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Integer Points on A^4+242*B^4+968*C^4=D^4


[2026.05.10]A^4+242*B^4+968*C^4=D^4の整点


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

ここで、ある有理数uに対して、
       n*(x^2+2*x+2)=u*(t^2+y^2) ----------(3a)
       ±(x^2-2*x+2)=(1/u)*(t^2-y^2) ----------(3b±)
を満たす有理数の組(n1,n2,x,y,t)が存在すれば、(x,y,t)が(2)を満たすことが分かる。
(3a)より、u > 0として良い。
(3a)-u^2*(3b+)より、
       2*u*y^2=(n-u^2)*x^2+2*(n+u^2)*x+2*(n-u^2) ----------(4a+)
(3a)+u^2*(3b+)より、
       2*u*t^2=(n+u^2)*x^2+2*(n-u^2)*x+2*(n+u^2) ----------(4b+)
となる。

また、(3a)+u^2*(3b-)より、
       2*u*t^2=(n-u^2)*x^2+2*(n+u^2)*x+2*(n-u^2) ----------(4a-)
(3a)-u^2*(3b-)より、
       2*u*y^2=(n+u^2)*x^2+2*(n-u^2)*x+2*(n+u^2) ----------(4b-)
となり、それぞれ(4b+),(4a+)と一致する。
よって、(4a+),(4b+)のみ、調べれば十分である。

[pari/gpによる計算]
gp >  YY2(n,u,x)
%1 = (1/(2*u)*n - 1/2*u)*x^2 + (1/u*n + u)*x + (1/u*n - u)
gp > TT2(n,u,x)
%2 = (1/(2*u)*n + 1/2*u)*x^2 + (1/u*n - u)*x + (1/u*n + u)
gp > n*(x^4+4)+YY2(n,u,x)^2-TT2(n,u,x)^2
time = 1 ms.
%3 = 0

■2次曲線(4a+),(4b+)は、常にnon-singularである。
2次曲線(4a+)の右辺の判別式は
    4*(n-u^2)^2-4*2*(n+u^2)^2=-4*(n^2-6*n*u^2+u^4)
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(4b+)の右辺の判別式は
    4*(n+u^2)^2-4*2*(n-u^2)^2=-4*(n^2+6*n*u^2+u^4)
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=242とする。

■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600以下の範囲で、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509個のuが抽出される。
[pari/gpによる計算]
> PP(242,1,600);
**u= 4/17 ;  69922*x^2 - 136*y^2 + 139908*x*z + 139844*z^2
; C4a (349/488 : -43941/976 : 1)  C4b (2483/228 : -41133/152 : 1)
**u= 4/113 ;  3090082*x^2 - 904*y^2 + 6180228*x*z + 6180164*z^2
; C4a (-21511/24243 : 2852683/48486 : 1)  C4b (-55351/11619 : 587899/2582 : 1)
**u= 4/225 ;  12251234*x^2 - 1800*y^2 + 24502532*x*z + 24502468*z^2
; C4a (-625/104 : 1314913/3120 : 1)  C4b (82329/463 : -40982707/2778 : 1)
**u= 4/233 ;  13137922*x^2 - 1864*y^2 + 26275908*x*z + 26275844*z^2
; C4a (13474259/12053728 : -4740145953/24107456 : 1)  C4b (40301/32260 : 13333403/64520 : 1)
**u= 4/257 ;  15983842*x^2 - 2056*y^2 + 31967748*x*z + 31967684*z^2
; C4a (-4337/33168 : 7749767/66336 : 1)  C4b (-172631/27080 : -26107439/54160 : 1)
**u= 4/289 ;  20212066*x^2 - 2312*y^2 + 40424196*x*z + 40424132*z^2
; C4a (-18519/20128 : -64190911/684352 : 1)  C4b (-19847/7035 : 911089/4690 : 1)
**u= 4/313 ;  23708482*x^2 - 2504*y^2 + 47417028*x*z + 47416964*z^2
; C4a (-184935/229427 : -45480511/458854 : 1)  C4b (43291543/42990028 : 18760081463/85980056 : 1)
**u= 4/401 ;  38913826*x^2 - 3208*y^2 + 77827716*x*z + 77827652*z^2
; C4a (-32075/203159 : 58504959/406318 : 1)  C4b (41459/212965 : -73085347/425930 : 1)
**u= 4/481 ;  55989346*x^2 - 3848*y^2 + 111978756*x*z + 111978692*z^2
; C4a (70543/427664 : -158400873/855328 : 1)  C4b (9819/38492 : -14902047/76984 : 1)
**u= 4/521 ;  65688706*x^2 - 4168*y^2 + 131377476*x*z + 131377412*z^2
; C4a (-444799/156079 : -82406091/312158 : 1)  C4b (-83463/183460 : 52461231/366920 : 1)
**u= 8/45 ;  489986*x^2 - 720*y^2 + 980228*x*z + 979972*z^2
; C4a (-6286/18401 : 3448151/110406 : 1)  C4b (-4822/8341 : -1417355/50046 : 1)
**u= 8/53 ;  679714*x^2 - 848*y^2 + 1359684*x*z + 1359428*z^2
; C4a (153284/52541 : 12028623/105082 : 1)  C4b (-292/1319 : -94667/2638 : 1)
**u= 8/101 ;  2468578*x^2 - 1616*y^2 + 4937412*x*z + 4937156*z^2
; C4a (-321556/7123 : -24585087/14246 : 1)  C4b (-83532/47543 : 4661463/95086 : 1)
**u= 8/109 ;  2875138*x^2 - 1744*y^2 + 5750532*x*z + 5750276*z^2
; C4a (-55708/58677 : -4770797/117354 : 1)  C4b (-2036/13239 : 156487/2942 : 1)
**u= 8/157 ;  5964994*x^2 - 2512*y^2 + 11930244*x*z + 11929988*z^2
; C4a (-79540/32409 : -5574461/64818 : 1)  C4b (48212/1473 : -1614821/982 : 1)
**u= 8/181 ;  7928098*x^2 - 2896*y^2 + 15856452*x*z + 15856196*z^2
; C4a (-99418/51819 : -7362899/103638 : 1)  C4b (558638/1561483 : 275538887/3122966 : 1)
**u= 8/205 ;  10169986*x^2 - 3280*y^2 + 20340228*x*z + 20339972*z^2
; C4a (-173434/181359 : -20216287/362718 : 1)  C4b (22902/30419 : 6836535/60838 : 1)
**u= 8/261 ;  16485218*x^2 - 4176*y^2 + 32970692*x*z + 32970436*z^2
; C4a (-145586/20899 : -47660131/125394 : 1)  C4b (-60628/39265 : 16851347/235590 : 1)
**u= 8/317 ;  24318274*x^2 - 5072*y^2 + 48636804*x*z + 48636548*z^2
; C4a (-131460/76577 : -13047197/153154 : 1)  C4b (11366356/77298639 : -5430009257/51532426 : 1)
**u= 8/333 ;  26835074*x^2 - 5328*y^2 + 53670404*x*z + 53670148*z^2
; C4a (-15294/16849 : -1029287/14442 : 1)  C4b (-72646/74241 : -31620419/445446 : 1)
**u= 8/445 ;  47921986*x^2 - 7120*y^2 + 95844228*x*z + 95843972*z^2
; C4a (471146/154389 : 105718177/308778 : 1)  C4b (-299764/236797 : -40204183/473594 : 1)
**u= 8/533 ;  68749474*x^2 - 8528*y^2 + 137499204*x*z + 137498948*z^2
; C4a (65214/196171 : -58686383/392342 : 1)  C4b (284468/79959 : 22332661/53306 : 1)
**u= 16/5 ;  5794*x^2 - 160*y^2 + 12612*x*z + 11588*z^2
; C4a (83/6 : 2159/24 : 1)  C4b (613/177 : 6685/236 : 1)
**u= 16/13 ;  40642*x^2 - 416*y^2 + 82308*x*z + 81284*z^2
; C4a (2841/1897 : -28901/1084 : 1)  C4b (419/659 : -50159/2636 : 1)
**u= 16/61 ;  900226*x^2 - 1952*y^2 + 1801476*x*z + 1800452*z^2
; C4a (-1293/3466 : -351353/13864 : 1)  C4b (-59773/44495 : -4045091/177980 : 1)
**u= 16/173 ;  7242562*x^2 - 5536*y^2 + 14486148*x*z + 14485124*z^2
; C4a (-72325/57611 : -8601993/230444 : 1)  C4b (-147179/114345 : 1912667/50820 : 1)
**u= 16/221 ;  11819266*x^2 - 7072*y^2 + 23639556*x*z + 23638532*z^2
; C4a (-150613/84346 : -17539503/337384 : 1)  C4b (6808003/4845602 : 2063853823/19382408 : 1)
**u= 16/245 ;  14525794*x^2 - 7840*y^2 + 29052612*x*z + 29051588*z^2
; C4a (-8113/51839 : 81735705/1451492 : 1)  C4b (-2431/3886 : 5001239/108808 : 1)
**u= 16/333 ;  26834882*x^2 - 10656*y^2 + 53670788*x*z + 53669764*z^2
; C4a (-51899/17062 : -23359211/204744 : 1)  C4b (-55917/22646 : 24236807/271752 : 1)
**u= 16/445 ;  47921794*x^2 - 14240*y^2 + 95844612*x*z + 95843588*z^2
; C4a (125881/55982 : -44154555/223928 : 1)  C4b (-4920877/2829962 : 816488551/11319848 : 1)
**u= 20/17 ;  69538*x^2 - 680*y^2 + 140676*x*z + 139076*z^2
; C4a (-3303/3161 : 63223/6322 : 1)  C4b (-1889/2443 : -51379/4886 : 1)
**u= 20/73 ;  1289218*x^2 - 2920*y^2 + 2580036*x*z + 2578436*z^2
; C4a (20357/18526 : -1810257/37052 : 1)  C4b (1167/22351 : -1363875/44702 : 1)
**u= 20/81 ;  1587362*x^2 - 3240*y^2 + 3176324*x*z + 3174724*z^2
; C4a (-128619/183446 : 76257757/3302028 : 1)  C4b (59/3614 : -2053495/65052 : 1)
**u= 20/241 ;  14055202*x^2 - 9640*y^2 + 28112004*x*z + 28110404*z^2
; C4a (-12667721/10599654 : -824680819/21199308 : 1)  C4b (1482163/2475263 : 356474423/4950526 : 1)
**u= 20/257 ;  15983458*x^2 - 10280*y^2 + 31968516*x*z + 31966916*z^2
; C4a (-217641/53942 : 13592219/107884 : 1)  C4b (-181399/512438 : 48112879/1024876 : 1)
**u= 20/361 ;  31537282*x^2 - 14440*y^2 + 63076164*x*z + 63074564*z^2
; C4a (171749/17934 : 48336581/97356 : 1)  C4b (-82743/33437 : -105800139/1270606 : 1)
**u= 20/481 ;  55988962*x^2 - 19240*y^2 + 111979524*x*z + 111977924*z^2
; C4a (-1040177/487983 : -79504375/975966 : 1)  C4b (-6890999/5931701 : 648297659/11863402 : 1)
**u= 20/521 ;  65688322*x^2 - 20840*y^2 + 131378244*x*z + 131376644*z^2
; C4a (-1757097/3470903 : -434651597/6941806 : 1)  C4b (-2955603/4670902 : -558730551/9341804 : 1)
**u= 22/25 ;  150766*x^2 - 1100*y^2 + 303468*x*z + 301532*z^2
; C4a (6/31 : 2827/155 : 1)  C4b (-826/429 : -1047/65 : 1)
**u= 32/13 ;  39874*x^2 - 832*y^2 + 83844*x*z + 79748*z^2
; C4a (268/1089 : -48419/4356 : 1)  C4b (-554/1979 : -69863/7916 : 1)
**u= 32/29 ;  202498*x^2 - 1856*y^2 + 409092*x*z + 404996*z^2
; C4a (-20958/17357 : -731917/69428 : 1)  C4b (38274/6109 : -1879107/24436 : 1)
**u= 32/157 ;  5964034*x^2 - 10048*y^2 + 11932164*x*z + 11928068*z^2
; C4a (-8756/62471 : -8028729/249884 : 1)  C4b (48652/62415 : -4138997/83220 : 1)
**u= 32/205 ;  10169026*x^2 - 13120*y^2 + 20342148*x*z + 20338052*z^2
; C4a (-66212/64317 : -7164023/257268 : 1)  C4b (-296284/814047 : 35817449/1085396 : 1)
**u= 32/261 ;  16484258*x^2 - 16704*y^2 + 32972612*x*z + 32968516*z^2
; C4a (271532/138317 : -163065647/1659804 : 1)  C4b (-64526/37853 : -17459699/454236 : 1)
**u= 32/365 ;  32239426*x^2 - 23360*y^2 + 64482948*x*z + 64478852*z^2
; C4a (-110036/63671 : -11703393/254684 : 1)  C4b (-251212/227861 : -34040795/911444 : 1)
**u= 32/421 ;  42891298*x^2 - 26944*y^2 + 85786692*x*z + 85782596*z^2
; C4a (25604/680993 : -156615237/2723972 : 1)  C4b (-2686566/8042989 : -90721227/1892468 : 1)
**u= 32/509 ;  62696578*x^2 - 32576*y^2 + 125397252*x*z + 125393156*z^2
; C4a (38500476/20773661 : -11021930479/83094644 : 1)  C4b (126026566/59184955 : -34120756151/236739820 : 1)
**u= 32/541 ;  70827778*x^2 - 34624*y^2 + 141659652*x*z + 141655556*z^2
; C4a (-4245892388/3545354787 : 653785334509/14181419148 : 1)  C4b (83578/67385 : 29908951/269540 : 1)
**u= 32/549 ;  72938018*x^2 - 35136*y^2 + 145880132*x*z + 145876036*z^2
; C4a (-30644/73007 : 46148743/876084 : 1)  C4b (26404/7449 : -18951799/89388 : 1)
**u= 36/17 ;  68642*x^2 - 1224*y^2 + 142468*x*z + 137284*z^2
; C4a (-805/1352 : 64253/8112 : 1)  C4b (-157/296 : -15203/1776 : 1)
**u= 36/41 ;  405506*x^2 - 2952*y^2 + 816196*x*z + 811012*z^2
; C4a (-3911/6091 : 453281/36546 : 1)  C4b (783/517 : -98567/3102 : 1)
**u= 36/65 ;  1021154*x^2 - 4680*y^2 + 2047492*x*z + 2042308*z^2
; C4a (-517/776 : 72395/4656 : 1)  C4b (-5431/2531 : 342379/15186 : 1)
**u= 36/169 ;  6910466*x^2 - 12168*y^2 + 13826116*x*z + 13820932*z^2
; C4a (-127/3999 : -10346833/311922 : 1)  C4b (-40711/3327 : -69780583/259506 : 1)
**u= 36/233 ;  13136642*x^2 - 16776*y^2 + 26278468*x*z + 26273284*z^2
; C4a (-160997/18376 : 24143249/110256 : 1)  C4b (-141501/62029 : -16931111/372174 : 1)
**u= 36/265 ;  16993154*x^2 - 19080*y^2 + 33991492*x*z + 33986308*z^2
; C4a (441937/405779 : -168291223/2434674 : 1)  C4b (-378631/336751 : -60778115/2020506 : 1)
**u= 36/409 ;  40480706*x^2 - 29448*y^2 + 80966596*x*z + 80961412*z^2
; C4a (136515025/135677096 : -67657565813/814062576 : 1)  C4b (-4223353/1576408 : -685402171/9458448 : 1)
