298*x^2 + 226178*y^2 + 706324*x*z - 445298*z^2
  (110318/257431 : -15083/15143 : 1)  C2b (24901846/1892879 : 1919991/1892879 : 1)
** u= 133/153 ; tau(u)= 173/20 ; 16889*x^2 + 29129*y^2 + 47618*x*z + 16889*z^2
  (-64579/119891 : 43644/119891 : 1)  C1b (10781610/2301433 : 689821/2301433 : 1)
** u= 136/233 ; tau(u)= 330/97 ; -322*x^2 + 90082*y^2 + 127396*x*z - 322*z^2
  (-14021/18943 : 19432/18943 : 1)  C1b (1735730/1030047 : -109663/1030047 : 1)
** u= 136/261 ; tau(u)= 386/125 ; -12754*x^2 + 117746*y^2 + 167492*x*z - 12754*z^2
  (29531/484199 : 71760/484199 : 1)  C1b (-46159223/464873950 : -25674569/464873950 : 1)
** u= 136/333 ; tau(u)= 530/197 ; -59122*x^2 + 203282*y^2 + 299396*x*z - 59122*z^2
  (-25553/93979 : 79344/93979 : 1)  C1b (3109125/2384078 : -195647/2384078 : 1)
** u= 137/40 ; tau(u)= 57/97 ; -49*x^2 - 15569*y^2 + 22018*x*z - 49*z^2
  (2551/3427 : -3508/3427 : 1)  C1a (138336214/1492705 : -7524807/1492705 : 1)
** u= -137/257 ; tau(u)= 651/394 ; -291703*x^2 + 113329*y^2 + 442570*x*z - 291703*z^2
  (34681/36037 : 39470/36037 : 1)  C2b (-13835527/2743886 : 1426269/2743886 : 1)
** u= 138/85 ; tau(u)= -32/53 ; 13426*x^2 - 4594*y^2 + 20068*x*z + 13426*z^2
  (-17961/8711 : 21934/8711 : 1)  C1a (10078/4595 : 1299/4595 : 1)
** u= -140/101 ; tau(u)= 342/241 ; -96562*x^2 + 802*y^2 + 136564*x*z - 96562*z^2
  (-2709/3610 : -64171/3610 : 1)  C2b (20893/71538 : -35009/71538 : 1)
** u= -140/149 ; tau(u)= 438/289 ; -147442*x^2 + 24802*y^2 + 211444*x*z - 147442*z^2
  (3568/44661 : -102833/44661 : 1)  C2b (-17766/36625 : 6763/36625 : 1)
** u= 140/181 ; tau(u)= 222/41 ; 16238*x^2 + 45922*y^2 + 68884*x*z + 16238*z^2
  (-12728/48349 : 6263/48349 : 1)  C1b (518449/26419 : 29427/26419 : 1)
** u= 140/333 ; tau(u)= 526/193 ; -54898*x^2 + 202178*y^2 + 296276*x*z - 54898*z^2
  (-179282/326641 : -351447/326641 : 1)  C1b (8132887/214590 : -448261/214590 : 1)
** u= 141/80 ; tau(u)= -19/61 ; 12439*x^2 - 7081*y^2 + 20242*x*z + 12439*z^2
  (-65107/357717 : 407008/357717 : 1)  C1a (-405521/65130 : -28543/65130 : 1)
** u= -141/373 ; tau(u)= 887/514 ; -508511*x^2 + 258377*y^2 + 806650*x*z - 508511*z^2
  (-4531451/6772557 : -105348730/47407899 : 1)  C2b (-1600351/157342 : -963939/1101394 : 1)
** u= -143/261 ; tau(u)= 665/404 ; -305983*x^2 + 115793*y^2 + 462674*x*z - 305983*z^2
  (41209/130555 : 167424/130555 : 1)  C2b (519293/622745 : -43823/622745 : 1)
** u= 145/197 ; tau(u)= 249/52 ; 15617*x^2 + 56593*y^2 + 83026*x*z + 15617*z^2
  (-20227/103455 : -1888/103455 : 1)  C1b (794333/852090 : -70331/852090 : 1)
** u= 147/205 ; tau(u)= 263/58 ; 14881*x^2 + 62441*y^2 + 90778*x*z + 14881*z^2
  (-17235/87149 : -17402/87149 : 1)  C1b (145239871/1693346 : 8025741/1693346 : 1)
** u= -147/365 ; tau(u)= 877/512 ; -502679*x^2 + 244841*y^2 + 790738*x*z - 502679*z^2
  (-995403/1914475 : -3964064/1914475 : 1)  C2b (-267072758/39675125 : -24157503/39675125 : 1)
** u= 148/221 ; tau(u)= 294/73 ; 11246*x^2 + 75778*y^2 + 108340*x*z + 11246*z^2
  (-5498/577 : -7/577 : 1)  C1b (-147281622/61912189 : -8407339/61912189 : 1)
** u= -148/241 ; tau(u)= 630/389 ; -280738*x^2 + 94258*y^2 + 418804*x*z - 280738*z^2
  (9416/683 : -15391/683 : 1)  C2b (215004450/225237721 : -17256019/225237721 : 1)
** u= 149/181 ; tau(u)= 213/32 ; 20153*x^2 + 43321*y^2 + 67570*x*z + 20153*z^2
  (-63077/63853 : -50344/63853 : 1)  C1b (-222858/3451 : -437/119 : 1)
** u= -149/245 ; tau(u)= 639/394 ; -288271*x^2 + 97849*y^2 + 430522*x*z - 288271*z^2
  (2914313/11746801 : -16760646/11746801 : 1)  C2b (-57570/3942793 : -381997/3942793 : 1)
** u= -151/241 ; tau(u)= 633/392 ; -284527*x^2 + 93361*y^2 + 423490*x*z - 284527*z^2
  (295653/22347359 : 38630060/22347359 : 1)  C2b (1741785/302741 : -151445/302741 : 1)
** u= -152/113 ; tau(u)= 378/265 ; -117346*x^2 + 2434*y^2 + 165988*x*z - 117346*z^2
  (-3373/4375 : -49776/4375 : 1)  C2b (1530/16391 : -5797/16391 : 1)
** u= -152/197 ; tau(u)= 546/349 ; -220498*x^2 + 54514*y^2 + 321220*x*z - 220498*z^2
  (36083/46527 : 64264/46527 : 1)  C2b (21015802/17294579 : -1726411/17294579 : 1)
** u= -152/257 ; tau(u)= 666/409 ; -311458*x^2 + 108994*y^2 + 466660*x*z - 311458*z^2
  (-9043/8353 : 27504/8353 : 1)  C2b (3649242/1762895 : -52991/352579 : 1)
** u= 152/261 ; tau(u)= 370/109 ; -658*x^2 + 113138*y^2 + 160004*x*z - 658*z^2
  (-20824/4097 : -11103/4097 : 1)  C1b (-14296510/38355543 : -2229503/38355543 : 1)
** u= 154/65 ; tau(u)= 24/89 ; 7874*x^2 - 15266*y^2 + 24292*x*z + 7874*z^2
  (-610/2699 : -1153/2699 : 1)  C1a (-8303245/631271 : 468537/631271 : 1)
** u= 156/205 ; tau(u)= 254/49 ; 19534*x^2 + 59714*y^2 + 88852*x*z + 19534*z^2
  (-15871/39636 : -18431/39636 : 1)  C1b (1322894/103615 : 75291/103615 : 1)
** u= -157/117 ; tau(u)= 391/274 ; -125503*x^2 + 2729*y^2 + 177530*x*z - 125503*z^2
  (35143/986239 : 6521790/986239 : 1)  C2b (126246847/57516346 : 34958663/57516346 : 1)
** u= 157/369 ; tau(u)= 581/212 ; -65239*x^2 + 247673*y^2 + 362210*x*z - 65239*z^2
  (-48929/242917 : 3114120/4129589 : 1)  C1b (3400330/91729 : 187235/91729 : 1)
** u= 158/37 ; tau(u)= 84/121 ; -4318*x^2 - 22226*y^2 + 32020*x*z - 4318*z^2
  (2757/18968 : -1991/18968 : 1)  C1a (-27242791/328853 : -1498149/328853 : 1)
** u= -159/181 ; tau(u)= 521/340 ; -205919*x^2 + 40241*y^2 + 296722*x*z - 205919*z^2
  (8013/153559 : 47792/21937 : 1)  C2b (350978770/11293613 : -42630591/11293613 : 1)
** u= 159/377 ; tau(u)= 595/218 ; -69767*x^2 + 258977*y^2 + 379306*x*z - 69767*z^2
  (729/6685 : -2246/6685 : 1)  C1b (1393058806/611070065 : 78299649/611070065 : 1)
** u= -161/153 ; tau(u)= 467/314 ; -171271*x^2 + 20897*y^2 + 244010*x*z - 171271*z^2
  (-28021/1811231 : -5242746/1811231 : 1)  C2b (219913/449365 : -10441/89873 : 1)
** u= -161/377 ; tau(u)= 915/538 ; -552967*x^2 + 258337*y^2 + 863146*x*z - 552967*z^2
  (2648833/1555053 : 2536126/1555053 : 1)  C2b (-13632637/3346287 : -1336373/3346287 : 1)
** u= 162/41 ; tau(u)= 80/121 ; -3038*x^2 - 22882*y^2 + 32644*x*z - 3038*z^2
  (490/3767 : 847/3767 : 1)  C1a (3360310/160963 : 182969/160963 : 1)
** u= 164/229 ; tau(u)= 294/65 ; 18446*x^2 + 77986*y^2 + 113332*x*z + 18446*z^2
  (-2719/5342 : -3551/5342 : 1)  C1b (3337/186938 : -10339/186938 : 1)
** u= -164/233 ; tau(u)= 630/397 ; -288322*x^2 + 81682*y^2 + 423796*x*z - 288322*z^2
  (6211/17018 : 24699/17018 : 1)  C2b (376506/433969 : -34201/433969 : 1)
** u= 164/277 ; tau(u)= 390/113 ; 1358*x^2 + 126562*y^2 + 178996*x*z + 1358*z^2
  (-347605/700676 : -581291/700676 : 1)  C1b (55106606/32790475 : 3499639/32790475 : 1)
** u= 164/333 ; tau(u)= 502/169 ; -30226*x^2 + 194882*y^2 + 278900*x*z - 30226*z^2
  (641/5846 : 39/5846 : 1)  C1b (-55597611/29073938 : -3582521/29073938 : 1)
** u= 165/52 ; tau(u)= 61/113 ; 1687*x^2 - 21817*y^2 + 30946*x*z + 1687*z^2
  (-79315/2559901 : 468196/2559901 : 1)  C1a (-1200135/83987 : 65287/83987 : 1)
** u= -165/389 ; tau(u)= 943/554 ; -586607*x^2 + 275417*y^2 + 916474*x*z - 586607*z^2
  (1253/3709 : 70462/63053 : 1)  C2b (16856030/1304209 : -22768989/22171553 : 1)
** u= 166/85 ; tau(u)= -4/81 ; 14434*x^2 - 13106*y^2 + 27572*x*z + 14434*z^2
  (5875/922232 : -973719/922232 : 1)  C1a (1623927/90347 : -110989/90347 : 1)
** u= -167/125 ; tau(u)= 417/292 ; -142639*x^2 + 3361*y^2 + 201778*x*z - 142639*z^2
  (13053/73843 : -60740/10549 : 1)  C2b (-239390/32853 : -401/141 : 1)
** u= 168/173 ; tau(u)= 178/5 ; 28174*x^2 + 31634*y^2 + 59908*x*z + 28174*z^2
  (-3079/4197 : 584/4197 : 1)  C1b (-2452690/22813 : -153711/22813 : 1)
** u= 169/32 ; tau(u)= 105/137 ; -8977*x^2 - 26513*y^2 + 39586*x*z - 8977*z^2
  (174929/435449 : -197912/435449 : 1)  C1a (-43399802/1934605 : 2452359/1934605 : 1)
** u= 169/305 ; tau(u)= 441/136 ; -8431*x^2 + 157489*y^2 + 223042*x*z - 8431*z^2
  (19681/629667 : 60788/629667 : 1)  C1b (12535151/1659051 : 684871/1659051 : 1)
** u= 172/261 ; tau(u)= 350/89 ; 13742*x^2 + 106658*y^2 + 152084*x*z + 13742*z^2
  (-5357/42700 : -9357/42700 : 1)  C1b (97166570/5651553 : 5343727/5651553 : 1)
** u= -172/277 ; tau(u)= 726/449 ; -373618*x^2 + 123874*y^2 + 556660*x*z - 373618*z^2
  (-80334/5147539 : -9044123/5147539 : 1)  C2b (5170047/1429054 : -421009/1429054 : 1)
** u= 172/353 ; tau(u)= 534/181 ; -35938*x^2 + 219634*y^2 + 314740*x*z - 35938*z^2
  (-11801/235594 : 114407/235594 : 1)  C1b (203215/229261 : -15795/229261 : 1)
** u= 172/365 ; tau(u)= 558/193 ; -44914*x^2 + 236866*y^2 + 340948*x*z - 44914*z^2
  (2465/48508 : -116127/339556 : 1)  C1b (8809130/972337 : 3355129/6806359 : 1)
** u= 173/20 ; tau(u)= 133/153 ; -16889*x^2 - 29129*y^2 + 47618*x*z - 16889*z^2
  (37621/30677 : -22812/30677 : 1)  C1a (-77843/25847 : -5281/25847 : 1)
** u= 173/181 ; tau(u)= 189/8 ; 29801*x^2 + 35593*y^2 + 65650*x*z + 29801*z^2
  (-26497/20221 : -7620/20221 : 1)  C1b (6434250/4224481 : 569065/4224481 : 1)
** u= 174/61 ; tau(u)= 52/113 ; 4738*x^2 - 22834*y^2 + 32980*x*z + 4738*z^2
  (-1896/13439 : 8339/94073 : 1)  C1a (164569/8518 : -63877/59626 : 1)