**u= 36/425 ;  43709954*x^2 - 30600*y^2 + 87425092*x*z + 87419908*z^2
; C4a (504909/42019 : 621957371/1260570 : 1)  C4b (11189/13820 : 32398247/414600 : 1)
**u= 36/457 ;  50540162*x^2 - 32904*y^2 + 101085508*x*z + 101080324*z^2
; C4a (41677985/96444 : 9823289609/578664 : 1)  C4b (69481/3195 : -17106679/19170 : 1)
**u= 36/521 ;  65687426*x^2 - 37512*y^2 + 131380036*x*z + 131374852*z^2
; C4a (116223/316777 : 134704627/1900662 : 1)  C4b (41481/29660 : 19352327/177960 : 1)
**u= 36/569 ;  78348866*x^2 - 40968*y^2 + 156702916*x*z + 156697732*z^2
; C4a (-9145/44021 : -14736247/264126 : 1)  C4b (788583/115280 : 239087747/691680 : 1)
**u= 36/577 ;  80567522*x^2 - 41544*y^2 + 161140228*x*z + 161135044*z^2
; C4a (-45385/53692 : -14355283/322152 : 1)  C4b (-1856927/1850696 : -489030167/11104176 : 1)
**u= 40/37 ;  329698*x^2 - 2960*y^2 + 665796*x*z + 659396*z^2
; C4a (-84504/45413 : -1251595/90826 : 1)  C4b (-19774/48251 : -10547/854 : 1)
**u= 40/53 ;  678178*x^2 - 4240*y^2 + 1362756*x*z + 1356356*z^2
; C4a (4322/3051 : 202027/6102 : 1)  C4b (6128/1969 : 211099/3938 : 1)
**u= 40/317 ;  24316738*x^2 - 25360*y^2 + 48639876*x*z + 48633476*z^2
; C4a (-96494/50231 : -4228641/100462 : 1)  C4b (-48792966/36658547 : 2391979947/73317094 : 1)
**u= 40/477 ;  55060418*x^2 - 38160*y^2 + 110127236*x*z + 110120836*z^2
; C4a (-1872342/1576459 : -365542871/9458754 : 1)  C4b (-18554/2761 : 3654151/16566 : 1)
**u= 52/25 ;  148546*x^2 - 2600*y^2 + 307908*x*z + 297092*z^2
; C4a (213/361 : 10313/722 : 1)  C4b (747/935 : 147099/9350 : 1)
**u= 52/97 ;  2274274*x^2 - 10088*y^2 + 4559364*x*z + 4548548*z^2
; C4a (-85/359 : 13557/718 : 1)  C4b (5283/2195 : -234207/4390 : 1)
**u= 52/113 ;  3087394*x^2 - 11752*y^2 + 6185604*x*z + 6174788*z^2
; C4a (2163365/616933 : -92347143/1233866 : 1)  C4b (-36701/12827 : -880303/25654 : 1)
**u= 52/137 ;  4539394*x^2 - 14248*y^2 + 9089604*x*z + 9078788*z^2
; C4a (28967/2071 : 1110561/4142 : 1)  C4b (-6397/11347 : 442451/22694 : 1)
**u= 52/361 ;  31534978*x^2 - 37544*y^2 + 63080772*x*z + 63069956*z^2
; C4a (-11967/17926 : -20802157/681188 : 1)  C4b (-448781/579043 : -653781751/22003634 : 1)
**u= 64/13 ;  36802*x^2 - 1664*y^2 + 89988*x*z + 73604*z^2
; C4a (165/53 : -8761/424 : 1)  C4b (-1127/610 : -39239/4880 : 1)
**u= 64/37 ;  327202*x^2 - 4736*y^2 + 670788*x*z + 654404*z^2
; C4a (-15255/40598 : 3160777/324784 : 1)  C4b (-6219/137 : -409791/1096 : 1)
**u= 64/45 ;  485954*x^2 - 5760*y^2 + 988292*x*z + 971908*z^2
; C4a (-122691/35338 : -20600743/848112 : 1)  C4b (-7211/921 : -1416983/22104 : 1)
**u= 64/125 ;  3777154*x^2 - 16000*y^2 + 7570692*x*z + 7554308*z^2
; C4a (-71/126 : -84407/5040 : 1)  C4b (-18257/2502 : -3272857/33360 : 1)
**u= 64/181 ;  7924066*x^2 - 23168*y^2 + 15864516*x*z + 15848132*z^2
; C4a (16351/11578 : -4474089/92624 : 1)  C4b (-57277/44802 : -2297561/119472 : 1)
**u= 64/269 ;  17507266*x^2 - 34432*y^2 + 35030916*x*z + 35014532*z^2
; C4a (428239/28006 : -82460217/224048 : 1)  C4b (-26123/33725 : 6239983/269800 : 1)
**u= 64/485 ;  56920354*x^2 - 62080*y^2 + 113857092*x*z + 113840708*z^2
; C4a (12553/39066 : 15681845/312528 : 1)  C4b (-101943/11113 : -22168863/88904 : 1)
**u= 64/549 ;  72934946*x^2 - 70272*y^2 + 145886276*x*z + 145869892*z^2
; C4a (-76603/65226 : -7312451/223632 : 1)  C4b (-77491/28666 : 43782659/687984 : 1)
**u= 68/9 ;  14978*x^2 - 1224*y^2 + 48452*x*z + 29956*z^2
; C4a (-235/52 : 3049/312 : 1)  C4b (-349/12 : 9127/72 : 1)
**u= 68/73 ;  1284994*x^2 - 9928*y^2 + 2588484*x*z + 2569988*z^2
; C4a (-66025/105753 : 2560309/211506 : 1)  C4b (-14543/4083 : 85757/2722 : 1)
**u= 68/97 ;  2272354*x^2 - 13192*y^2 + 4563204*x*z + 4544708*z^2
; C4a (19825/8331 : 771341/16662 : 1)  C4b (-63321/99797 : 2801067/199594 : 1)
**u= 68/145 ;  5083426*x^2 - 19720*y^2 + 10185348*x*z + 10166852*z^2
; C4a (226651/51909 : -9101267/103818 : 1)  C4b (1774357/2174919 : -48285381/1449946 : 1)
**u= 68/185 ;  8277826*x^2 - 25160*y^2 + 16574148*x*z + 16555652*z^2
; C4a (-684986509/3865727689 : 181585199205/7731455378 : 1)  C4b (-207883/127424 : -5477135/254848 : 1)
**u= 68/225 ;  12246626*x^2 - 30600*y^2 + 24511748*x*z + 24493252*z^2
; C4a (-248587/271360 : -163320251/8140800 : 1)  C4b (-10187/10380 : 6237727/311400 : 1)
**u= 68/265 ;  16989826*x^2 - 36040*y^2 + 33998148*x*z + 33979652*z^2
; C4a (-25547/5871 : 891467/11742 : 1)  C4b (1803257/68959 : -81375227/137918 : 1)
**u= 68/433 ;  45367714*x^2 - 58888*y^2 + 90753924*x*z + 90735428*z^2
; C4a (-5460847/3638919 : 225854671/7277838 : 1)  C4b (-2315463/9678388 : 675162171/19356776 : 1)
**u= 68/577 ;  80564194*x^2 - 78472*y^2 + 161146884*x*z + 161128388*z^2
; C4a (-34747/53679 : 3647353/107358 : 1)  C4b (-1452027/993080 : 70120779/1986160 : 1)
**u= 72/5 ;  866*x^2 - 720*y^2 + 22468*x*z + 1732*z^2
; C4a (1084/261 : 19355/1566 : 1)  C4b (-98/23 : -2407/138 : 1)
**u= 72/53 ;  674594*x^2 - 7632*y^2 + 1369924*x*z + 1349188*z^2
; C4a (-298/151 : 11701/906 : 1)  C4b (2764/19335 : -1667491/116010 : 1)
**u= 72/197 ;  9386594*x^2 - 28368*y^2 + 18793924*x*z + 18773188*z^2
; C4a (-31180/35811 : -3937291/214866 : 1)  C4b (-51964/1025493 : 154416127/6152958 : 1)
**u= 72/229 ;  12685538*x^2 - 32976*y^2 + 25391812*x*z + 25371076*z^2
; C4a (-101450/142963 : -17509603/857778 : 1)  C4b (208876/37465 : 29331991/224790 : 1)
**u= 72/421 ;  42887138*x^2 - 60624*y^2 + 85795012*x*z + 85774276*z^2
; C4a (-289878/147689 : -32708749/886134 : 1)  C4b (723678/209531 : -152646359/1257186 : 1)
**u= 72/485 ;  56919266*x^2 - 69840*y^2 + 113859268*x*z + 113838532*z^2
; C4a (-333238/350209 : -60046861/2101254 : 1)  C4b (-64228/141459 : 27610615/848754 : 1)
**u= 72/557 ;  75075074*x^2 - 80208*y^2 + 150170884*x*z + 150150148*z^2
; C4a (-96524/172719 : -34651021/1036314 : 1)  C4b (4885214/2515195 : -1434832843/15091170 : 1)
**u= 80/13 ;  34498*x^2 - 2080*y^2 + 94596*x*z + 68996*z^2
; C4a (-2819/3103 : 29223/12412 : 1)  C4b (-56923/54436 : -1300223/217744 : 1)
**u= 80/229 ;  12684322*x^2 - 36640*y^2 + 25394244*x*z + 25368644*z^2
; C4a (-205829/99221 : -10828407/396884 : 1)  C4b (96859/32484 : 3309489/43312 : 1)
**u= 80/277 ;  18562018*x^2 - 44320*y^2 + 37149636*x*z + 37124036*z^2
; C4a (-13829/26388 : -2391595/105552 : 1)  C4b (-1384261/284977 : -93013867/1139908 : 1)
**u= 80/293 ;  20769058*x^2 - 46880*y^2 + 41563716*x*z + 41538116*z^2
; C4a (-455511/272984 : -27627931/1091936 : 1)  C4b (60257/104927 : -16479259/419708 : 1)
**u= 80/349 ;  29469442*x^2 - 55840*y^2 + 58964484*x*z + 58938884*z^2
; C4a (60791/46741 : -10775307/186964 : 1)  C4b (-221059/830316 : -31554301/1107088 : 1)
**u= 80/557 ;  75073858*x^2 - 89120*y^2 + 150173316*x*z + 150147716*z^2
; C4a (-9729753/2920121 : 860116889/11680484 : 1)  C4b (-172737341/282015217 : 35119037959/1128060868 : 1)
**u= 100/41 ;  396802*x^2 - 8200*y^2 + 833604*x*z + 793604*z^2
; C4a (48761/2535 : -3581101/25350 : 1)  C4b (4897/41912 : 893663/83824 : 1)
**u= 100/89 ;  1906882*x^2 - 17800*y^2 + 3853764*x*z + 3813764*z^2
; C4a (-4211/5535 : -584587/55350 : 1)  C4b (-23531/14651 : -1804087/146510 : 1)
**u= 100/97 ;  2266978*x^2 - 19400*y^2 + 4573956*x*z + 4533956*z^2
; C4a (-4580805/5128717 : -553204411/51287170 : 1)  C4b (15243541/13157223 : -226157009/8771482 : 1)
**u= 100/153 ;  5654978*x^2 - 30600*y^2 + 11349956*x*z + 11309956*z^2
; C4a (-771/60988 : -442439/23160 : 1)  C4b (-1741/393 : -574351/11790 : 1)
**u= 100/257 ;  15973858*x^2 - 51400*y^2 + 31987716*x*z + 31947716*z^2
; C4a (-279751/221904 : 8073325/443808 : 1)  C4b (6991/28137 : -2646093/93790 : 1)
**u= 100/313 ;  23698498*x^2 - 62600*y^2 + 47436996*x*z + 47396996*z^2
; C4a (-2895855/1270528 : 401100643/12705280 : 1)  C4b (-45353/37489 : -7463371/374890 : 1)
**u= 100/337 ;  27473698*x^2 - 67400*y^2 + 54987396*x*z + 54947396*z^2
; C4a (-21967/8524 : -642399/17048 : 1)  C4b (-54673/21917 : -1592903/43834 : 1)
**u= 100/353 ;  30145378*x^2 - 70600*y^2 + 60330756*x*z + 60290756*z^2
; C4a (-1269353/103241 : -48377805/206482 : 1)  C4b (-234447/2716 : -47903739/27160 : 1)
**u= 104/109 ;  2864386*x^2 - 22672*y^2 + 5772036*x*z + 5728772*z^2
; C4a (-10680344/5348769 : -168485087/10697538 : 1)  C4b (-382422/12899 : -8345607/25798 : 1)
**u= 104/229 ;  12679906*x^2 - 47632*y^2 + 25403076*x*z + 25359812*z^2
; C4a (-32361872/21506437 : -784512261/43012874 : 1)  C4b (-1592258/976653 : -4197719/217034 : 1)
**u= 104/493 ;  58807042*x^2 - 102544*y^2 + 117657348*x*z + 117614084*z^2
; C4a (-41362/92061 : -5033029/184122 : 1)  C4b (138022/264305 : 23058439/528610 : 1)
**u= 104/509 ;  62686786*x^2 - 105872*y^2 + 125416836*x*z + 125373572*z^2
; C4a (-6253648/21795791 : -1302692139/43591582 : 1)  C4b (-51202/45809 : -2245987/91618 : 1)
**u= 110/29 ;  191422*x^2 - 6380*y^2 + 431244*x*z + 382844*z^2
; C4a (8124/229 : -45925/229 : 1)  C4b (-2174/1111 : -901/101 : 1)
**u= 110/293 ;  20763358*x^2 - 64460*y^2 + 41575116*x*z + 41526716*z^2
; C4a (1845258/235489 : 37586923/235489 : 1)  C4b (512878/102949 : 1019153/9359 : 1)
**u= 110/521 ;  65676622*x^2 - 114620*y^2 + 131401644*x*z + 131353244*z^2
; C4a (-24544/8383 : 435699/8383 : 1)  C4b (-1728634/1421871 : -1055763/43087 : 1)
**u= 116/41 ;  393346*x^2 - 9512*y^2 + 840516*x*z + 786692*z^2
; C4a (-63131/17266 : -610407/34532 : 1)  C4b (-120813/100766 : -1463223/201532 : 1)
**u= 116/73 ;  1276162*x^2 - 16936*y^2 + 2606148*x*z + 2552324*z^2
; C4a (-102995/114433 : 1958703/228866 : 1)  C4b (-538379/493497 : -2961797/328998 : 1)
**u= 116/89 ;  1903426*x^2 - 20648*y^2 + 3860676*x*z + 3806852*z^2
; C4a (-7023/4946 : -101237/9892 : 1)  C4b (-11349/6938 : 161547/13876 : 1)
**u= 116/121 ;  3529666*x^2 - 28072*y^2 + 7113156*x*z + 7059332*z^2
; C4a (-10045/10278 : 2517179/226116 : 1)  C4b (-55321/45502 : -11627879/1001044 : 1)
**u= 116/289 ;  20198626*x^2 - 67048*y^2 + 40451076*x*z + 40397252*z^2
; C4a (-2653795/4542201 : 2900983277/154434834 : 1)  C4b (-221291/193581 : 38550349/2193918 : 1)
**u= 116/441 ;  47050946*x^2 - 102312*y^2 + 94155716*x*z + 94101892*z^2
; C4a (39771/18278 : 54820253/767676 : 1)  C4b (-6520373/7915243 : 7244324471/332440206 : 1)
**u= 116/593 ;  85085602*x^2 - 137576*y^2 + 170225028*x*z + 170171204*z^2
; C4a (-527139/1320946 : -76644461/2641892 : 1)  C4b (145037/33617 : -9042811/67234 : 1)