** u= -175/373 ; tau(u)= 921/548 ; -569983*x^2 + 247633*y^2 + 878866*x*z - 569983*z^2
  (78643/81153 : 82120/81153 : 1)  C2b (-26204997/5199983 : -2571329/5199983 : 1)
** u= -176/221 ; tau(u)= 618/397 ; -284242*x^2 + 66706*y^2 + 412900*x*z - 284242*z^2
  (61198/116389 : 24575/16627 : 1)  C2b (829307/124401 : -85247/124401 : 1)
** u= -176/245 ; tau(u)= 666/421 ; -323506*x^2 + 89074*y^2 + 474532*x*z - 323506*z^2
  (-2945/4041 : -12418/4041 : 1)  C2b (-3322450/495921 : 388339/495921 : 1)
** u= -176/333 ; tau(u)= 842/509 ; -487186*x^2 + 190802*y^2 + 739940*x*z - 487186*z^2
  (-23113/35381 : 87930/35381 : 1)  C2b (343137/57971 : 27749/57971 : 1)
** u= -177/289 ; tau(u)= 755/466 ; -402983*x^2 + 135713*y^2 + 601354*x*z - 402983*z^2
  (151039/151719 : -185878/151719 : 1)  C2b (11636075/651226 : -1079319/651226 : 1)
** u= 178/5 ; tau(u)= 168/173 ; -28174*x^2 - 31634*y^2 + 59908*x*z - 28174*z^2
  (2281/3162 : 347/3162 : 1)  C1a (622918/573895 : 38859/573895 : 1)
** u= 186/65 ; tau(u)= 56/121 ; 5314*x^2 - 26146*y^2 + 37732*x*z + 5314*z^2
  (-939/48635 : 20372/48635 : 1)  C1a (5974710/182627 : -329851/182627 : 1)
** u= 189/8 ; tau(u)= 173/181 ; -29801*x^2 - 35593*y^2 + 65650*x*z - 29801*z^2
  (15399/22699 : 3844/22699 : 1)  C1a (-264819307/14151279 : 16867417/14151279 : 1)
** u= 190/73 ; tau(u)= 44/117 ; 8722*x^2 - 25442*y^2 + 38036*x*z + 8722*z^2
  (-4217/18476 : -2577/18476 : 1)  C1a (240797/135897 : -16913/135897 : 1)
** u= 192/205 ; tau(u)= 218/13 ; 36526*x^2 + 47186*y^2 + 84388*x*z + 36526*z^2
  (-7713/13289 : 746/13289 : 1)  C1b (7341565/188039 : 454161/188039 : 1)
** u= 192/277 ; tau(u)= 362/85 ; 22414*x^2 + 116594*y^2 + 167908*x*z + 22414*z^2
  (-3587/2913 : -3308/2913 : 1)  C1b (-150402458/29154365 : 8196681/29154365 : 1)
** u= 192/313 ; tau(u)= 434/121 ; 7582*x^2 + 159074*y^2 + 225220*x*z + 7582*z^2
  (-3541/99417 : 5170/99417 : 1)  C1b (-7196858/8432201 : 593223/8432201 : 1)
** u= 194/41 ; tau(u)= 112/153 ; -9182*x^2 - 34274*y^2 + 50180*x*z - 9182*z^2
  (137/181 : 150/181 : 1)  C1a (9705334/13491203 : -836201/13491203 : 1)
** u= 197/265 ; tau(u)= 333/68 ; 29561*x^2 + 101641*y^2 + 149698*x*z + 29561*z^2
  (-49559/72143 : 55116/72143 : 1)  C1b (1836102/1098247 : 128677/1098247 : 1)
** u= 199/74 ; tau(u)= 51/125 ; 8351*x^2 - 28649*y^2 + 42202*x*z + 8351*z^2
  (107/1017 : 682/1017 : 1)  C1a (-3580598/1146685 : 196353/1146685 : 1)
** u= -199/157 ; tau(u)= 513/356 ; -213871*x^2 + 9697*y^2 + 302770*x*z - 213871*z^2
  (18581/12043 : 61860/12043 : 1)  C2b (6650010/1890841 : -1400645/1890841 : 1)
** u= -203/185 ; tau(u)= 573/388 ; -259879*x^2 + 27241*y^2 + 369538*x*z - 259879*z^2
  (38897/31059 : 5008/1827 : 1)  C2b (-416733367/42756805 : -5803351/3288985 : 1)
** u= 208/281 ; tau(u)= 354/73 ; 32606*x^2 + 114658*y^2 + 168580*x*z + 32606*z^2
  (-5951/27483 : 3950/27483 : 1)  C1b (71239273/177419 : -3952909/177419 : 1)
** u= -209/153 ; tau(u)= 515/362 ; -218407*x^2 + 3137*y^2 + 308906*x*z - 218407*z^2
  (803/65411 : 541074/65411 : 1)  C2b (-260837802/175837 : -118445753/175837 : 1)
** u= 210/41 ; tau(u)= 128/169 ; -13022*x^2 - 40738*y^2 + 60484*x*z - 13022*z^2
  (5821/7127 : 5876/7127 : 1)  C1a (10074978/2460173 : 548573/2460173 : 1)
** u= 210/109 ; tau(u)= -8/101 ; 23698*x^2 - 20338*y^2 + 44164*x*z + 23698*z^2
  (2265/3023 : 5612/3023 : 1)  C1a (209520271/7223051 : -14388969/7223051 : 1)
** u= 210/113 ; tau(u)= -16/97 ; 25282*x^2 - 18562*y^2 + 44356*x*z + 25282*z^2
  (2161/11357 : -15514/11357 : 1)  C1a (2471274/201109 : -183209/201109 : 1)
** u= -211/277 ; tau(u)= 765/488 ; -431767*x^2 + 108937*y^2 + 629746*x*z - 431767*z^2
  (491393/1405819 : 2190132/1405819 : 1)  C2b (-1358081/910035 : 229819/910035 : 1)
** u= -211/337 ; tau(u)= 885/548 ; -556087*x^2 + 182617*y^2 + 827746*x*z - 556087*z^2
  (-927237/1466249 : -3914992/1466249 : 1)  C2b (201091195/88648743 : 15193667/88648743 : 1)
** u= 213/32 ; tau(u)= 149/181 ; -20153*x^2 - 43321*y^2 + 67570*x*z - 20153*z^2
  (109311/184631 : -100312/184631 : 1)  C1a (22224038/2727085 : -246411/545417 : 1)
** u= 217/333 ; tau(u)= 449/116 ; 20177*x^2 + 174689*y^2 + 248690*x*z + 20177*z^2
  (-6839/54463 : 13500/54463 : 1)  C1b (2275826/1447737 : 152513/1447737 : 1)
** u= 217/365 ; tau(u)= 513/148 ; 3281*x^2 + 219361*y^2 + 310258*x*z + 3281*z^2
  (-2989/180337 : 16608/180337 : 1)  C1b (7775986/7782645 : 46277/598665 : 1)
** u= 218/13 ; tau(u)= 192/205 ; -36526*x^2 - 47186*y^2 + 84388*x*z - 36526*z^2
  (16983/29269 : 1604/29269 : 1)  C1a (-3311575/268829 : 210201/268829 : 1)
** u= 218/137 ; tau(u)= -56/81 ; 34402*x^2 - 9986*y^2 + 50660*x*z + 34402*z^2
  (-3758/2363 : -4779/2363 : 1)  C1a (3899785/613946 : 447125/613946 : 1)
** u= 221/369 ; tau(u)= 517/148 ; 5033*x^2 + 223481*y^2 + 316130*x*z + 5033*z^2
  (-334313/20913049 : 194460/20913049 : 1)  C1b (5094334/6511003 : -453193/6511003 : 1)
** u= 222/41 ; tau(u)= 140/181 ; -16238*x^2 - 45922*y^2 + 68884*x*z - 16238*z^2
  (1414/5249 : -827/5249 : 1)  C1a (-72587/8862 : 4211/8862 : 1)
** u= 222/149 ; tau(u)= -76/73 ; 38626*x^2 - 4882*y^2 + 55060*x*z + 38626*z^2
  (7343/6852 : -36953/6852 : 1)  C1a (-17645/9399 : 1985/9399 : 1)
** u= 223/225 ; tau(u)= 227/2 ; 49721*x^2 + 51521*y^2 + 101258*x*z + 49721*z^2
  (-399221/337459 : -32670/337459 : 1)  C1b (122771806/18018505 : 8499539/18018505 : 1)
** u= -223/361 ; tau(u)= 945/584 ; -632383*x^2 + 210913*y^2 + 942754*x*z - 632383*z^2
  (-177407/246179 : 686508/246179 : 1)  C2b (6036055/272507 : 566357/272507 : 1)
** u= 226/101 ; tau(u)= 24/125 ; 19826*x^2 - 30674*y^2 + 51652*x*z + 19826*z^2
  (2491/11829 : 84020/82803 : 1)  C1a (223129/29101 : -97983/203707 : 1)
** u= 227/2 ; tau(u)= 223/225 ; -49721*x^2 - 51521*y^2 + 101258*x*z - 49721*z^2
  (3221/3799 : 330/3799 : 1)  C1a (-270302798/35179173 : 18544483/35179173 : 1)
** u= 227/333 ; tau(u)= 439/106 ; 29057*x^2 + 170249*y^2 + 244250*x*z + 29057*z^2
  (-113719/847601 : 116022/847601 : 1)  C1b (11494151/1991075 : 130349/398215 : 1)
** u= -227/369 ; tau(u)= 965/596 ; -658903*x^2 + 220793*y^2 + 982754*x*z - 658903*z^2
  (732685/1677907 : 304116/239701 : 1)  C2b (-27126571/6247626 : -3054781/6247626 : 1)
** u= 228/229 ; tau(u)= 230 ; 51982*x^2 + 52898*y^2 + 104884*x*z + 51982*z^2
  (-28810/27793 : 3593/27793 : 1)  C1b (14684042/708265 : 969147/708265 : 1)
** u= 230 ; tau(u)= 228/229 ; -51982*x^2 - 52898*y^2 + 104884*x*z - 51982*z^2
  (22833/21986 : -2833/21986 : 1)  C1a (-510250879/8496941 : -33137451/8496941 : 1)
** u= -232/169 ; tau(u)= 570/401 ; -267778*x^2 + 3298*y^2 + 378724*x*z - 267778*z^2
  (81/121 : 772/121 : 1)  C2b (-333547/211630 : 247927/211630 : 1)
** u= -232/193 ; tau(u)= 618/425 ; -307426*x^2 + 20674*y^2 + 435748*x*z - 307426*z^2
  (34669/32181 : 98780/32181 : 1)  C2b (-3381495/989219 : -869177/989219 : 1)
** u= 232/305 ; tau(u)= 378/73 ; 43166*x^2 + 132226*y^2 + 196708*x*z + 43166*z^2
  (-9601/23955 : -11168/23955 : 1)  C1b (682020630/47838209 : 38721661/47838209 : 1)
** u= -232/325 ; tau(u)= 882/557 ; -566674*x^2 + 157426*y^2 + 831748*x*z - 566674*z^2
  (643/141843 : 268220/141843 : 1)  C2b (-4307/3855 : -787/3855 : 1)
** u= 235/317 ; tau(u)= 399/82 ; 41777*x^2 + 145753*y^2 + 214426*x*z + 41777*z^2
  (-3069/13199 : -2638/13199 : 1)  C1b (-5555978/399577 : -304689/399577 : 1)
** u= -236/225 ; tau(u)= 686/461 ; -369346*x^2 + 45554*y^2 + 526292*x*z - 369346*z^2
  (9122/46367 : -114975/46367 : 1)  C2b (177993/1440370 : 205457/1440370 : 1)
** u= 238/121 ; tau(u)= -4/117 ; 29266*x^2 - 27362*y^2 + 56660*x*z + 29266*z^2
  (-62356/42463 : 24585/42463 : 1)  C1a (-592785/371587 : 33685/371587 : 1)
** u= 238/125 ; tau(u)= -12/113 ; 31106*x^2 - 25394*y^2 + 56788*x*z + 31106*z^2
  (-321/140 : -223/140 : 1)  C1a (50693837/12100385 : 3981429/12100385 : 1)
** u= -240/181 ; tau(u)= 602/421 ; -296882*x^2 + 7922*y^2 + 420004*x*z - 296882*z^2
  (25461/96379 : -492242/96379 : 1)  C2b (13229941/1308446 : 4109643/1308446 : 1)
** u= 243/146 ; tau(u)= -49/97 ; 40231*x^2 - 16417*y^2 + 61450*x*z + 40231*z^2
  (-15893/15193 : 16758/15193 : 1)  C1a (-3521086/599193 : -279757/599193 : 1)
** u= 246/97 ; tau(u)= 52/149 ; 16114*x^2 - 41698*y^2 + 63220*x*z + 16114*z^2
  (-77/828 : -413/828 : 1)  C1a (230246/475993 : 32619/475993 : 1)
** u= 246/137 ; tau(u)= -28/109 ; 36754*x^2 - 22978*y^2 + 61300*x*z + 36754*z^2
  (1359/8786 : 547/382 : 1)  C1a (37357525/1812577 : 2874095/1812577 : 1)
** u= -247/265 ; tau(u)= 777/512 ; -463279*x^2 + 79441*y^2 + 664738*x*z - 463279*z^2
  (-100235/635691 : -1717088/635691 : 1)  C2b (9442609/3860085 : 965561/3860085 : 1)
** u= 248/289 ; tau(u)= 330/41 ; 58142*x^2 + 105538*y^2 + 170404*x*z + 58142*z^2
  (-2053/3710 : -221/530 : 1)  C1b (-79190/500963 : -27883/500963 : 1)
** u= -248/353 ; tau(u)= 954/601 ; -660898*x^2 + 187714*y^2 + 971620*x*z - 660898*z^2
  (-7609/20558 : 50015/20558 : 1)  C2b (273857121/1192809083 : 106802921/1192809083 : 1)