**u= 128/5 ;  -10334*x^2 - 1280*y^2 + 44868*x*z - 20668*z^2
; C4a (8186/9569 : 215595/76552 : 1)  C4b (5028/1031 : -159327/8248 : 1)
**u= 128/29 ;  187138*x^2 - 7424*y^2 + 439812*x*z + 374276*z^2
; C4a (-10356/2003 : 327589/16024 : 1)  C4b (85554/35725 : -5345691/285800 : 1)
**u= 128/101 ;  2452258*x^2 - 25856*y^2 + 4970052*x*z + 4904516*z^2
; C4a (-98244/37277 : 5513837/298216 : 1)  C4b (209282/80957 : -23573767/647656 : 1)
**u= 128/149 ;  5356258*x^2 - 38144*y^2 + 10778052*x*z + 10712516*z^2
; C4a (-1386724/16585841 : 2132094321/132686728 : 1)  C4b (-130454/209877 : -7136233/559672 : 1)
**u= 128/197 ;  9375394*x^2 - 50432*y^2 + 18816324*x*z + 18750788*z^2
; C4a (-63068/445601 : -64039707/3564808 : 1)  C4b (-61682/10479 : 1905157/27944 : 1)
**u= 128/245 ;  14509666*x^2 - 62720*y^2 + 29084868*x*z + 29019332*z^2
; C4a (-2759932/6212707 : 6049362189/347911592 : 1)  C4b (828/1277 : -2098611/71512 : 1)
**u= 128/277 ;  18552034*x^2 - 70912*y^2 + 37169604*x*z + 37104068*z^2
; C4a (-29866/53371 : -7539909/426968 : 1)  C4b (40084/63191 : -15675679/505528 : 1)
**u= 128/349 ;  29459458*x^2 - 89344*y^2 + 58984452*x*z + 58918916*z^2
; C4a (-753292/318483 : -78223303/2547864 : 1)  C4b (-7212844/7050951 : -114031147/6267512 : 1)
**u= 128/365 ;  32224066*x^2 - 93440*y^2 + 64513668*x*z + 64448132*z^2
; C4a (2078196/74368249 : 15844904639/594945992 : 1)  C4b (-476322/465271 : -69249051/3722168 : 1)
**u= 128/405 ;  39677666*x^2 - 103680*y^2 + 79420868*x*z + 79355332*z^2
; C4a (-932/37 : -1261643/2664 : 1)  C4b (-113618/297539 : -493003087/21422808 : 1)
**u= 136/5 ;  -12446*x^2 - 1360*y^2 + 49092*x*z - 24892*z^2
; C4a (1006/647 : -5127/1294 : 1)  C4b (268/1047 : 3985/698 : 1)
**u= 136/45 ;  471554*x^2 - 12240*y^2 + 1017092*x*z + 943108*z^2
; C4a (-7444/8707 : 305375/52242 : 1)  C4b (-1772/367 : 57407/2202 : 1)
**u= 136/53 ;  661282*x^2 - 14416*y^2 + 1396548*x*z + 1322564*z^2
; C4a (-3796/152933 : -2891469/305866 : 1)  C4b (6012/19939 : 452823/39878 : 1)
**u= 136/125 ;  3762754*x^2 - 34000*y^2 + 7599492*x*z + 7525508*z^2
; C4a (-21394/20167 : -2103279/201670 : 1)  C4b (11462/22243 : -4262587/222430 : 1)
**u= 136/181 ;  7909666*x^2 - 49232*y^2 + 15893316*x*z + 15819332*z^2
; C4a (504060/754271 : -37221803/1508542 : 1)  C4b (318196/113143 : 11321399/226286 : 1)
**u= 136/205 ;  10151554*x^2 - 55760*y^2 + 20377092*x*z + 20303108*z^2
; C4a (-7669226/9391303 : 256914225/18782606 : 1)  C4b (-1568758/3957773 : 125111839/7915546 : 1)
**u= 136/389 ;  36601186*x^2 - 105808*y^2 + 73276356*x*z + 73202372*z^2
; C4a (-2771866/2205267 : -84594589/4410534 : 1)  C4b (-2411194/2100679 : -79119379/4201358 : 1)
**u= 136/461 ;  51411586*x^2 - 125392*y^2 + 102897156*x*z + 102823172*z^2
; C4a (-1171148/994813 : 40881579/1989626 : 1)  C4b (-53577772/28186597 : 1538045411/56373194 : 1)
**u= 144/5 ;  -14686*x^2 - 1440*y^2 + 53572*x*z - 29372*z^2
; C4a (7467/2794 : 83389/33528 : 1)  C4b (-187/197 : 20243/2364 : 1)
**u= 144/85 ;  1727714*x^2 - 24480*y^2 + 3538372*x*z + 3455428*z^2
; C4a (-19133/4859 : 1505083/58308 : 1)  C4b (-1949/3527 : 398407/42324 : 1)
**u= 144/149 ;  5351906*x^2 - 42912*y^2 + 10786756*x*z + 10703812*z^2
; C4a (-3405/3326 : -442303/39912 : 1)  C4b (-74851/60665 : -8456551/727980 : 1)
**u= 144/173 ;  7222082*x^2 - 49824*y^2 + 14527108*x*z + 14444164*z^2
; C4a (46555/47266 : -15195137/567192 : 1)  C4b (-26601/6598 : -3058703/79176 : 1)
**u= 144/373 ;  33648482*x^2 - 107424*y^2 + 67379908*x*z + 67296964*z^2
; C4a (-79805/1922 : -16545301/23064 : 1)  C4b (-4099903/3255322 : 715732027/39063864 : 1)
**u= 144/533 ;  68728802*x^2 - 153504*y^2 + 137540548*x*z + 137457604*z^2
; C4a (-211275/174281 : -45207097/2091372 : 1)  C4b (514624157/421495397 : -260725602683/5057944764 : 1)
**u= 148/9 ;  -2302*x^2 - 2664*y^2 + 83012*x*z - 4604*z^2
; C4a (2303/23943 : 161321/143658 : 1)  C4b (759/695 : -28847/4170 : 1)
**u= 148/17 ;  48034*x^2 - 5032*y^2 + 183684*x*z + 96068*z^2
; C4a (4663/1347 : 43427/2694 : 1)  C4b (103633/107277 : 606761/71518 : 1)
**u= 148/41 ;  384898*x^2 - 12136*y^2 + 857412*x*z + 769796*z^2
; C4a (-88495/38373 : 638311/76746 : 1)  C4b (-5249269/7167202 : 94152407/14334404 : 1)
**u= 148/65 ;  1000546*x^2 - 19240*y^2 + 2088708*x*z + 2001092*z^2
; C4a (-18419/35889 : 565129/71778 : 1)  C4b (-45391/28473 : 170525/18982 : 1)
**u= 148/73 ;  1267714*x^2 - 21608*y^2 + 2623044*x*z + 2535428*z^2
; C4a (-95925/99311 : 1470613/198622 : 1)  C4b (-81299/60729 : 346121/40486 : 1)
**u= 148/153 ;  5643074*x^2 - 45288*y^2 + 11373764*x*z + 11286148*z^2
; C4a (189/3686 : -358261/22116 : 1)  C4b (-9187/27474 : 2222959/164844 : 1)
**u= 148/265 ;  16972546*x^2 - 78440*y^2 + 34032708*x*z + 33945092*z^2
; C4a (-755451/5532761 : 215008877/11065522 : 1)  C4b (-390611/216198 : -911743/48044 : 1)
**u= 148/281 ;  19086658*x^2 - 83176*y^2 + 38260932*x*z + 38173316*z^2
; C4a (-2995855/664157 : 73395609/1328314 : 1)  C4b (-13044189/17974906 : -566219199/35949812 : 1)
**u= 148/305 ;  22490146*x^2 - 90280*y^2 + 45067908*x*z + 44980292*z^2
; C4a (13907/181114 : 8402061/362228 : 1)  C4b (-1207221/220243 : 31969227/440486 : 1)
**u= 148/433 ;  45350434*x^2 - 128168*y^2 + 90788484*x*z + 90700868*z^2
; C4a (-3039537/328459 : -102726139/656918 : 1)  C4b (44561/1248690 : 22554297/832460 : 1)
**u= 148/441 ;  47042498*x^2 - 130536*y^2 + 94172612*x*z + 94084996*z^2
; C4a (-386209/430247 : 344548793/18070374 : 1)  C4b (24641/11005 : -29753147/462210 : 1)
**u= 148/529 ;  67699618*x^2 - 156584*y^2 + 135486852*x*z + 135399236*z^2
; C4a (5131/53546 : -75981843/2463116 : 1)  C4b (-11385879/7257341 : 7994840499/333837686 : 1)
**u= 148/593 ;  85077154*x^2 - 175528*y^2 + 170241924*x*z + 170154308*z^2
; C4a (-110969/256099 : 12959037/512198 : 1)  C4b (729901/3533838 : 81296913/2355892 : 1)
**u= 160/29 ;  177922*x^2 - 9280*y^2 + 458244*x*z + 355844*z^2
; C4a (-5086/9819 : -166225/39276 : 1)  C4b (17888/3493 : 417587/13972 : 1)
**u= 160/61 ;  874882*x^2 - 19520*y^2 + 1852164*x*z + 1749764*z^2
; C4a (-94986/35669 : -1775155/142676 : 1)  C4b (-237536/144009 : -1675093/192012 : 1)
**u= 160/101 ;  2443042*x^2 - 32320*y^2 + 4988484*x*z + 4886084*z^2
; C4a (-28894/45991 : 1686507/183964 : 1)  C4b (-46504/33831 : 433501/45108 : 1)
**u= 160/197 ;  9366178*x^2 - 63040*y^2 + 18834756*x*z + 18732356*z^2
; C4a (-125066/34397 : -4716297/137588 : 1)  C4b (-32671024/24837553 : -1281515795/99350212 : 1)
**u= 160/221 ;  11793922*x^2 - 70720*y^2 + 23690244*x*z + 23587844*z^2
; C4a (-910688/518191 : -33416007/2072764 : 1)  C4b (-85766/32667 : 1079129/43556 : 1)
**u= 160/397 ;  38115778*x^2 - 127040*y^2 + 76333956*x*z + 76231556*z^2
; C4a (-322872/219409 : 16780045/877636 : 1)  C4b (-1552592/1733359 : 120972503/6933436 : 1)
**u= 160/509 ;  62672002*x^2 - 162880*y^2 + 125446404*x*z + 125344004*z^2
; C4a (-406184/804011 : -70361625/3216044 : 1)  C4b (-709426/69529 : -50529055/278116 : 1)
**u= 164/49 ;  554146*x^2 - 16072*y^2 + 1215876*x*z + 1108292*z^2
; C4a (-1001/577 : 52029/8078 : 1)  C4b (-9151/4027 : -602687/56378 : 1)
**u= 164/89 ;  1889986*x^2 - 29192*y^2 + 3887556*x*z + 3779972*z^2
; C4a (-370077/235009 : -4212521/470018 : 1)  C4b (14747/127376 : 3110227/254752 : 1)
**u= 164/121 ;  3516226*x^2 - 39688*y^2 + 7140036*x*z + 7032452*z^2
; C4a (6161/1503 : 1621019/33066 : 1)  C4b (-88287/74359 : 16055691/1635898 : 1)
**u= 164/137 ;  4515202*x^2 - 44936*y^2 + 9137988*x*z + 9030404*z^2
; C4a (-20771897/7217893 : 305517957/14435786 : 1)  C4b (-9956713/10431765 : 70981601/6954510 : 1)
**u= 164/153 ;  5638082*x^2 - 50184*y^2 + 11383748*x*z + 11276164*z^2
; C4a (-31925/11044 : 1493179/66264 : 1)  C4b (87821/134476 : -16574027/806856 : 1)
**u= 164/281 ;  19081666*x^2 - 92168*y^2 + 38270916*x*z + 38163332*z^2
; C4a (5771595/441568 : 179281403/883136 : 1)  C4b (-15422029/12244865 : 365761007/24489730 : 1)
**u= 164/425 ;  43684354*x^2 - 139400*y^2 + 87476292*x*z + 87368708*z^2
; C4a (1399477/872155 : 430861887/8721550 : 1)  C4b (-195613/35885 : -29007631/358850 : 1)
**u= 164/441 ;  47037506*x^2 - 144648*y^2 + 94182596*x*z + 94075012*z^2
; C4a (-169311/226471 : -176761891/9511782 : 1)  C4b (-32639/48040 : 38257403/2017680 : 1)
**u= 180/113 ;  3057698*x^2 - 40680*y^2 + 6244996*x*z + 6115396*z^2
; C4a (15733/24729 : 2475769/148374 : 1)  C4b (-178331/91197 : -6769547/547182 : 1)
**u= 180/169 ;  6879362*x^2 - 60840*y^2 + 13888324*x*z + 13758724*z^2
; C4a (6329/4529 : 1396697/50466 : 1)  C4b (-10119/3581 : 6249611/279318 : 1)
**u= 180/361 ;  31505282*x^2 - 129960*y^2 + 63140164*x*z + 63010564*z^2
; C4a (-51417/61883 : 111215237/7054662 : 1)  C4b (-939/1153 : -2086999/131442 : 1)
**u= 180/401 ;  38881442*x^2 - 144360*y^2 + 77892484*x*z + 77762884*z^2
; C4a (-753977/575018 : 59181919/3450108 : 1)  C4b (-321817/168658 : 22491167/1011948 : 1)
**u= 180/521 ;  65656322*x^2 - 187560*y^2 + 131442244*x*z + 131312644*z^2
; C4a (-166747/171349 : -19223849/1028094 : 1)  C4b (42643/1619 : -4974391/9714 : 1)
**u= 180/577 ;  80536418*x^2 - 207720*y^2 + 161202436*x*z + 161072836*z^2
; C4a (-796299/724513 : -85939961/4347078 : 1)  C4b (-926197/1203179 : -146009659/7219074 : 1)
**u= 196/17 ;  31522*x^2 - 6664*y^2 + 216708*x*z + 63044*z^2
; C4a (1397/4164 : 266527/58296 : 1)  C4b (5381/1032 : -110233/4816 : 1)
**u= 196/145 ;  5049634*x^2 - 56840*y^2 + 10252932*x*z + 10099268*z^2
; C4a (354489/27548 : -50594339/385672 : 1)  C4b (6527/12633 : -1014725/58954 : 1)
**u= 196/353 ;  30116962*x^2 - 138376*y^2 + 60387588*x*z + 60233924*z^2
; C4a (-1133369/717077 : 10043301/590534 : 1)  C4b (19087/83669 : -27397411/1171366 : 1)
**u= 196/377 ;  34356802*x^2 - 147784*y^2 + 68867268*x*z + 68713604*z^2
; C4a (-10891/10539 : -2245729/147546 : 1)  C4b (675839/377700 : -79688093/1762600 : 1)
**u= 196/401 ;  38875426*x^2 - 157192*y^2 + 77904516*x*z + 77750852*z^2
; C4a (-200797/59964 : -33665993/839496 : 1)  C4b (-106557/145705 : 33294519/2039870 : 1)
**u= 196/425 ;  43672834*x^2 - 166600*y^2 + 87499332*x*z + 87345668*z^2
; C4a (-9173/22908 : 6051259/320712 : 1)  C4b (-13429/97740 : -16271287/760200 : 1)