** u= 249/52 ; tau(u)= 145/197 ; -15617*x^2 - 56593*y^2 + 83026*x*z - 15617*z^2
  (95/471 : 44/471 : 1)  C1a (223402438/86421337 : -12402011/86421337 : 1)
** u= -249/193 ; tau(u)= 635/442 ; -328727*x^2 + 12497*y^2 + 465226*x*z - 328727*z^2
  (-2713/3099 : -27554/3099 : 1)  C2b (3666178/1976267 : -743997/1976267 : 1)
** u= 249/317 ; tau(u)= 385/68 ; 52753*x^2 + 138977*y^2 + 210226*x*z + 52753*z^2
  (-637863/2308247 : -224324/2308247 : 1)  C1b (-85963174/3711985 : 4787691/3711985 : 1)
** u= -251/293 ; tau(u)= 837/544 ; -528871*x^2 + 108697*y^2 + 763570*x*z - 528871*z^2
  (673227/1101853 : -1703368/1101853 : 1)  C2b (1411570/6013277 : 622805/6013277 : 1)
** u= 251/349 ; tau(u)= 447/98 ; 43793*x^2 + 180601*y^2 + 262810*x*z + 43793*z^2
  (-489259/745053 : 581210/745053 : 1)  C1b (-6236135/1426726 : -339945/1426726 : 1)
** u= 253/136 ; tau(u)= -19/117 ; 36631*x^2 - 27017*y^2 + 64370*x*z + 36631*z^2
  (36647/109987 : -166812/109987 : 1)  C1a (-93746685/6096826 : -6383455/6096826 : 1)
** u= 254/49 ; tau(u)= 156/205 ; -19534*x^2 - 59714*y^2 + 88852*x*z - 19534*z^2
  (16126/67387 : -6811/67387 : 1)  C1a (-887122/975905 : 81237/975905 : 1)
** u= -255/233 ; tau(u)= 721/488 ; -411263*x^2 + 43553*y^2 + 584866*x*z - 411263*z^2
  (-141133/78601 : -628804/78601 : 1)  C2b (75246250/5975801 : 11929143/5975801 : 1)
** u= 257/337 ; tau(u)= 417/80 ; 53249*x^2 + 161089*y^2 + 239938*x*z + 53249*z^2
  (-674165/1773181 : 768752/1773181 : 1)  C1b (19362999/6242035 : -1207007/6242035 : 1)
** u= 258/169 ; tau(u)= -80/89 ; 50722*x^2 - 9442*y^2 + 72964*x*z + 50722*z^2
  (-8256/935 : -17641/935 : 1)  C1a (234650238/8125127 : 30562421/8125127 : 1)
** u= 260/277 ; tau(u)= 294/17 ; 67022*x^2 + 85858*y^2 + 154036*x*z + 67022*z^2
  (-3245/5386 : 701/5386 : 1)  C1b (8648603/1352198 : 570789/1352198 : 1)
** u= 261/68 ; tau(u)= 125/193 ; -6377*x^2 - 58873*y^2 + 83746*x*z - 6377*z^2
  (317/177 : 256/177 : 1)  C1a (-46159223/464873950 : -25674569/464873950 : 1)
** u= 262/65 ; tau(u)= 132/197 ; -8974*x^2 - 60194*y^2 + 86068*x*z - 8974*z^2
  (200/1083 : 359/1083 : 1)  C1a (-2243650/2831417 : -207369/2831417 : 1)
** u= 263/58 ; tau(u)= 147/205 ; -14881*x^2 - 62441*y^2 + 90778*x*z - 14881*z^2
  (293/1583 : -238/1583 : 1)  C1a (31409/155555 : -8469/155555 : 1)
** u= -268/349 ; tau(u)= 966/617 ; -689554*x^2 + 171778*y^2 + 1004980*x*z - 689554*z^2
  (-560887/3796608 : 8460677/3796608 : 1)  C2b (13838922294/15123463 : -1529880931/15123463 : 1)
** u= -269/221 ; tau(u)= 711/490 ; -407839*x^2 + 25321*y^2 + 577882*x*z - 407839*z^2
  (-24295/98733 : 470386/98733 : 1)  C2b (3457622/2334625 : 535751/2334625 : 1)
** u= 270/73 ; tau(u)= 124/197 ; -4718*x^2 - 62242*y^2 + 88276*x*z - 4718*z^2
  (9004/56023 : -21711/56023 : 1)  C1a (-27993322/694205 : 1527313/694205 : 1)
** u= -272/257 ; tau(u)= 786/529 ; -485698*x^2 + 58114*y^2 + 691780*x*z - 485698*z^2
  (-654/401 : -19849/2807 : 1)  C2b (5532355/59626 : 6065295/417382 : 1)
** u= -272/269 ; tau(u)= 810/541 ; -511378*x^2 + 70738*y^2 + 730084*x*z - 511378*z^2
  (28541/178387 : 428238/178387 : 1)  C2b (150659/215866 : -22639/215866 : 1)
** u= -272/293 ; tau(u)= 858/565 ; -564466*x^2 + 97714*y^2 + 810148*x*z - 564466*z^2
  (2235/88124 : -207983/88124 : 1)  C2b (-473950/1109071 : -194773/1109071 : 1)
** u= 272/325 ; tau(u)= 378/53 ; 68366*x^2 + 137266*y^2 + 216868*x*z + 68366*z^2
  (-21967/18283 : 15090/18283 : 1)  C1b (2508862/796197 : -164507/796197 : 1)
** u= 274/193 ; tau(u)= -112/81 ; 61954*x^2 - 578*y^2 + 87620*x*z + 61954*z^2
  (-199/217 : -28170/3689 : 1)  C1a (8581/1193 : 90587/20281 : 1)
** u= -275/317 ; tau(u)= 909/592 ; -625303*x^2 + 125353*y^2 + 901906*x*z - 625303*z^2
  (86279/9287065 : 20603736/9287065 : 1)  C2b (83723757/8563825 : 9573379/8563825 : 1)
** u= -276/289 ; tau(u)= 854/565 ; -562274*x^2 + 90866*y^2 + 805492*x*z - 562274*z^2
  (-2577/14780 : -41599/14780 : 1)  C2b (377202466/112105565 : -42153003/112105565 : 1)
** u= 284/373 ; tau(u)= 462/89 ; 64814*x^2 + 197602*y^2 + 294100*x*z + 64814*z^2
  (-54529/210578 : 39625/210578 : 1)  C1b (-178477581/43841750 : 1943507/8768350 : 1)
** u= -291/221 ; tau(u)= 733/512 ; -439607*x^2 + 13001*y^2 + 621970*x*z - 439607*z^2
  (87457/230207 : -1042784/230207 : 1)  C2b (137946299/4861783 : -42567573/4861783 : 1)
** u= -292/337 ; tau(u)= 966/629 ; -706018*x^2 + 141874*y^2 + 1018420*x*z - 706018*z^2
  (83048/76763 : 133729/76763 : 1)  C2b (6326970/2590961 : 600535/2590961 : 1)
** u= 293/136 ; tau(u)= 21/157 ; 36551*x^2 - 48857*y^2 + 86290*x*z + 36551*z^2
  (41221/35329 : -69116/35329 : 1)  C1a (-31711054/14274407 : 1746867/14274407 : 1)
** u= 294/17 ; tau(u)= 260/277 ; -67022*x^2 - 85858*y^2 + 154036*x*z - 67022*z^2
  (38656/26735 : 11389/26735 : 1)  C1a (-13189370/848541 : -831973/848541 : 1)
** u= 294/65 ; tau(u)= 164/229 ; -18446*x^2 - 77986*y^2 + 113332*x*z - 18446*z^2
  (1931/1614 : 1741/1614 : 1)  C1a (-83718217/14294818 : 4807689/14294818 : 1)
** u= 294/73 ; tau(u)= 148/221 ; -11246*x^2 - 75778*y^2 + 108340*x*z - 11246*z^2
  (58/93 : 77/93 : 1)  C1a (152287722/59342039 : 8619011/59342039 : 1)
** u= 294/113 ; tau(u)= 68/181 ; 20914*x^2 - 60898*y^2 + 91060*x*z + 20914*z^2
  (-7752/52777 : 19117/52777 : 1)  C1a (1380854/1282437 : -116851/1282437 : 1)
** u= 294/149 ; tau(u)= -4/145 ; 44386*x^2 - 42034*y^2 + 86452*x*z + 44386*z^2
  (-5209/5368 : -1253/5368 : 1)  C1a (-65591/8710 : -4039/8710 : 1)
** u= 304/305 ; tau(u)= 306 ; 92414*x^2 + 93634*y^2 + 186052*x*z + 92414*z^2
  (-6745/6368 : -649/6368 : 1)  C1b (-17379770/2551949 : -4351/10589 : 1)
** u= -304/397 ; tau(u)= 1098/701 ; -890386*x^2 + 222802*y^2 + 1298020*x*z - 890386*z^2
  (68569/385819 : 96842/55117 : 1)  C2b (258123898/4156439 : -28183969/4156439 : 1)
** u= 306 ; tau(u)= 304/305 ; -92414*x^2 - 93634*y^2 + 186052*x*z - 92414*z^2
  (447/422 : -43/422 : 1)  C1a (2019145/154717 : 125527/154717 : 1)
** u= 306/125 ; tau(u)= 56/181 ; 28114*x^2 - 62386*y^2 + 96772*x*z + 28114*z^2
  (317/854 : -891/854 : 1)  C1a (885321466/253889041 : 56360723/253889041 : 1)
** u= 306/169 ; tau(u)= -32/137 ; 56098*x^2 - 36514*y^2 + 94660*x*z + 56098*z^2
  (13321/6301 : 23478/6301 : 1)  C1a (38553902/8166719 : 3232213/8166719 : 1)
** u= 306/205 ; tau(u)= -104/101 ; 73234*x^2 - 9586*y^2 + 104452*x*z + 73234*z^2
  (16169/32135 : -124692/32135 : 1)  C1a (-4054234/598155 : 552563/598155 : 1)
** u= 308/325 ; tau(u)= 342/17 ; 94286*x^2 + 116386*y^2 + 211828*x*z + 94286*z^2
  (-581/694 : 265/694 : 1)  C1b (-159826350/8432557 : 9641903/8432557 : 1)
** u= -308/365 ; tau(u)= 1038/673 ; -810994*x^2 + 171586*y^2 + 1172308*x*z - 810994*z^2
  (15632/12609 : 23659/12609 : 1)  C2b (4252675/5606782 : -486093/5606782 : 1)
** u= 309/196 ; tau(u)= -83/113 ; 69943*x^2 - 18649*y^2 + 102370*x*z + 69943*z^2
  (-117251/23813 : 195860/23813 : 1)  C1a (-14977430/4552079 : -1320675/4552079 : 1)
** u= 313/160 ; tau(u)= -7/153 ; 51151*x^2 - 46769*y^2 + 98018*x*z + 51151*z^2
  (-2039/2273 : 696/2273 : 1)  C1a (1961803/779513 : -162901/779513 : 1)
** u= 317/349 ; tau(u)= 381/32 ; 98441*x^2 + 143113*y^2 + 245650*x*z + 98441*z^2
  (-70293/117997 : 35512/117997 : 1)  C1b (922617486/93868175 : 2310877/3754727 : 1)
** u= 319/353 ; tau(u)= 387/34 ; 99449*x^2 + 147457*y^2 + 251530*x*z + 99449*z^2
  (-385919/747701 : -121326/747701 : 1)  C1b (10991769/28298213 : -2041219/28298213 : 1)
** u= 321/116 ; tau(u)= 89/205 ; 18991*x^2 - 76129*y^2 + 110962*x*z + 18991*z^2
  (-161873/1668231 : 554236/1668231 : 1)  C1a (-1219598/769255 : 73217/769255 : 1)
** u= -323/389 ; tau(u)= 1101/712 ; -909559*x^2 + 198313*y^2 + 1316530*x*z - 909559*z^2
  (26667/93793 : -23476/13399 : 1)  C2b (628957/722321 : -63419/722321 : 1)
** u= -325/397 ; tau(u)= 1119/722 ; -936943*x^2 + 209593*y^2 + 1357786*x*z - 936943*z^2
  (4011453/3360281 : 5923478/3360281 : 1)  C2b (7952390/5990353 : -672599/5990353 : 1)
** u= 329/104 ; tau(u)= 121/225 ; 6991*x^2 - 86609*y^2 + 122882*x*z + 6991*z^2
  (-149/8399 : -1980/8399 : 1)  C1a (762019273/20125062 : 41592703/20125062 : 1)
** u= 330/41 ; tau(u)= 248/289 ; -58142*x^2 - 105538*y^2 + 170404*x*z - 58142*z^2
  (2511/1042 : 391/1042 : 1)  C1a (-273132215/20933333 : -16329507/20933333 : 1)
** u= 330/97 ; tau(u)= 136/233 ; 322*x^2 - 90082*y^2 + 127396*x*z + 322*z^2
  (15557/847719 : 145672/847719 : 1)  C1a (103536250/32154129 : -5901221/32154129 : 1)
** u= 330/109 ; tau(u)= 112/221 ; 11218*x^2 - 85138*y^2 + 121444*x*z + 11218*z^2
  (-361/63162 : -22207/63162 : 1)  C1a (-83529/208675 : 11881/208675 : 1)
** u= 330/229 ; tau(u)= -128/101 ; 88498*x^2 - 4018*y^2 + 125284*x*z + 88498*z^2
  (-66191/160751 : 4044784/1125257 : 1)  C1a (-7905/598 : -13399/4186 : 1)
** u= 332/337 ; tau(u)= 342/5 ; 110174*x^2 + 116914*y^2 + 227188*x*z + 110174*z^2
  (-2695/2102 : -47/14714 : 1)  C1b (-67403/114935 : 45163/804545 : 1)