**u= 196/545 ;  71841634*x^2 - 213640*y^2 + 143836932*x*z + 143683268*z^2
; C4a (-203677/99576 : -36944909/1394064 : 1)  C4b (-497433/706613 : 189421923/9892582 : 1)
**u= 198/61 ;  861278*x^2 - 24156*y^2 + 1879372*x*z + 1722556*z^2
; C4a (-1555624/862977 : 17734013/2588931 : 1)  C4b (70318/35211 : -186049/9603 : 1)
**u= 198/137 ;  4502894*x^2 - 54252*y^2 + 9162604*x*z + 9005788*z^2
; C4a (-179412/3979 : -208439/519 : 1)  C4b (93146/113003 : -587257/30819 : 1)
**u= 200/29 ;  163522*x^2 - 11600*y^2 + 487044*x*z + 327044*z^2
; C4a (-162/311 : 9907/3110 : 1)  C4b (-95996/21943 : -3927931/219430 : 1)
**u= 200/157 ;  5925058*x^2 - 62800*y^2 + 12010116*x*z + 11850116*z^2
; C4a (21644/5007 : -527843/10014 : 1)  C4b (222698/36237 : -8508949/120790 : 1)
**u= 200/173 ;  7202818*x^2 - 69200*y^2 + 14565636*x*z + 14405636*z^2
; C4a (-1948/67085 : -9538101/670850 : 1)  C4b (542684/509921 : 119721467/5099210 : 1)
**u= 200/261 ;  16445282*x^2 - 104400*y^2 + 33050564*x*z + 32890564*z^2
; C4a (-399350/71769 : -126110663/2153070 : 1)  C4b (-21996/20209 : -1539467/121254 : 1)
**u= 200/533 ;  68709538*x^2 - 213200*y^2 + 137579076*x*z + 137419076*z^2
; C4a (52452/98143 : -32275279/981430 : 1)  C4b (-144684/125399 : -22819503/1253990 : 1)
**u= 208/29 ;  160258*x^2 - 12064*y^2 + 493572*x*z + 320516*z^2
; C4a (-1033/57 : -13771/228 : 1)  C4b (-268167/174428 : -4854903/697712 : 1)
**u= 208/85 ;  1705186*x^2 - 35360*y^2 + 3583428*x*z + 3410372*z^2
; C4a (52777/8888 : 1741167/35552 : 1)  C4b (31033/10732 : 1217155/42928 : 1)
**u= 208/109 ;  2831938*x^2 - 45344*y^2 + 5836932*x*z + 5663876*z^2
; C4a (-125365/34793 : -3023349/139172 : 1)  C4b (-1417473/1720045 : 57357591/6880180 : 1)
**u= 208/245 ;  14482786*x^2 - 101920*y^2 + 29138628*x*z + 28965572*z^2
; C4a (30731/10104 : 14055467/282912 : 1)  C4b (-53611/36688 : -13622179/1027264 : 1)
**u= 208/269 ;  17468098*x^2 - 111904*y^2 + 35109252*x*z + 34936196*z^2
; C4a (-4429/3017 : 165477/12068 : 1)  C4b (58689/411503 : -31294203/1646012 : 1)
**u= 208/549 ;  72895778*x^2 - 228384*y^2 + 145964612*x*z + 145791556*z^2
; C4a (72095/109209 : 45385619/1310508 : 1)  C4b (1783581/277135 : 445973171/3325620 : 1)
**u= 212/25 ;  106306*x^2 - 10600*y^2 + 392388*x*z + 212612*z^2
; C4a (-10213/17139 : -42817/34278 : 1)  C4b (-5829/806 : 236367/8060 : 1)
**u= 212/49 ;  536098*x^2 - 20776*y^2 + 1251972*x*z + 1072196*z^2
; C4a (-5713/4467 : 255907/62538 : 1)  C4b (-949033/1017859 : 88230523/14250026 : 1)
**u= 212/89 ;  1871938*x^2 - 37736*y^2 + 3923652*x*z + 3743876*z^2
; C4a (-193515/89078 : -1846679/178156 : 1)  C4b (-237673/93314 : -2562619/186628 : 1)
**u= 212/145 ;  5043106*x^2 - 61480*y^2 + 10265988*x*z + 10086212*z^2
; C4a (2303/8691 : 254315/17382 : 1)  C4b (-343/170014 : -4389527/340028 : 1)
**u= 212/529 ;  67676578*x^2 - 224296*y^2 + 135532932*x*z + 135353156*z^2
; C4a (-14327/8366 : 8195673/384836 : 1)  C4b (-284003/320702 : 258395059/14752292 : 1)
**u= 212/593 ;  85054114*x^2 - 251432*y^2 + 170288004*x*z + 170108228*z^2
; C4a (-39741849/52188278 : -1972067621/104376556 : 1)  C4b (473298783/102232622 : -21510307443/204465244 : 1)
**u= 232/13 ;  -12926*x^2 - 6032*y^2 + 189444*x*z - 25852*z^2
; C4a (3600/2381 : 29471/4762 : 1)  C4b (-45302/7 : -359047/14 : 1)
**u= 232/45 ;  436226*x^2 - 20880*y^2 + 1087748*x*z + 872452*z^2
; C4a (-1928/4499 : -130289/26994 : 1)  C4b (-934538/1965429 : -72805603/11792574 : 1)
**u= 232/53 ;  625954*x^2 - 24592*y^2 + 1467204*x*z + 1251908*z^2
; C4a (9424/64911 : 143783/18546 : 1)  C4b (-4072/5037 : -20701/3358 : 1)
**u= 232/101 ;  2414818*x^2 - 46864*y^2 + 5044932*x*z + 4829636*z^2
; C4a (-96349720/51755437 : -932925513/103510874 : 1)  C4b (-228546/373573 : -6011991/747146 : 1)
**u= 232/109 ;  2821378*x^2 - 50576*y^2 + 5858052*x*z + 5642756*z^2
; C4a (10/167 : -3639/334 : 1)  C4b (280144/58989 : 1737413/39326 : 1)
**u= 232/125 ;  3727426*x^2 - 58000*y^2 + 7670148*x*z + 7454852*z^2
; C4a (45944/28281 : 6405371/282810 : 1)  C4b (-351224/236397 : 1471985/157598 : 1)
**u= 232/149 ;  5318818*x^2 - 69136*y^2 + 10852932*x*z + 10637636*z^2
; C4a (-657574/273391 : -8135187/546782 : 1)  C4b (-193246/137163 : 895941/91442 : 1)
**u= 232/157 ;  5911234*x^2 - 72848*y^2 + 12037764*x*z + 11822468*z^2
; C4a (-732998/100243 : -11504241/200486 : 1)  C4b (324434/91947 : -2576377/61298 : 1)
**u= 232/181 ;  7874338*x^2 - 83984*y^2 + 15963972*x*z + 15748676*z^2
; C4a (-632272/192013 : -9234483/384026 : 1)  C4b (-268678/467507 : 9970331/935014 : 1)
**u= 232/229 ;  12636898*x^2 - 106256*y^2 + 25489092*x*z + 25273796*z^2
; C4a (-1221272/981373 : -21813351/1962746 : 1)  C4b (-534472/627863 : -14001227/1255726 : 1)
**u= 232/349 ;  29422018*x^2 - 161936*y^2 + 59059332*x*z + 58844036*z^2
; C4a (815872/124037 : 25568679/248074 : 1)  C4b (-52442/68733 : 637589/45822 : 1)
**u= 232/365 ;  32186626*x^2 - 169360*y^2 + 64588548*x*z + 64373252*z^2
; C4a (715558/229137 : -26817553/458274 : 1)  C4b (141104/122851 : -8035231/245702 : 1)
**u= 232/373 ;  33615394*x^2 - 173072*y^2 + 67446084*x*z + 67230788*z^2
; C4a (-2157240/1190053 : -42594247/2380106 : 1)  C4b (-754112/1293277 : 39179323/2586554 : 1)
**u= 232/445 ;  47868226*x^2 - 206480*y^2 + 95951748*x*z + 95736452*z^2
; C4a (-237816/846161 : 31722175/1692322 : 1)  C4b (402522/468419 : -30135183/936838 : 1)
**u= 232/549 ;  72885218*x^2 - 254736*y^2 + 145985732*x*z + 145770436*z^2
; C4a (271106/39111 : -31738429/234666 : 1)  C4b (-1982626/1187629 : -145399403/7125774 : 1)
**u= 244/25 ;  91714*x^2 - 12200*y^2 + 421572*x*z + 183428*z^2
; C4a (2457/386 : 89663/3860 : 1)  C4b (4875/158 : -205683/1580 : 1)
**u= 244/49 ;  521506*x^2 - 23912*y^2 + 1281156*x*z + 1043012*z^2
; C4a (-49633/13538 : -2245227/189532 : 1)  C4b (-18771/6425 : 1119147/89950 : 1)
**u= 244/81 ;  1528226*x^2 - 39528*y^2 + 3294596*x*z + 3056452*z^2
; C4a (-74467/27549 : 5751247/495882 : 1)  C4b (-56997/46559 : 5993411/838062 : 1)
**u= 244/193 ;  8954722*x^2 - 94184*y^2 + 18147588*x*z + 17909444*z^2
; C4a (-39571185/43009102 : 831124639/86018204 : 1)  C4b (-997624349/1092320191 : -21777971491/2184640382 : 1)
**u= 244/241 ;  13996066*x^2 - 117608*y^2 + 28230276*x*z + 27992132*z^2
; C4a (-2540567/2736389 : 59382927/5472778 : 1)  C4b (6524547/8477126 : -376950531/16954252 : 1)
**u= 244/257 ;  15924322*x^2 - 125416*y^2 + 32086788*x*z + 31848644*z^2
; C4a (34595/65771 : -2707479/131542 : 1)  C4b (-12846431/12606710 : -287369531/25213420 : 1)
**u= 244/441 ;  47004866*x^2 - 215208*y^2 + 94247876*x*z + 94009732*z^2
; C4a (-29653/9786 : 13725967/411012 : 1)  C4b (-3443611/79717 : -2091373943/3348114 : 1)
**u= 244/449 ;  48727906*x^2 - 219112*y^2 + 97693956*x*z + 97455812*z^2
; C4a (698093/68022 : 22944049/136044 : 1)  C4b (758797/162518 : 27927271/325036 : 1)
**u= 244/529 ;  67661986*x^2 - 258152*y^2 + 135562116*x*z + 135323972*z^2
; C4a (-11157/5759 : -5867627/264914 : 1)  C4b (-80263/91178 : 68551223/4194188 : 1)
**u= 244/577 ;  80509282*x^2 - 281576*y^2 + 161256708*x*z + 161018564*z^2
; C4a (-49522089/49010351 : 1655071339/98020702 : 1)  C4b (-575463749/627091666 : 21323465927/1254183332 : 1)
**u= 256/37 ;  265762*x^2 - 18944*y^2 + 793668*x*z + 531524*z^2
; C4a (2577/14 : -22241/32 : 1)  C4b (-5209/287 : -368311/4592 : 1)
**u= 256/61 ;  834946*x^2 - 31232*y^2 + 1932036*x*z + 1669892*z^2
; C4a (-1931/1102 : -91881/17632 : 1)  C4b (-3571/290 : 296867/4640 : 1)
**u= 256/117 ;  3247202*x^2 - 59904*y^2 + 6756548*x*z + 6494404*z^2
; C4a (-41681/14059 : -10680223/674832 : 1)  C4b (13967/1042 : 5409667/50016 : 1)
**u= 256/157 ;  5899522*x^2 - 80384*y^2 + 12061188*x*z + 11799044*z^2
; C4a (6979/28583 : -6267141/457328 : 1)  C4b (73483/8815 : 11446883/141040 : 1)
**u= 256/173 ;  7177282*x^2 - 88576*y^2 + 14616708*x*z + 14354564*z^2
; C4a (-77815/48041 : 1137771/109808 : 1)  C4b (-42467/22961 : 4462219/367376 : 1)
**u= 256/477 ;  54996482*x^2 - 244224*y^2 + 110255108*x*z + 109992964*z^2
; C4a (10827/2167 : 9491921/104016 : 1)  C4b (-9327127/5421678 : 4831640047/260240544 : 1)
**u= 260/9 ;  -47998*x^2 - 4680*y^2 + 174404*x*z - 95996*z^2
; C4a (3/4 : 31/24 : 1)  C4b (-2731/8084 : 330119/48504 : 1)
**u= 260/97 ;  2209378*x^2 - 50440*y^2 + 4689156*x*z + 4418756*z^2
; C4a (-67649/110896 : 1523655/221792 : 1)  C4b (-56847/62459 : -898515/124918 : 1)
**u= 260/137 ;  4474498*x^2 - 71240*y^2 + 9219396*x*z + 8948996*z^2
; C4a (-252676143/97471987 : 2839866217/194943974 : 1)  C4b (-143291/286132 : -5603/616 : 1)
**u= 260/193 ;  8946658*x^2 - 100360*y^2 + 18163716*x*z + 17893316*z^2
; C4a (-3430169/1396713 : 46026511/2793426 : 1)  C4b (1632729/1240907 : 59368563/2481814 : 1)
**u= 260/433 ;  45304738*x^2 - 225160*y^2 + 90879876*x*z + 90609476*z^2
; C4a (82179277/4560367 : -2464549785/9120734 : 1)  C4b (-84232949/36920933 : -1709475347/73841866 : 1)
**u= 260/529 ;  67653922*x^2 - 275080*y^2 + 135578244*x*z + 135307844*z^2
; C4a (21643/43273 : 56298537/1990558 : 1)  C4b (-1699021/1695124 : -1226527727/77975704 : 1)
**u= 272/37 ;  257314*x^2 - 20128*y^2 + 810564*x*z + 514628*z^2
; C4a (-325/498 : 4333/1992 : 1)  C4b (-20087/11262 : -115069/15016 : 1)
**u= 272/45 ;  416066*x^2 - 24480*y^2 + 1128068*x*z + 832132*z^2
; C4a (-2939/3514 : -16321/6024 : 1)  C4b (411/494 : 2965/312 : 1)
**u= 272/53 ;  605794*x^2 - 28832*y^2 + 1507524*x*z + 1211588*z^2
; C4a (-13565/8251 : 118317/33004 : 1)  C4b (-45405971/21799630 : 770996851/87198520 : 1)
**u= 272/61 ;  826498*x^2 - 33184*y^2 + 1948932*x*z + 1652996*z^2
; C4a (88152203/9913146 : 1999048121/39652584 : 1)  C4b (-264121/176710 : -4992127/706840 : 1)
**u= 272/245 ;  14452066*x^2 - 133280*y^2 + 29200068*x*z + 28904132*z^2
; C4a (372529/213838 : -182360655/5987464 : 1)  C4b (123119/87498 : -22232269/816648 : 1)
**u= 272/365 ;  32166466*x^2 - 198560*y^2 + 64628868*x*z + 64332932*z^2
; C4a (-24669/27299 : -1390505/109196 : 1)  C4b (266117/86673 : 6174273/115564 : 1)
**u= 272/421 ;  42818338*x^2 - 229024*y^2 + 85932612*x*z + 85636676*z^2
; C4a (185225/179121 : -22220687/716484 : 1)  C4b (-956363/1130094 : -20940257/1506792 : 1)