** u= 333/68 ; tau(u)= 197/265 ; -29561*x^2 - 101641*y^2 + 149698*x*z - 29561*z^2
  (10165/9981 : -9508/9981 : 1)  C1a (3109125/2384078 : -195647/2384078 : 1)
** u= 333/196 ; tau(u)= -59/137 ; 73351*x^2 - 34057*y^2 + 114370*x*z + 73351*z^2
  (-8963/9797 : 9212/9797 : 1)  C1a (9165345/1781998 : 871585/1781998 : 1)
** u= 335/218 ; tau(u)= -101/117 ; 84847*x^2 - 17177*y^2 + 122426*x*z + 84847*z^2
  (38713/1046219 : -77034/33749 : 1)  C1a (-34773285/2062558 : 4075643/2062558 : 1)
** u= -335/293 ; tau(u)= 921/628 ; -676543*x^2 + 59473*y^2 + 960466*x*z - 676543*z^2
  (4675/7717 : -18532/7717 : 1)  C2b (2042230/585791 : 309133/585791 : 1)
** u= 337/353 ; tau(u)= 369/16 ; 113057*x^2 + 135649*y^2 + 249730*x*z + 113057*z^2
  (-38681/57337 : -1400/8191 : 1)  C1b (-2404157/5191854 : -287317/5191854 : 1)
** u= 338/113 ; tau(u)= 112/225 ; 12994*x^2 - 88706*y^2 + 126788*x*z + 12994*z^2
  (7/3023 : -1170/3023 : 1)  C1a (-4265269/52095 : -232961/52095 : 1)
** u= -341/365 ; tau(u)= 1071/706 ; -880591*x^2 + 150169*y^2 + 1263322*x*z - 880591*z^2
  (43039/18307 : 78734/18307 : 1)  C2b (-414956684070/23825778523 : -57297867263/23825778523 : 1)
** u= 342/5 ; tau(u)= 332/337 ; -110174*x^2 - 116914*y^2 + 227188*x*z - 110174*z^2
  (506/643 : 257/4501 : 1)  C1a (93510/85141 : 40591/595987 : 1)
** u= 342/17 ; tau(u)= 308/325 ; -94286*x^2 - 116386*y^2 + 211828*x*z - 94286*z^2
  (1024/1123 : -471/1123 : 1)  C1a (-72830/1005451 : 64169/1005451 : 1)
** u= 342/241 ; tau(u)= -140/101 ; 96562*x^2 - 802*y^2 + 136564*x*z + 96562*z^2
  (-931/21062 : 224001/21062 : 1)  C1a (-3065/18066 : -9577/18066 : 1)
** u= 343/353 ; tau(u)= 363/10 ; 117449*x^2 + 131569*y^2 + 249418*x*z + 117449*z^2
  (-25639/33693 : -6118/33693 : 1)  C1b (-271150/339923 : -20139/339923 : 1)
** u= -343/397 ; tau(u)= 1137/740 ; -977551*x^2 + 197569*y^2 + 1410418*x*z - 977551*z^2
  (25267/72909 : -127708/72909 : 1)  C2b (3109390598/1057337455 : 305005541/1057337455 : 1)
** u= 349/389 ; tau(u)= 429/40 ; 118601*x^2 + 180841*y^2 + 305842*x*z + 118601*z^2
  (-712767/617795 : -401524/617795 : 1)  C1b (62190/325967 : -21101/325967 : 1)
** u= 350/89 ; tau(u)= 172/261 ; -13742*x^2 - 106658*y^2 + 152084*x*z - 13742*z^2
  (1948/983 : 1455/983 : 1)  C1a (-195521/268370 : -18899/268370 : 1)
** u= -352/289 ; tau(u)= 930/641 ; -697858*x^2 + 43138*y^2 + 988804*x*z - 697858*z^2
  (-7887/953 : 34544/953 : 1)  C2b (-13001613/662353 : -2951293/662353 : 1)
** u= 354/73 ; tau(u)= 208/281 ; -32606*x^2 - 114658*y^2 + 168580*x*z - 32606*z^2
  (5357/23998 : 4133/23998 : 1)  C1a (117602870/1145143 : -6510375/1145143 : 1)
** u= 354/233 ; tau(u)= -112/121 ; 96034*x^2 - 16738*y^2 + 137860*x*z + 96034*z^2
  (-12217/8103 : -20438/8103 : 1)  C1a (1619507706/1227490753 : 344787121/1227490753 : 1)
** u= -355/337 ; tau(u)= 1029/692 ; -831703*x^2 + 101113*y^2 + 1184866*x*z - 831703*z^2
  (-433305/3329849 : -10471636/3329849 : 1)  C2b (-1132910/184437 : 198721/184437 : 1)
** u= -356/261 ; tau(u)= 878/617 ; -634642*x^2 + 9506*y^2 + 897620*x*z - 634642*z^2
  (-4796/61 : 276789/427 : 1)  C2b (2192310/222547 : 6350135/1557829 : 1)
** u= 357/116 ; tau(u)= 125/241 ; 11287*x^2 - 100537*y^2 + 143074*x*z + 11287*z^2
  (-60785/7723503 : 2455468/7723503 : 1)  C1a (-9834406/1103251 : -535227/1103251 : 1)
** u= 357/365 ; tau(u)= 373/8 ; 127321*x^2 + 139001*y^2 + 266578*x*z + 127321*z^2
  (-874859/753647 : 207748/753647 : 1)  C1b (-24111977/51595355 : 2871483/51595355 : 1)
** u= 358/241 ; tau(u)= -124/117 ; 100786*x^2 - 12002*y^2 + 143540*x*z + 100786*z^2
  (-21208/40753 : -85947/40753 : 1)  C1a (-3113/415139 : -65321/415139 : 1)
** u= -361/313 ; tau(u)= 987/674 ; -778231*x^2 + 65617*y^2 + 1104490*x*z - 778231*z^2
  (277/4153 : -13642/4153 : 1)  C2b (186488018/2264631 : 34697173/2264631 : 1)
** u= 362/85 ; tau(u)= 192/277 ; -22414*x^2 - 116594*y^2 + 167908*x*z - 22414*z^2
  (1773/8447 : -2692/8447 : 1)  C1a (-32792722/29787143 : 2588181/29787143 : 1)
** u= 363/10 ; tau(u)= 343/353 ; -117449*x^2 - 131569*y^2 + 249418*x*z - 117449*z^2
  (300579/242873 : -71302/242873 : 1)  C1a (714655/525941 : 3189/40457 : 1)
** u= -364/265 ; tau(u)= 894/629 ; -658786*x^2 + 7954*y^2 + 931732*x*z - 658786*z^2
  (-57/350 : -3571/350 : 1)  C2b (133246/663491 : -285649/663491 : 1)
** u= 365/208 ; tau(u)= -51/157 ; 83927*x^2 - 46697*y^2 + 135826*x*z + 83927*z^2
  (-7527/43001 : 348856/301007 : 1)  C1a (6589085/2822 : 3598911/19754 : 1)