**u= 272/445 ;  47848066*x^2 - 242080*y^2 + 95992068*x*z + 95696132*z^2
; C4a (3772607/1287318 : -7165247/125592 : 1)  C4b (24801677/26110534 : -3220662047/104442136 : 1)
**u= 286/269 ;  17429566*x^2 - 153868*y^2 + 35186316*x*z + 34859132*z^2
; C4a (-187570/491219 : -6130377/491219 : 1)  C4b (-443608/102103 : -3824029/102103 : 1)
**u= 286/281 ;  19026766*x^2 - 160732*y^2 + 38380716*x*z + 38053532*z^2
; C4a (-2521040/2997663 : -32790703/2997663 : 1)  C4b (327734/268315 : 7129793/268315 : 1)
**u= 288/29 ;  120578*x^2 - 16704*y^2 + 572932*x*z + 241156*z^2
; C4a (8326/12671 : -962759/152052 : 1)  C4b (114788/72945 : 8730823/875340 : 1)
**u= 288/37 ;  248354*x^2 - 21312*y^2 + 828484*x*z + 496708*z^2
; C4a (-39942/15569 : -97787/186828 : 1)  C4b (-22812/2677 : -1136527/32124 : 1)
**u= 288/157 ;  5882114*x^2 - 90432*y^2 + 12096004*x*z + 11764228*z^2
; C4a (-1024518/617153 : 69193543/7405836 : 1)  C4b (-108428/16081 : -9248831/192972 : 1)
**u= 288/221 ;  11736578*x^2 - 127296*y^2 + 23804932*x*z + 23473156*z^2
; C4a (-161150/138093 : -15870979/1657116 : 1)  C4b (282836/156205 : -53919307/1874460 : 1)
**u= 288/277 ;  18485474*x^2 - 159552*y^2 + 37302724*x*z + 36970948*z^2
; C4a (-1158846/126037 : 134229791/1512444 : 1)  C4b (-19404/10385 : 1801403/124620 : 1)
**u= 288/317 ;  24235394*x^2 - 182592*y^2 + 48802564*x*z + 48470788*z^2
; C4a (-464492/71327 : 55163813/855924 : 1)  C4b (232618/164109 : -59473759/1969308 : 1)
**u= 288/373 ;  33586274*x^2 - 214848*y^2 + 67504324*x*z + 67172548*z^2
; C4a (333966/2231263 : -510262487/26775156 : 1)  C4b (70876/177985 : -45987599/2135820 : 1)
**u= 288/445 ;  47839106*x^2 - 256320*y^2 + 96009988*x*z + 95678212*z^2
; C4a (-448076/212191 : -7406269/363756 : 1)  C4b (-910676/491653 : 106478815/5899836 : 1)
**u= 288/461 ;  51347138*x^2 - 265536*y^2 + 103026052*x*z + 102694276*z^2
; C4a (123076/82547 : 36998633/990564 : 1)  C4b (-526466/3363819 : 735739739/40365828 : 1)
**u= 292/17 ;  -15326*x^2 - 9928*y^2 + 310404*x*z - 30652*z^2
; C4a (367/3476 : -39/88 : 1)  C4b (226743/161552 : -2454891/323104 : 1)
**u= 292/41 ;  321538*x^2 - 23944*y^2 + 984132*x*z + 643076*z^2
; C4a (1109/16023 : 24977/4578 : 1)  C4b (-25781/11889 : -70669/7926 : 1)
**u= 292/49 ;  495778*x^2 - 28616*y^2 + 1332612*x*z + 991556*z^2
; C4a (-9461/5288 : 192921/74032 : 1)  C4b (-137171/285340 : -23731819/3994760 : 1)
**u= 292/121 ;  3457858*x^2 - 70664*y^2 + 7256772*x*z + 6915716*z^2
; C4a (88755/1861 : 13962199/40942 : 1)  C4b (-841043/1199092 : -203161291/26380024 : 1)
**u= 292/137 ;  4456834*x^2 - 80008*y^2 + 9254724*x*z + 8913668*z^2
; C4a (-990133/248968 : 11489499/497936 : 1)  C4b (468301/417419 : -14780603/834838 : 1)
**u= 292/153 ;  5579714*x^2 - 89352*y^2 + 11500484*x*z + 11159428*z^2
; C4a (-85023/48748 : 397207/41784 : 1)  C4b (-85753/76853 : -3843551/461118 : 1)
**u= 292/169 ;  6826498*x^2 - 98696*y^2 + 13994052*x*z + 13652996*z^2
; C4a (-18077/7213 : 2765247/187538 : 1)  C4b (12659/34109 : 12632167/886834 : 1)
**u= 292/185 ;  8197186*x^2 - 108040*y^2 + 16735428*x*z + 16394372*z^2
; C4a (58469/152991 : -4559273/305982 : 1)  C4b (565127/31644 : -3502625/21096 : 1)
**u= 292/281 ;  19023298*x^2 - 164104*y^2 + 38387652*x*z + 38046596*z^2
; C4a (-717685249/758251281 : 16212178079/1516502562 : 1)  C4b (-3622951/1740139 : 55924843/3480278 : 1)
**u= 292/337 ;  27398434*x^2 - 196808*y^2 + 55137924*x*z + 54796868*z^2
; C4a (-220044037/10423909 : -4951080441/20847818 : 1)  C4b (-65323547/47902639 : -1215521147/95805278 : 1)
**u= 292/409 ;  40396738*x^2 - 238856*y^2 + 81134532*x*z + 80793476*z^2
; C4a (464253/1301311 : 57077639/2602622 : 1)  C4b (-9614293/9167049 : -80089597/6111366 : 1)
**u= 292/569 ;  78264898*x^2 - 332296*y^2 + 156870852*x*z + 156529796*z^2
; C4a (-41976637/215030256 : -8469839101/430060512 : 1)  C4b (-1247461/446329 : -28219639/892658 : 1)
**u= 296/13 ;  -46718*x^2 - 7696*y^2 + 257028*x*z - 93436*z^2
; C4a (160/291 : -1219/582 : 1)  C4b (845704/484373 : 7695599/968746 : 1)
**u= 296/53 ;  592162*x^2 - 31376*y^2 + 1534788*x*z + 1184324*z^2
; C4a (-191720/124799 : -666969/249598 : 1)  C4b (286784/51293 : 3283591/102586 : 1)
**u= 296/181 ;  7840546*x^2 - 107152*y^2 + 16031556*x*z + 15681092*z^2
; C4a (-154024/248269 : -641109/70934 : 1)  C4b (-911534/499199 : -11462827/998398 : 1)
**u= 296/317 ;  24230722*x^2 - 187664*y^2 + 48811908*x*z + 48461444*z^2
; C4a (391856/1773031 : -63634473/3546062 : 1)  C4b (-25461752/15530023 : -423946267/31060046 : 1)
**u= 296/477 ;  54974402*x^2 - 282384*y^2 + 110299268*x*z + 109948804*z^2
; C4a (-684920/942487 : -11659801/807846 : 1)  C4b (-344376/473983 : -41290871/2843898 : 1)
**u= 320/29 ;  101122*x^2 - 18560*y^2 + 611844*x*z + 202244*z^2
; C4a (-5721/16304 : -1217/130432 : 1)  C4b (-181149/268376 : 12356067/2147008 : 1)
**u= 320/37 ;  228898*x^2 - 23680*y^2 + 867396*x*z + 457796*z^2
; C4a (-922007/3151559 : 77479197/25212472 : 1)  C4b (-33963/34291 : -1633311/274328 : 1)
**u= 320/181 ;  7825762*x^2 - 115840*y^2 + 16061124*x*z + 15651524*z^2
; C4a (-2844713/2442692 : -22553457/2791648 : 1)  C4b (-164269/258481 : 18585499/2067848 : 1)
**u= 320/197 ;  9289378*x^2 - 126080*y^2 + 18988356*x*z + 18578756*z^2
; C4a (-164797/12904 : -10446759/103232 : 1)  C4b (-245083/119171 : 12285023/953368 : 1)
**u= 320/269 ;  17408962*x^2 - 172160*y^2 + 35227524*x*z + 34817924*z^2
; C4a (4077/1796 : 495191/14368 : 1)  C4b (-96351/46252 : -5578587/370016 : 1)
**u= 324/25 ;  46274*x^2 - 16200*y^2 + 512452*x*z + 92548*z^2
; C4a (-3529/312 : 20525/5616 : 1)  C4b (12665/292 : 4554403/26280 : 1)
**u= 324/113 ;  2985122*x^2 - 73224*y^2 + 6390148*x*z + 5970244*z^2
; C4a (-124889/86161 : -9893137/1550898 : 1)  C4b (-91481/54688 : -8409263/984384 : 1)
**u= 324/137 ;  4437122*x^2 - 88776*y^2 + 9294148*x*z + 8874244*z^2
; C4a (71983/9733 : -10523423/175194 : 1)  C4b (-4959/18707 : -3046799/336726 : 1)
**u= 324/193 ;  8909282*x^2 - 125064*y^2 + 18238468*x*z + 17818564*z^2
; C4a (193381/42467 : -36529787/764406 : 1)  C4b (-18701/44748 : -8015287/805464 : 1)
**u= 324/281 ;  19003586*x^2 - 182088*y^2 + 38427076*x*z + 38007172*z^2
; C4a (-109141/49496 : -14110231/890928 : 1)  C4b (78861/66988 : 29609243/1205784 : 1)
**u= 324/337 ;  27378722*x^2 - 218376*y^2 + 55177348*x*z + 54757444*z^2
; C4a (307015/107088 : 86325577/1927584 : 1)  C4b (-134671/44944 : -20396087/808992 : 1)
**u= 324/433 ;  45267362*x^2 - 280584*y^2 + 90954628*x*z + 90534724*z^2
; C4a (-401221/365164 : -83469073/6572952 : 1)  C4b (-86651/44808 : 14116027/806544 : 1)
**u= 324/449 ;  48682466*x^2 - 290952*y^2 + 97784836*x*z + 97364932*z^2
; C4a (-22995/22924 : -5314393/412632 : 1)  C4b (-122099/153499 : 36678283/2762982 : 1)
**u= 324/505 ;  61611074*x^2 - 327240*y^2 + 123642052*x*z + 123222148*z^2
; C4a (-85097/68832 : 17398741/1238976 : 1)  C4b (55458449/23532096 : 20378076475/423577728 : 1)
**u= 324/593 ;  84994082*x^2 - 384264*y^2 + 170408068*x*z + 169988164*z^2
; C4a (-3119/37876 : 13760147/681768 : 1)  C4b (1415577/977060 : 692362259/17587080 : 1)
**u= 328/61 ;  792898*x^2 - 40016*y^2 + 2016132*x*z + 1585796*z^2
; C4a (-27948/46837 : -381889/93674 : 1)  C4b (-95764436/52392063 : 275273609/34928042 : 1)
**u= 328/85 ;  1640866*x^2 - 55760*y^2 + 3712068*x*z + 3281732*z^2
; C4a (-24882/5227 : 211363/10454 : 1)  C4b (-1260332/2179141 : -28800059/4358282 : 1)
**u= 328/101 ;  2361058*x^2 - 66256*y^2 + 5152452*x*z + 4722116*z^2
; C4a (-5729956/2929209 : 43647547/5858418 : 1)  C4b (-1124564/279905 : -11459803/559810 : 1)
**u= 328/109 ;  2767618*x^2 - 71504*y^2 + 5965572*x*z + 5535236*z^2
; C4a (-1748830/789781 : 14343081/1579562 : 1)  C4b (-39021414/20913937 : -383848251/41827874 : 1)
**u= 328/173 ;  7135234*x^2 - 113488*y^2 + 14700804*x*z + 14270468*z^2
; C4a (-1385114/794823 : -15159403/1589646 : 1)  C4b (-1216284/776423 : -14853471/1552846 : 1)
**u= 328/269 ;  17403778*x^2 - 176464*y^2 + 35237892*x*z + 34807556*z^2
; C4a (-985076530/491761263 : -1951879799/140503218 : 1)  C4b (-14072988/2528759 : 236908767/5057518 : 1)
**u= 328/277 ;  18460834*x^2 - 181712*y^2 + 37352004*x*z + 36921668*z^2
; C4a (-1283180/810011 : -18648519/1620022 : 1)  C4b (-5516332/3643769 : 84204079/7287538 : 1)
**u= 328/293 ;  20667874*x^2 - 192208*y^2 + 41766084*x*z + 41335748*z^2
; C4a (-7797802/18286019 : 435726879/36572038 : 1)  C4b (-220844/375773 : 8517131/751546 : 1)
**u= 328/493 ;  58710274*x^2 - 323408*y^2 + 117850884*x*z + 117420548*z^2
; C4a (237765950/485933863 : 23503042809/971867726 : 1)  C4b (563628/3169295 : -132161427/6338590 : 1)
**u= 340/121 ;  3427522*x^2 - 82280*y^2 + 7317444*x*z + 6855044*z^2
; C4a (-7777713/10618622 : -212441491/33372812 : 1)  C4b (-5853/12686 : -2161119/279092 : 1)
**u= 340/137 ;  4426498*x^2 - 93160*y^2 + 9315396*x*z + 8852996*z^2
; C4a (-71479/28613 : -681345/57226 : 1)  C4b (-11545943/7073561 : -125012323/14147122 : 1)
**u= 340/521 ;  65573122*x^2 - 354280*y^2 + 131608644*x*z + 131146244*z^2
; C4a (-247373/1968387 : 71125513/3936774 : 1)  C4b (-1607791287/2204671378 : 62405378727/4409342756 : 1)
**u= 356/17 ;  -56798*x^2 - 12104*y^2 + 393348*x*z - 113596*z^2
; C4a (27569/20348 : -207633/40696 : 1)  C4b (477319/120385 : -3812443/240770 : 1)
**u= 356/25 ;  24514*x^2 - 17800*y^2 + 555972*x*z + 49028*z^2
; C4a (1085/30407 : 598227/304070 : 1)  C4b (-188885/209372 : -13481339/2093720 : 1)
**u= 356/49 ;  454306*x^2 - 34888*y^2 + 1415556*x*z + 908612*z^2
; C4a (-446275/564723 : 11489279/7906122 : 1)  C4b (-231323/309663 : -2743571/481698 : 1)
**u= 356/81 ;  1461026*x^2 - 57672*y^2 + 3428996*x*z + 2922052*z^2
; C4a (-23355/13852 : 1181021/249336 : 1)  C4b (-7381/20925 : -2534599/376650 : 1)
**u= 356/257 ;  15857122*x^2 - 182984*y^2 + 32221188*x*z + 31714244*z^2
; C4a (-547845/377069 : -7556783/754138 : 1)  C4b (-6003/25175 : -31329/2650 : 1)
**u= 356/305 ;  22385314*x^2 - 217160*y^2 + 45277572*x*z + 44770628*z^2
; C4a (86527583/59697721 : -3214660059/119395442 : 1)  C4b (142361/61959 : 1450161/41306 : 1)
**u= 356/409 ;  40355266*x^2 - 291208*y^2 + 81217476*x*z + 80710532*z^2
; C4a (-166949/81573 : -2762989/163146 : 1)  C4b (-44559221/9670925 : 856805923/19341850 : 1)