** u= 368/369 ; tau(u)= 370 ; 135422*x^2 + 136898*y^2 + 272324*x*z + 135422*z^2
  (-117179/125947 : 9138/125947 : 1)  C1b (-120290/4436481 : -282421/4436481 : 1)
** u= 369/16 ; tau(u)= 337/353 ; -113057*x^2 - 135649*y^2 + 249730*x*z - 113057*z^2
  (196233/156017 : 63104/156017 : 1)  C1a (16594282/6104215 : -14191/93911 : 1)
** u= 370 ; tau(u)= 368/369 ; -135422*x^2 - 136898*y^2 + 272324*x*z - 135422*z^2
  (10412/9679 : 747/9679 : 1)  C1a (-2447178/1823087 : 239207/1823087 : 1)
** u= 370/109 ; tau(u)= 152/261 ; 658*x^2 - 113138*y^2 + 160004*x*z + 658*z^2
  (77/9868 : 1281/9868 : 1)  C1a (-279618/834395 : 47807/834395 : 1)
** u= 373/8 ; tau(u)= 357/365 ; -127321*x^2 - 139001*y^2 + 266578*x*z - 127321*z^2
  (17/21 : -4/21 : 1)  C1a (-52928395/7732391 : 3612219/7732391 : 1)
** u= 378/53 ; tau(u)= 272/325 ; -68366*x^2 - 137266*y^2 + 216868*x*z - 68366*z^2
  (7073/18829 : 2986/18829 : 1)  C1a (353082/561685 : 32273/561685 : 1)
** u= 378/73 ; tau(u)= 232/305 ; -43166*x^2 - 132226*y^2 + 196708*x*z - 43166*z^2
  (7367/3397 : 3968/3397 : 1)  C1a (213805/241578 : -15917/241578 : 1)
** u= 378/197 ; tau(u)= -16/181 ; 77362*x^2 - 65266*y^2 + 143140*x*z + 77362*z^2
  (-846/1813 : -1175/1813 : 1)  C1a (597083/577095 : 13961/115419 : 1)
** u= 378/221 ; tau(u)= -64/157 ; 93586*x^2 - 45202*y^2 + 146980*x*z + 93586*z^2
  (-6121/11237 : 10740/11237 : 1)  C1a (187038/218879 : 30307/218879 : 1)
** u= 378/265 ; tau(u)= -152/113 ; 117346*x^2 - 2434*y^2 + 165988*x*z + 117346*z^2
  (-335/643 : 3264/643 : 1)  C1a (3538114/9969 : -1339063/9969 : 1)
** u= 381/32 ; tau(u)= 317/349 ; -98441*x^2 - 143113*y^2 + 245650*x*z - 98441*z^2
  (390283/543843 : -236872/543843 : 1)  C1a (-247772222/30327451 : 15664669/30327451 : 1)
** u= 382/197 ; tau(u)= -12/185 ; 77474*x^2 - 68306*y^2 + 146068*x*z + 77474*z^2
  (-1315/2664 : 11111/18648 : 1)  C1a (-8518/5483 : -3411/38381 : 1)
** u= 385/68 ; tau(u)= 249/317 ; -52753*x^2 - 138977*y^2 + 210226*x*z - 52753*z^2
  (278189/1033697 : 4328/1033697 : 1)  C1a (1447601/5440910 : -296319/5440910 : 1)
** u= 386/125 ; tau(u)= 136/261 ; 12754*x^2 - 117746*y^2 + 167492*x*z + 12754*z^2
  (-92/2393 : -555/2393 : 1)  C1a (12237379/33113295 : 1972907/33113295 : 1)
** u= 386/241 ; tau(u)= -96/145 ; 106946*x^2 - 32834*y^2 + 158212*x*z + 106946*z^2
  (-14307/17213 : -3014/2459 : 1)  C1a (344157635/7943486 : 35098269/7943486 : 1)
** u= 387/34 ; tau(u)= 319/353 ; -99449*x^2 - 147457*y^2 + 251530*x*z - 99449*z^2
  (1735463/2428121 : -1086510/2428121 : 1)  C1a (5131746/12982877 : -712373/12982877 : 1)
** u= -388/369 ; tau(u)= 1126/757 ; -995554*x^2 + 121778*y^2 + 1418420*x*z - 995554*z^2
  (4934/1247 : 11835/1247 : 1)  C2b (2837281/152278923 : 23462063/152278923 : 1)
** u= 390/113 ; tau(u)= 164/277 ; -1358*x^2 - 126562*y^2 + 178996*x*z - 1358*z^2
  (2606/341715 : 2539/341715 : 1)  C1a (-2479410/3796021 : -247481/3796021 : 1)
** u= 391/274 ; tau(u)= -157/117 ; 125503*x^2 - 2729*y^2 + 177530*x*z + 125503*z^2
  (-47443/132067 : -705714/132067 : 1)  C1a (-3976630/616141 : 1316185/616141 : 1)
** u= -391/397 ; tau(u)= 1185/788 ; -1089007*x^2 + 162337*y^2 + 1557106*x*z - 1089007*z^2
  (-490045/9077 : 9003044/63539 : 1)  C2b (1740751/564694 : 1393227/3952858 : 1)
** u= -392/333 ; tau(u)= 1058/725 ; -897586*x^2 + 68114*y^2 + 1273028*x*z - 897586*z^2
  (-983/592 : 5313/592 : 1)  C2b (-3155787994/10030349 : -625414477/10030349 : 1)
** u= 399/82 ; tau(u)= 235/317 ; -41777*x^2 - 145753*y^2 + 214426*x*z - 41777*z^2
  (378255/775913 : -467122/775913 : 1)  C1a (-22411862/4049597 : 1305849/4049597 : 1)
** u= 399/218 ; tau(u)= -37/181 ; 93679*x^2 - 64153*y^2 + 160570*x*z + 93679*z^2
  (-5146717/45607773 : -49885622/45607773 : 1)  C1a (11863954/11798097 : 1523509/11798097 : 1)
** u= 399/242 ; tau(u)= -85/157 ; 109903*x^2 - 42073*y^2 + 166426*x*z + 109903*z^2
  (-5/17 : -22/17 : 1)  C1a (350807/2767685 : 273899/2767685 : 1)
** u= -400/361 ; tau(u)= 1122/761 ; -998242*x^2 + 100642*y^2 + 1418884*x*z - 998242*z^2
  (82731/66049 : -184718/66049 : 1)  C2b (-9205910/1947647 : -1831831/1947647 : 1)
390
>

ここからは、 "A^4+B^4+C^4=3362*D^4の整点" と同様なので、最終的に得られた(1)の整点のみを記述する。
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 <=C を満たすように、A,B,Cを交換して、Dの小さい順に(1)の等式を並べ替えると、以下のようになる。



[2026.01.07追記] u=284/373のときの整点を追加した。

[参考文献]

Last Update: 2026.01.11
H.Nakao

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