**u= 356/577 ;  80442082*x^2 - 410824*y^2 + 161391108*x*z + 160884164*z^2
; C4a (-10669621/10530364 : -293788197/21060728 : 1)  C4b (-4458723/3588775 : -103888419/7177550 : 1)
**u= 360/53 ;  550178*x^2 - 38160*y^2 + 1618756*x*z + 1100356*z^2
; C4a (-7953986/7476937 : -7049699/44861622 : 1)  C4b (-3534/131 : 95299/786 : 1)
**u= 360/109 ;  2745602*x^2 - 78480*y^2 + 6009604*x*z + 5491204*z^2
; C4a (-125242/134413 : 4342477/806478 : 1)  C4b (-2201714/1330281 : -64671415/7981686 : 1)
**u= 360/221 ;  11689922*x^2 - 159120*y^2 + 23898244*x*z + 23379844*z^2
; C4a (-2804478/1828907 : -103740497/10973442 : 1)  C4b (-882274/543521 : -34133575/3261126 : 1)
**u= 360/269 ;  17381762*x^2 - 193680*y^2 + 35281924*x*z + 34763524*z^2
; C4a (-22081928/12981817 : 885668483/77890902 : 1)  C4b (-340654/239963 : -15163535/1439778 : 1)
**u= 360/293 ;  20645858*x^2 - 210960*y^2 + 41810116*x*z + 41291716*z^2
; C4a (-784714/136253 : 39210377/817518 : 1)  C4b (-8504262/5213479 : 373521527/31280874 : 1)
**u= 360/541 ;  70699202*x^2 - 389520*y^2 + 141916804*x*z + 141398404*z^2
; C4a (-231938/170081 : 14564599/1020486 : 1)  C4b (-4141654/2201791 : 238554395/13210746 : 1)
**u= 374/37 ;  191422*x^2 - 27676*y^2 + 942348*x*z + 382844*z^2
; C4a (-8750/1747 : -7161/1747 : 1)  C4b (1000758/7075 : -4141269/7075 : 1)
**u= 374/389 ;  36479806*x^2 - 290972*y^2 + 73519116*x*z + 72959612*z^2
; C4a (195352/287143 : 6295377/287143 : 1)  C4b (966394/127045 : -12363197/127045 : 1)
**u= 374/565 ;  77112574*x^2 - 422620*y^2 + 154784652*x*z + 154225148*z^2
; C4a (-86194/1113137 : 20454489/1113137 : 1)  C4b (-1035924/702779 : 960945/63889 : 1)
**u= 388/65 ;  871906*x^2 - 50440*y^2 + 2345988*x*z + 1743812*z^2
; C4a (-4225421/14112876 : -132979631/28225752 : 1)  C4b (59929003/47507361 : -357100349/31671574 : 1)
**u= 388/121 ;  3392578*x^2 - 93896*y^2 + 7387332*x*z + 6785156*z^2
; C4a (-32339/33551 : 577521/105446 : 1)  C4b (-40019349/42460597 : 6301929363/934133134 : 1)
**u= 388/145 ;  4937506*x^2 - 112520*y^2 + 10477188*x*z + 9875012*z^2
; C4a (-353563/219488 : 3154347/438976 : 1)  C4b (-206819/78112 : -2137067/156224 : 1)
**u= 388/401 ;  38763298*x^2 - 311176*y^2 + 78128772*x*z + 77526596*z^2
; C4a (-3189761/916848 : 54501473/1833696 : 1)  C4b (-2647921/2015745 : 15924669/1343830 : 1)
**u= 388/529 ;  67570978*x^2 - 410504*y^2 + 135744132*x*z + 135141956*z^2
; C4a (9301/12931 : -15191013/594826 : 1)  C4b (-395411/435460 : -259686727/20031160 : 1)
**u= 392/61 ;  746818*x^2 - 47824*y^2 + 2108292*x*z + 1493636*z^2
; C4a (-9308/6829 : 37731/95606 : 1)  C4b (-35068/23755 : 2255959/332570 : 1)
**u= 392/85 ;  1594786*x^2 - 66640*y^2 + 3804228*x*z + 3189572*z^2
; C4a (-357172/167657 : 13858401/2347198 : 1)  C4b (-74034/136487 : -12012711/1910818 : 1)
**u= 392/109 ;  2721538*x^2 - 85456*y^2 + 6057732*x*z + 5443076*z^2
; C4a (557732/271637 : -70482477/3802918 : 1)  C4b (-34854/25621 : 2532063/358694 : 1)
**u= 392/117 ;  3159074*x^2 - 91728*y^2 + 6932804*x*z + 6318148*z^2
; C4a (-109898/38063 : -18763391/1598646 : 1)  C4b (281494/122827 : 107212559/5158734 : 1)
**u= 392/157 ;  5811394*x^2 - 123088*y^2 + 12237444*x*z + 11622788*z^2
; C4a (-39386/17967 : -2557351/251538 : 1)  C4b (-57212/77009 : -8118599/1078126 : 1)
**u= 392/173 ;  7089154*x^2 - 135632*y^2 + 14792964*x*z + 14178308*z^2
; C4a (-93150/97781 : -9490933/1368934 : 1)  C4b (-26778/50371 : -5853807/705194 : 1)
**u= 392/261 ;  16331618*x^2 - 204624*y^2 + 33277892*x*z + 32663236*z^2
; C4a (93428/89723 : -76814713/3768366 : 1)  C4b (-23202/47315 : -20256763/1987230 : 1)
**u= 392/269 ;  17357698*x^2 - 210896*y^2 + 35330052*x*z + 34715396*z^2
; C4a (-465606/638749 : 83038831/8942486 : 1)  C4b (-165756/78233 : -15285591/1095262 : 1)
**u= 392/293 ;  20621794*x^2 - 229712*y^2 + 41858244*x*z + 41243588*z^2
; C4a (-455514/106619 : 48128923/1492666 : 1)  C4b (-417562/830699 : 124710587/11629786 : 1)
**u= 392/389 ;  36466018*x^2 - 304976*y^2 + 73546692*x*z + 72932036*z^2
; C4a (470172/307997 : -128342563/4311958 : 1)  C4b (15324/573223 : 7428627/472066 : 1)
**u= 392/485 ;  56770786*x^2 - 380240*y^2 + 114156228*x*z + 113541572*z^2
; C4a (-38676/37013 : -6302141/518182 : 1)  C4b (11068/246301 : 61096963/3448214 : 1)
**u= 392/557 ;  74926594*x^2 - 436688*y^2 + 150467844*x*z + 149853188*z^2
; C4a (-204588/90373 : 26613163/1265222 : 1)  C4b (-375578/11031 : 22342693/51478 : 1)
**u= 392/565 ;  77098786*x^2 - 442960*y^2 + 154812228*x*z + 154197572*z^2
; C4a (-99958/152673 : -29762827/2137422 : 1)  C4b (-335262/575581 : 115661247/8058134 : 1)
**u= 400/221 ;  11659522*x^2 - 176800*y^2 + 23959044*x*z + 23319044*z^2
; C4a (-609563/271777 : 13738089/1087108 : 1)  C4b (-10698929/3711791 : 264883447/14847164 : 1)
**u= 400/269 ;  17351362*x^2 - 215200*y^2 + 35342724*x*z + 34702724*z^2
; C4a (8606999/9183447 : -103101377/5247684 : 1)  C4b (1315807/1359458 : -541903531/27189160 : 1)
**u= 400/389 ;  36459682*x^2 - 311200*y^2 + 73559364*x*z + 72919364*z^2
; C4a (690049/495361 : -278626743/9907220 : 1)  C4b (-704629/893914 : 199970707/17878280 : 1)
**u= 400/461 ;  51270082*x^2 - 368800*y^2 + 103180164*x*z + 102540164*z^2
; C4a (-203863/118077 : -6834643/472308 : 1)  C4b (1201121/921534 : -182227577/6143560 : 1)
**u= 400/493 ;  58657858*x^2 - 394400*y^2 + 117955716*x*z + 117315716*z^2
; C4a (-45745/5258 : 9950157/105160 : 1)  C4b (20319/320563 : 114424623/6411260 : 1)
**u= 404/17 ;  -93278*x^2 - 13736*y^2 + 466308*x*z - 186556*z^2
; C4a (69/58 : -481/116 : 1)  C4b (109143/4475 : -885987/8950 : 1)
**u= 404/49 ;  417826*x^2 - 39592*y^2 + 1488516*x*z + 835652*z^2
; C4a (-13765/1031 : -540129/14434 : 1)  C4b (15091/18975 : 720869/88550 : 1)
**u= 404/65 ;  859234*x^2 - 52520*y^2 + 2371332*x*z + 1718468*z^2
; C4a (-218839/128722 : 463773/257444 : 1)  C4b (-17353/3974 : -144979/7948 : 1)
**u= 404/73 ;  1126402*x^2 - 58984*y^2 + 2905668*x*z + 2252804*z^2
; C4a (-882925/277978 : 208473/24172 : 1)  C4b (-63029/42650 : 582367/85300 : 1)
**u= 404/89 ;  1753666*x^2 - 71912*y^2 + 4160196*x*z + 3507332*z^2
; C4a (-5718745/4962931 : 37784313/9925862 : 1)  C4b (-40041467/4235914 : 395689643/8471828 : 1)
**u= 404/153 ;  5501762*x^2 - 123624*y^2 + 11656388*x*z + 11003524*z^2
; C4a (165713/299541 : 22360483/1797246 : 1)  C4b (222761/1012777 : -65489159/6076662 : 1)
**u= 404/169 ;  6748546*x^2 - 136552*y^2 + 14149956*x*z + 13497092*z^2
; C4a (-35555/61041 : -11796881/1587066 : 1)  C4b (-68093/36123 : -3152609/313066 : 1)
**u= 404/225 ;  12088034*x^2 - 181800*y^2 + 24828932*x*z + 24176068*z^2
; C4a (27345/3418 : 7591651/102540 : 1)  C4b (44801/88838 : 39620327/2665140 : 1)
**u= 404/241 ;  13892386*x^2 - 194728*y^2 + 28437636*x*z + 27784772*z^2
; C4a (-1182425/159982 : 17409477/319964 : 1)  C4b (355841/111910 : 8187023/223820 : 1)
**u= 404/265 ;  16831234*x^2 - 214120*y^2 + 34315332*x*z + 33662468*z^2
; C4a (734119/2109963 : -62944663/4219926 : 1)  C4b (-6470191/10452453 : -67434181/6968302 : 1)
**u= 404/305 ;  22348834*x^2 - 246440*y^2 + 45350532*x*z + 44697668*z^2
; C4a (67988951/51797162 : -2493090159/103594324 : 1)  C4b (-2838571/3083141 : -60110755/6166282 : 1)
**u= 404/377 ;  34232002*x^2 - 304616*y^2 + 69116868*x*z + 68464004*z^2
; C4a (-333/367 : 7747/734 : 1)  C4b (323753/861266 : -31168567/1722532 : 1)
**u= 404/433 ;  45209122*x^2 - 349864*y^2 + 91071108*x*z + 90418244*z^2
; C4a (-1108567985/1363593934 : 31359333453/2727187868 : 1)  C4b (-1913499/1204621 : -32160171/2409242 : 1)
**u= 404/449 ;  48624226*x^2 - 362792*y^2 + 97901316*x*z + 97248452*z^2
; C4a (-1108339/604949 : -18089283/1209898 : 1)  C4b (403061/2390 : 9419099/4780 : 1)
**u= 404/569 ;  78186946*x^2 - 459752*y^2 + 157026756*x*z + 156373892*z^2
; C4a (25291395/41011486 : -2034817027/82022972 : 1)  C4b (-44259673/52822886 : -1403344607/105645772 : 1)
**u= 416/109 ;  2702146*x^2 - 90688*y^2 + 6096516*x*z + 5404292*z^2
; C4a (-75970/60873 : 1144741/243492 : 1)  C4b (-3643086/4141555 : 105834459/16566220 : 1)
**u= 416/125 ;  3608194*x^2 - 104000*y^2 + 7908612*x*z + 7216388*z^2
; C4a (-15266/7513 : 1145487/150260 : 1)  C4b (-4792/27077 : 4364527/541540 : 1)
**u= 416/181 ;  7755106*x^2 - 150592*y^2 + 16202436*x*z + 15510212*z^2
; C4a (31214/3897 : 1018441/15588 : 1)  C4b (-56192/208235 : -7621099/832940 : 1)
**u= 416/205 ;  9996994*x^2 - 170560*y^2 + 20686212*x*z + 19993988*z^2
; C4a (-147586/196293 : -6039709/785172 : 1)  C4b (45882/11099 : -1799103/44396 : 1)
**u= 416/293 ;  20602402*x^2 - 243776*y^2 + 41897028*x*z + 41204804*z^2
; C4a (181398/310361 : -21443221/1241444 : 1)  C4b (-1515814/488387 : -42579067/1953548 : 1)
**u= 416/317 ;  24145282*x^2 - 263744*y^2 + 48982788*x*z + 48290564*z^2
; C4a (171384/140749 : 1877573/80428 : 1)  C4b (-1757992/1451963 : -58125971/5807852 : 1)
**u= 416/373 ;  33496162*x^2 - 310336*y^2 + 67684548*x*z + 66992324*z^2
; C4a (-215575678/130290499 : 6393355959/521161996 : 1)  C4b (-14507198/8727659 : -442386839/34910636 : 1)
**u= 424/13 ;  -138878*x^2 - 11024*y^2 + 441348*x*z - 277756*z^2
; C4a (2554/1223 : 4557/2446 : 1)  C4b (3738/3011 : -37899/6022 : 1)
**u= 424/37 ;  151522*x^2 - 31376*y^2 + 1022148*x*z + 303044*z^2
; C4a (242304/99349 : 2156929/198698 : 1)  C4b (-11014/35231 : -393263/70462 : 1)
**u= 424/85 ;  1568674*x^2 - 72080*y^2 + 3856452*x*z + 3137348*z^2
; C4a (-70032/52261 : -345247/104522 : 1)  C4b (12832/42943 : 712891/85886 : 1)
**u= 424/101 ;  2288866*x^2 - 85648*y^2 + 5296836*x*z + 4577732*z^2
; C4a (-1660848944/884229273 : -9936334909/1768458546 : 1)  C4b (-92414/102975 : 427521/68650 : 1)
**u= 424/149 ;  5192866*x^2 - 126352*y^2 + 11104836*x*z + 10385732*z^2
; C4a (-608295200/314755437 : -5108131871/629510874 : 1)  C4b (-2093234/909173 : 20858059/1818346 : 1)
**u= 424/205 ;  9990274*x^2 - 173840*y^2 + 20699652*x*z + 19980548*z^2
; C4a (367626/60247 : -6579125/120494 : 1)  C4b (-1556632/3127871 : -54757795/6255742 : 1)
**u= 424/221 ;  11639746*x^2 - 187408*y^2 + 23998596*x*z + 23279492*z^2
; C4a (473576/1113543 : 30691171/2227086 : 1)  C4b (37832/2593 : -647107/5186 : 1)
**u= 424/245 ;  14346274*x^2 - 207760*y^2 + 29411652*x*z + 28692548*z^2
; C4a (-36832/82167 : -10823051/1150338 : 1)  C4b (-1637392/3680157 : 166625205/17174066 : 1)
**u= 424/317 ;  24138562*x^2 - 268816*y^2 + 48996228*x*z + 48277124*z^2
; C4a (11170258/6368691 : 50672999/1819626 : 1)  C4b (-174582138/137235245 : -2762292963/274470490 : 1)
**u= 424/485 ;  56744674*x^2 - 411280*y^2 + 114208452*x*z + 113489348*z^2
; C4a (-21558146/80028233 : 2325776259/160056466 : 1)  C4b (-16728958/32952703 : 867821443/65905406 : 1)
**u= 424/549 ;  72759266*x^2 - 465552*y^2 + 146237636*x*z + 145518532*z^2
; C4a (39872/3833 : 3292127/22998 : 1)  C4b (-4991616/2487937 : -266703383/14927622 : 1)
**u= 436/41 ;  216706*x^2 - 35752*y^2 + 1193796*x*z + 433412*z^2
; C4a (149155/127782 : -1968961/255564 : 1)  C4b (-14183/11673 : 17071/2594 : 1)
**u= 436/49 ;  390946*x^2 - 42728*y^2 + 1542276*x*z + 781892*z^2
; C4a (48011/4958 : 2430213/69412 : 1)  C4b (4117/3913 : -475459/54782 : 1)
**u= 436/65 ;  832354*x^2 - 56680*y^2 + 2425092*x*z + 1664708*z^2
; C4a (-4183/2178 : -5089/4356 : 1)  C4b (-933/659 : 8751/1318 : 1)
**u= 436/265 ;  16804354*x^2 - 231080*y^2 + 34369092*x*z + 33608708*z^2
; C4a (12678109/11790293 : -465356211/23580586 : 1)  C4b (-624839/955114 : 17653987/1910228 : 1)
**u= 436/337 ;  27293602*x^2 - 293864*y^2 + 55347588*x*z + 54587204*z^2
; C4a (17075/90734 : 388419/25924 : 1)  C4b (-51918813/53036330 : 1043330919/106072660 : 1)
**u= 436/369 ;  32760866*x^2 - 321768*y^2 + 66282116*x*z + 65521732*z^2
; C4a (-188325/62998 : -8432591/377988 : 1)  C4b (2936593/2323065 : -349291567/13938390 : 1)
**u= 436/425 ;  43521154*x^2 - 370600*y^2 + 87802692*x*z + 87042308*z^2
; C4a (-223529/226110 : -24291967/2261100 : 1)  C4b (5697419/2060251 : -174445883/4120502 : 1)
**u= 436/449 ;  48597346*x^2 - 391528*y^2 + 97955076*x*z + 97194692*z^2
; C4a (-5886135673/11698971 : 130892622367/23397942 : 1)  C4b (-156881851/119855137 : 2831970923/239710274 : 1)
**u= 436/481 ;  55799266*x^2 - 419432*y^2 + 112358916*x*z + 111598532*z^2
; C4a (-1359915/1276154 : -29287837/2552308 : 1)  C4b (-1331253/20472883 : 648894879/40945766 : 1)
**u= 452/17 ;  -134366*x^2 - 15368*y^2 + 548484*x*z - 268732*z^2
; C4a (819421/935368 : -4974003/1870736 : 1)  C4b (53179/43405 : 556211/86810 : 1)
**u= 452/49 ;  376738*x^2 - 44296*y^2 + 1570692*x*z + 753476*z^2
; C4a (-129431/35624 : 334239/498736 : 1)  C4b (-319/6055 : 498719/84770 : 1)
**u= 452/65 ;  818146*x^2 - 58760*y^2 + 2453508*x*z + 1636292*z^2
; C4a (-18781/7636 : 46767/15272 : 1)  C4b (30429/48023 : 790743/96046 : 1)
**u= 452/145 ;  4883746*x^2 - 131080*y^2 + 10584708*x*z + 9767492*z^2
; C4a (-1/8 : 129/16 : 1)  C4b (-2961647/2178656 : 32038847/4357312 : 1)
**u= 452/353 ;  29951074*x^2 - 319112*y^2 + 60719364*x*z + 59902148*z^2
; C4a (-9972135/15341911 : -312449609/30683822 : 1)  C4b (1765057/2663728 : -100579447/5327456 : 1)
**u= 452/425 ;  43506946*x^2 - 384200*y^2 + 87831108*x*z + 87013892*z^2
; C4a (17970453/14571791 : 760324661/29143582 : 1)  C4b (-90547/34679 : -7077527/346790 : 1)
**u= 452/441 ;  46860098*x^2 - 398664*y^2 + 94537412*x*z + 93720196*z^2
; C4a (-128577/136481 : 61739273/5732202 : 1)  C4b (-1766063/1784820 : -823254227/74962440 : 1)
**u= 452/505 ;  61511746*x^2 - 456520*y^2 + 123840708*x*z + 123023492*z^2
; C4a (16850293/6357432 : 559316047/12714864 : 1)  C4b (167745881/85652052 : -2074026677/57101368 : 1)
**u= 452/593 ;  84894754*x^2 - 536072*y^2 + 170606724*x*z + 169789508*z^2
; C4a (-65695479/68252719 : 1711058711/136505438 : 1)  C4b (-3106281/2089336 : 58960959/4178672 : 1)
**u= 464/13 ;  -174398*x^2 - 12064*y^2 + 512388*x*z - 348796*z^2
; C4a (179551/167541 : 30361/670164 : 1)  C4b (2221021/728435 : -35892631/2913740 : 1)
**u= 464/85 ;  1533154*x^2 - 78880*y^2 + 3927492*x*z + 3066308*z^2
; C4a (-130357/88236 : -981689/352944 : 1)  C4b (-508171/689743 : -16243807/2758972 : 1)
**u= 464/109 ;  2659906*x^2 - 101152*y^2 + 6180996*x*z + 5319812*z^2
; C4a (-383315/252327 : 4564163/1009308 : 1)  C4b (-86889/165173 : -4276407/660692 : 1)
**u= 464/125 ;  3565954*x^2 - 116000*y^2 + 7993092*x*z + 7131908*z^2
; C4a (-213/10969 : 243073/31340 : 1)  C4b (-61349/33244 : -5672087/664880 : 1)
**u= 464/221 ;  11604226*x^2 - 205088*y^2 + 24069636*x*z + 23208452*z^2
; C4a (3347337/511568 : -117613901/2046272 : 1)  C4b (-30699/14624 : 688167/58496 : 1)
**u= 464/245 ;  14310754*x^2 - 227360*y^2 + 29482692*x*z + 28621508*z^2
; C4a (-50419/1372 : 10890273/38416 : 1)  C4b (-66419/23484 : 3747157/219184 : 1)
**u= 464/277 ;  18353122*x^2 - 257056*y^2 + 37567428*x*z + 36706244*z^2
; C4a (-132796721/5647164 : 4297062203/22588656 : 1)  C4b (-173581647/184281971 : 6446160291/737127884 : 1)
**u= 464/485 ;  56709154*x^2 - 450080*y^2 + 114279492*x*z + 113418308*z^2
; C4a (-5027/67867 : -4151595/271468 : 1)  C4b (1772667663/1876721537 : 184675567983/7506886148 : 1)
**u= 464/509 ;  62482306*x^2 - 472352*y^2 + 125825796*x*z + 124964612*z^2
; C4a (-1874649/813173 : -61153361/3252692 : 1)  C4b (-6570027/7180600 : -334738431/28722400 : 1)
**u= 464/565 ;  77037154*x^2 - 524320*y^2 + 154935492*x*z + 154074308*z^2
; C4a (-1380517/868716 : 48563047/3474864 : 1)  C4b (-38423749/19703724 : -442984109/26271632 : 1)
**u= 468/25 ;  -67774*x^2 - 23400*y^2 + 740548*x*z - 135548*z^2
; C4a (9091/18195 : 1664321/545850 : 1)  C4b (-18737/24302 : 983771/145812 : 1)
**u= 468/89 ;  1697858*x^2 - 83304*y^2 + 4271812*x*z + 3395716*z^2
; C4a (-38949/56371 : 1312637/338226 : 1)  C4b (-40351/6614 : -1091791/39684 : 1)
**u= 468/113 ;  2871074*x^2 - 105768*y^2 + 6618244*x*z + 5742148*z^2
; C4a (30447/41758 : 2679167/250548 : 1)  C4b (-99887/24034 : -2801239/144204 : 1)
**u= 468/305 ;  22293026*x^2 - 285480*y^2 + 45462148*x*z + 44586052*z^2
; C4a (494149/396001 : -51865109/2376006 : 1)  C4b (1329141/1233482 : -151671763/7400892 : 1)
**u= 468/353 ;  29936354*x^2 - 330408*y^2 + 60748804*x*z + 59872708*z^2
; C4a (-711235/1207442 : -256067/25068 : 1)  C4b (-38803/62885 : 3903799/377310 : 1)
**u= 468/425 ;  43492226*x^2 - 397800*y^2 + 87860548*x*z + 86984452*z^2
; C4a (271173/169454 : -148394359/5083620 : 1)  C4b (-212713/53351 : 53193203/1600530 : 1)
**u= 484/13 ;  -193358*x^2 - 12584*y^2 + 550308*x*z - 386716*z^2
; C4a (59/38 : -27/76 : 1)  C4b (937/349 : -7609/698 : 1)
**u= 484/29 ;  -30734*x^2 - 28072*y^2 + 875556*x*z - 61468*z^2
; C4a (55/2 : -21/4 : 1)  C4b (-421/526 : 6893/1052 : 1)
**u= 484/37 ;  97042*x^2 - 35816*y^2 + 1131108*x*z + 194084*z^2
; C4a (3/11 : 83/22 : 1)  C4b (-897/818 : 10929/1636 : 1)
**u= 484/45 ;  255794*x^2 - 43560*y^2 + 1448612*x*z + 511588*z^2
; C4a (-57/151 : 1/6 : 1)  C4b (-181/11 : -4349/66 : 1)
**u= 484/117 ;  3078482*x^2 - 113256*y^2 + 7093988*x*z + 6156964*z^2
; C4a (29/9 : -1253/54 : 1)  C4b (-141/19 : -4241/114 : 1)
**u= 484/181 ;  7693906*x^2 - 175208*y^2 + 16324836*x*z + 15387812*z^2
; C4a (-38901/51182 : -666361/102364 : 1)  C4b (6247/430 : -91021/860 : 1)
**u= 484/205 ;  9935794*x^2 - 198440*y^2 + 20808612*x*z + 19871588*z^2
; C4a (-10467/6526 : -101735/13052 : 1)  C4b (-4257/1142 : 48993/2284 : 1)
**u= 484/269 ;  17277106*x^2 - 260392*y^2 + 35491236*x*z + 34554212*z^2
; C4a (105439/60286 : -2888817/120572 : 1)  C4b (-1739/5169 : 34351/3446 : 1)
**u= 484/389 ;  36385426*x^2 - 376552*y^2 + 73707876*x*z + 72770852*z^2
; C4a (-7111/6126 : -120193/12252 : 1)  C4b (729/1237 : 45861/2474 : 1)
**u= 484/445 ;  47687794*x^2 - 430760*y^2 + 96312612*x*z + 95375588*z^2
; C4a (-6951/11318 : -253939/22636 : 1)  C4b (-913647/1064957 : -22931649/2129914 : 1)
**u= 488/13 ;  -197246*x^2 - 12688*y^2 + 558084*x*z - 394492*z^2
; C4a (78250/54063 : 7129/108126 : 1)  C4b (98976/44143 : 813171/88286 : 1)
**u= 488/29 ;  -34622*x^2 - 28304*y^2 + 883332*x*z - 69244*z^2
; C4a (8/101 : 27/202 : 1)  C4b (238096/134875 : -2344159/269750 : 1)
**u= 488/37 ;  93154*x^2 - 36112*y^2 + 1138884*x*z + 186308*z^2
; C4a (57680/237141 : -1708909/474282 : 1)  C4b (8178/38755 : -447471/77510 : 1)
**u= 488/45 ;  251906*x^2 - 43920*y^2 + 1456388*x*z + 503812*z^2
; C4a (146/39 : 3439/234 : 1)  C4b (-1245648/2615909 : -88030619/15695454 : 1)
**u= 488/197 ;  9153634*x^2 - 192272*y^2 + 19259844*x*z + 18307268*z^2
; C4a (664280/285479 : -13822251/570958 : 1)  C4b (116736/60925 : -2631747/121850 : 1)
**u= 488/261 ;  16247138*x^2 - 254736*y^2 + 33446852*x*z + 32494276*z^2
; C4a (26667010/5204179 : 1553439739/31225074 : 1)  C4b (30127654/14594789 : -2274040583/87568734 : 1)
**u= 488/325 ;  25323106*x^2 - 317200*y^2 + 51598788*x*z + 50646212*z^2
; C4a (51328/90537 : 3016649/181074 : 1)  C4b (19268758/101291069 : 14180262167/1012910690 : 1)
**u= 488/333 ;  26596994*x^2 - 325008*y^2 + 54146564*x*z + 53193988*z^2
; C4a (-562000/6157687 : 451205993/36946122 : 1)  C4b (1472392/6013353 : -524925427/36080118 : 1)
**u= 488/349 ;  29237698*x^2 - 340624*y^2 + 59427972*x*z + 58475396*z^2
; C4a (-5001976/3155589 : -66429349/6311178 : 1)  C4b (-222367528/118001965 : 2992146347/236003930 : 1)
**u= 488/373 ;  33431074*x^2 - 364048*y^2 + 67814724*x*z + 66862148*z^2
; C4a (-1488626/917637 : 20365927/1835274 : 1)  C4b (-479080698/239066401 : -6629743683/478132802 : 1)
**u= 488/421 ;  42654178*x^2 - 410896*y^2 + 86260932*x*z + 85308356*z^2
; C4a (-1069240/434709 : 15535153/869418 : 1)  C4b (-6826424/4026125 : 101750903/8052250 : 1)
**u= 488/461 ;  51191938*x^2 - 449936*y^2 + 103336452*x*z + 102383876*z^2
; C4a (-7716990/4912403 : -119336171/9824806 : 1)  C4b (-85969926/45882815 : -1318546527/91765630 : 1)
**u= 488/485 ;  56686306*x^2 - 473360*y^2 + 114325188*x*z + 113372612*z^2
; C4a (-878022/2539907 : -66296179/5079814 : 1)  C4b (-329302/279951 : -2102257/186634 : 1)
**u= 488/493 ;  58579714*x^2 - 481168*y^2 + 118112004*x*z + 117159428*z^2
; C4a (1431992/1291333 : 66621189/2582666 : 1)  C4b (7468096/633069 : -59980621/422046 : 1)
**u= 500/81 ;  1337762*x^2 - 81000*y^2 + 3675524*x*z + 2675524*z^2
; C4a (327/907 : 586019/81630 : 1)  C4b (-28033/17367 : -11181287/1563030 : 1)
**u= 500/89 ;  1666882*x^2 - 89000*y^2 + 4333764*x*z + 3333764*z^2
; C4a (-27171/15209 : -97345/30418 : 1)  C4b (44933/10433 : 2683579/104330 : 1)
**u= 500/153 ;  5414978*x^2 - 153000*y^2 + 11829956*x*z + 10829956*z^2
; C4a (-10169/10383 : -1677593/311490 : 1)  C4b (-30689/142823 : -34249463/4284690 : 1)
**u= 500/193 ;  8764258*x^2 - 193000*y^2 + 18528516*x*z + 17528516*z^2
; C4a (-1478323/1558897 : -3204921/502870 : 1)  C4b (-73003/24046 : 3897427/240460 : 1)
**u= 500/369 ;  32700962*x^2 - 369000*y^2 + 66401924*x*z + 65401924*z^2
; C4a (-80347/55298 : -16825541/1658940 : 1)  C4b (14589/93814 : -40754671/2814420 : 1)
**u= 500/401 ;  38663842*x^2 - 401000*y^2 + 78327684*x*z + 77327684*z^2
; C4a (2293017/3049642 : -605502563/30496420 : 1)  C4b (-1999033/788822 : -144133819/7888220 : 1)
**u= 500/593 ;  84849058*x^2 - 593000*y^2 + 170698116*x*z + 169698116*z^2
; C4a (-1185681/882122 : -110797463/8821220 : 1)  C4b (-81218893/152744891 : -20286015059/1527448910 : 1)
**u= 512/37 ;  69154*x^2 - 37888*y^2 + 1186884*x*z + 138308*z^2
; C4a (-422/151497 : 4575557/2423952 : 1)  C4b (-452/1019 : 93359/16304 : 1)
**u= 512/61 ;  638338*x^2 - 62464*y^2 + 2325252*x*z + 1276676*z^2
; C4a (-64978/13607 : -1894389/217712 : 1)  C4b (16604/4159 : -1356391/66544 : 1)
**u= 512/109 ;  2613058*x^2 - 111616*y^2 + 6274692*x*z + 5226116*z^2
; C4a (-363334/249657 : -15259249/3994512 : 1)  C4b (-35028/14815 : 2401527/237040 : 1)
**u= 512/205 ;  9907906*x^2 - 209920*y^2 + 20864388*x*z + 19815812*z^2
; C4a (-19414/80649 : 11040599/1290384 : 1)  C4b (-229938/130699 : 19520403/2091184 : 1)
**u= 512/245 ;  14263906*x^2 - 250880*y^2 + 29576388*x*z + 28527812*z^2
; C4a (14588/667 : 12915057/74704 : 1)  C4b (-3788/1563 : -801201/58352 : 1)
**u= 512/261 ;  16223138*x^2 - 267264*y^2 + 33494852*x*z + 32446276*z^2
; C4a (-69274/45767 : 18481439/2196816 : 1)  C4b (-36612/50833 : -20471531/2439984 : 1)
**u= 512/333 ;  26572994*x^2 - 340992*y^2 + 54194564*x*z + 53145988*z^2
; C4a (-24750/32293 : 13848887/1550064 : 1)  C4b (-3106318/1018133 : 1005267623/48870384 : 1)
**u= 512/389 ;  36357538*x^2 - 398336*y^2 + 73763652*x*z + 72715076*z^2
; C4a (208294/146143 : 58778661/2338288 : 1)  C4b (7442338/8533285 : -2780767223/136532560 : 1)
**u= 512/405 ;  39431906*x^2 - 414720*y^2 + 79912388*x*z + 78863812*z^2
; C4a (-16486/10361 : -16633147/1491984 : 1)  C4b (28948/281 : 41310155/40464 : 1)
**u= 512/445 ;  47659906*x^2 - 455680*y^2 + 96368388*x*z + 95319812*z^2
; C4a (-3704068/12486543 : 2492509543/199784688 : 1)  C4b (-483108/418109 : -70466751/6689744 : 1)
**u= 512/541 ;  70566658*x^2 - 553984*y^2 + 142181892*x*z + 141133316*z^2
; C4a (-5083484/10376841 : 2097493633/166029456 : 1)  C4b (-224234/74255 : 30465727/1188080 : 1)
**u= 512/557 ;  74818114*x^2 - 570368*y^2 + 150684804*x*z + 149636228*z^2
; C4a (-475100/194807 : -62201907/3116912 : 1)  C4b (-936036/1374407 : 266425287/21990512 : 1)
**u= 520/53 ;  409378*x^2 - 55120*y^2 + 1900356*x*z + 818756*z^2
; C4a (-670154/124103 : -1669659/248206 : 1)  C4b (-118114/219643 : -2464463/439286 : 1)
**u= 520/101 ;  2198242*x^2 - 105040*y^2 + 5478084*x*z + 4396484*z^2
; C4a (-1062986/731519 : 4686675/1463038 : 1)  C4b (-164116/28189 : -1483435/56378 : 1)
**u= 520/181 ;  7657762*x^2 - 188240*y^2 + 16397124*x*z + 15315524*z^2
; C4a (-28721518/17019937 : 241212489/34039874 : 1)  C4b (-62179076/38395699 : 640506431/76791398 : 1)
**u= 520/197 ;  9121378*x^2 - 204880*y^2 + 19324356*x*z + 18242756*z^2
; C4a (3974252/984411 : -68073031/1968822 : 1)  C4b (6035932/503801 : 89729999/1007602 : 1)
**u= 520/421 ;  42621922*x^2 - 437840*y^2 + 86325444*x*z + 85243844*z^2
; C4a (-4159398/1684957 : -58484011/3369914 : 1)  C4b (-33151958/20479717 : -485199523/40959434 : 1)
**u= 520/493 ;  58547458*x^2 - 512720*y^2 + 118176516*x*z + 117094916*z^2
; C4a (-62802268/31261901 : 940324203/62523802 : 1)  C4b (2063356/3434683 : 138971411/6869366 : 1)
**u= 544/37 ;  35362*x^2 - 40256*y^2 + 1254468*x*z + 70724*z^2
; C4a (91100/107099 : -2302983/428396 : 1)  C4b (-722582/839053 : 21543883/3356212 : 1)
**u= 544/125 ;  3485314*x^2 - 136000*y^2 + 8154372*x*z + 6970628*z^2
; C4a (-36814/46577 : 4152801/931540 : 1)  C4b (-32956/135991 : 19096591/2719820 : 1)
**u= 544/293 ;  20479522*x^2 - 318784*y^2 + 42142788*x*z + 40959044*z^2
; C4a (-1794412/1071801 : -40040563/4287204 : 1)  C4b (-1396836/895289 : 34467927/3581156 : 1)
**u= 544/365 ;  31944514*x^2 - 397120*y^2 + 65072772*x*z + 63889028*z^2
; C4a (-7838/789 : 253885/3156 : 1)  C4b (-547412/121277 : -16139815/485108 : 1)
**u= 544/373 ;  33373282*x^2 - 405824*y^2 + 67930308*x*z + 66746564*z^2
; C4a (-3717780/4145443 : 148770113/16581772 : 1)  C4b (-100652/455803 : -21195619/1823212 : 1)
**u= 544/421 ;  42596386*x^2 - 458048*y^2 + 86376516*x*z + 85192772*z^2
; C4a (199494/2319287 : 132146227/9277148 : 1)  C4b (-5991036/2130197 : 172802439/8520788 : 1)
**u= 544/461 ;  51134146*x^2 - 501568*y^2 + 103452036*x*z + 102268292*z^2
; C4a (-2178772/1286367 : 62389009/5145468 : 1)  C4b (-3109134/2174089 : -97453467/8696356 : 1)
**u= 548/81 ;  1287458*x^2 - 88776*y^2 + 3776132*x*z + 2574916*z^2
; C4a (-15/4 : -617/72 : 1)  C4b (9647/6452 : 1341607/116136 : 1)
**u= 548/113 ;  2789794*x^2 - 123848*y^2 + 6780804*x*z + 5579588*z^2
; C4a (478032105/415585511 : -9758175533/831171022 : 1)  C4b (-193407/119720 : 1749963/239440 : 1)
**u= 548/169 ;  6611458*x^2 - 185224*y^2 + 14424132*x*z + 13222916*z^2
; C4a (-46433/21552 : 4664581/560352 : 1)  C4b (-206593/194457 : -11427561/1685294 : 1)
**u= 548/313 ;  23408194*x^2 - 343048*y^2 + 48017604*x*z + 46816388*z^2
; C4a (-73223455/3615851 : 1149926883/7231702 : 1)  C4b (-1824652039/1874110900 : -32122204979/3748221800 : 1)
**u= 548/337 ;  27183394*x^2 - 369352*y^2 + 55568004*x*z + 54366788*z^2
; C4a (-106038145/86610456 : -1483229149/173220912 : 1)  C4b (-474833839/478529380 : 8477144183/957058760 : 1)
**u= 548/529 ;  67421218*x^2 - 579784*y^2 + 136043652*x*z + 134842436*z^2
; C4a (-23095/35888 : 18803019/1650848 : 1)  C4b (-744609/600356 : -310811079/27616376 : 1)
**u= 550/541 ;  70526302*x^2 - 595100*y^2 + 142262604*x*z + 141052604*z^2
; C4a (26673320/5553877 : -254592591/3967055 : 1)  C4b (706284/326953 : -5376597/148615 : 1)
**u= 576/29 ;  -128254*x^2 - 33408*y^2 + 1070596*x*z - 256508*z^2
; C4a (413/1394 : -40691/33456 : 1)  C4b (2241/2914 : 417383/69936 : 1)
**u= 576/61 ;  568706*x^2 - 70272*y^2 + 2464516*x*z + 1137412*z^2
; C4a (-655/157 : -12343/3768 : 1)  C4b (61093/117509 : 19584959/2820216 : 1)
**u= 576/85 ;  1416674*x^2 - 97920*y^2 + 4160452*x*z + 2833348*z^2
; C4a (-28187/14001 : -479377/336024 : 1)  C4b (-164137/62487 : 15946279/1499688 : 1)
**u= 576/109 ;  2543426*x^2 - 125568*y^2 + 6413956*x*z + 5086852*z^2
; C4a (-1484609/70139 : 150884537/1683336 : 1)  C4b (-6857/4854 : -779903/116496 : 1)
**u= 576/173 ;  6911042*x^2 - 199296*y^2 + 15149188*x*z + 13822084*z^2
; C4a (18293/653 : 2687761/15672 : 1)  C4b (-21801/49510 : -8637743/1188240 : 1)
**u= 576/229 ;  12358946*x^2 - 263808*y^2 + 26044996*x*z + 24717892*z^2
; C4a (-528403/595038 : 93611939/14280912 : 1)  C4b (-60077/114107 : 21750451/2738568 : 1)
**u= 576/277 ;  18236642*x^2 - 319104*y^2 + 37800388*x*z + 36473284*z^2
; C4a (-104393/3647 : 18265727/87528 : 1)  C4b (-80653/95547 : 18370619/2293128 : 1)
**u= 576/461 ;  51098306*x^2 - 531072*y^2 + 103523716*x*z + 102196612*z^2
; C4a (671549/1332842 : -81114853/4569744 : 1)  C4b (-20469/325895 : -105873907/7821480 : 1)
**u= 576/533 ;  68417762*x^2 - 614016*y^2 + 138162628*x*z + 136835524*z^2
; C4a (212295/227398 : 125647069/5457552 : 1)  C4b (18611481/5576482 : 6308742043/133835568 : 1)
**u= 580/17 ;  -266462*x^2 - 19720*y^2 + 812676*x*z - 532924*z^2
; C4a (1831/1733 : 4149/3466 : 1)  C4b (-16703/5936 : -198799/11872 : 1)
**u= 580/113 ;  2753698*x^2 - 131080*y^2 + 6852996*x*z + 5507396*z^2
; C4a (-4684999/4738788 : -31235059/9477576 : 1)  C4b (-59809/62233 : -747271/124466 : 1)
**u= 580/137 ;  4205698*x^2 - 158920*y^2 + 9756996*x*z + 8411396*z^2
; C4a (-1525270621/594267852 : -9921589307/1188535704 : 1)  C4b (144139/15492 : -585265/10328 : 1)
**u= 580/281 ;  18772162*x^2 - 325960*y^2 + 38889924*x*z + 37544324*z^2
; C4a (-6911/7012 : -102609/14024 : 1)  C4b (-5179657/9747193 : -168767131/19494386 : 1)
**u= 580/361 ;  31201282*x^2 - 418760*y^2 + 63748164*x*z + 62402564*z^2
; C4a (-21791/66952 : 26361825/2544176 : 1)  C4b (-416683/301367 : -109665599/11451946 : 1)
**u= 584/53 ;  338722*x^2 - 61904*y^2 + 2041668*x*z + 677444*z^2
; C4a (-670/109 : -843/218 : 1)  C4b (34763778/16080373 : -371887083/32160746 : 1)
**u= 584/61 ;  559426*x^2 - 71248*y^2 + 2483076*x*z + 1118852*z^2
; C4a (-115258/25643 : 215667/51286 : 1)  C4b (10114598/2934679 : -100975411/5869358 : 1)
**u= 584/229 ;  12349666*x^2 - 267472*y^2 + 26063556*x*z + 24699332*z^2
; C4a (-1663070/885777 : 15047821/1771554 : 1)  C4b (-3518074/6906579 : 36560061/4604386 : 1)
**u= 584/245 ;  14184994*x^2 - 286160*y^2 + 29734212*x*z + 28369988*z^2
; C4a (-1004/1427 : -142071/19978 : 1)  C4b (-205268/369703 : 41689975/5175842 : 1)
**u= 584/373 ;  33328162*x^2 - 435664*y^2 + 68020548*x*z + 66656324*z^2
; C4a (-3111332/801553 : 42401541/1603106 : 1)  C4b (-493962484/370323465 : 2354381929/246882310 : 1)
**u= 584/405 ;  39352994*x^2 - 473040*y^2 + 80070212*x*z + 78705988*z^2
; C4a (-426452/146461 : -51311719/2636298 : 1)  C4b (4916/58999 : 351083/25902 : 1)
**u= 584/445 ;  47580994*x^2 - 519760*y^2 + 96526212*x*z + 95161988*z^2
; C4a (973142/23143 : 19075995/46286 : 1)  C4b (1818572/186133 : -38755867/372266 : 1)
**u= 592/45 ;  139586*x^2 - 53280*y^2 + 1681028*x*z + 279172*z^2
; C4a (-184167/15307 : -405785/183684 : 1)  C4b (-30539/14812 : 1665563/177744 : 1)
**u= 592/101 ;  2118178*x^2 - 119584*y^2 + 5638212*x*z + 4236356*z^2
; C4a (-13181/11688 : -102233/46752 : 1)  C4b (-159451/373248 : -2999101/497664 : 1)
**u= 592/149 ;  5022178*x^2 - 176416*y^2 + 11446212*x*z + 10044356*z^2
; C4a (-3784129/4441336 : -83932011/17765344 : 1)  C4b (-26193/22652 : -590151/90608 : 1)
**u= 592/269 ;  17160898*x^2 - 318496*y^2 + 35723652*x*z + 34321796*z^2
; C4a (-284309/84117 : 6242261/336468 : 1)  C4b (-996629/644381 : 23003267/2577524 : 1)
**u= 592/421 ;  42541858*x^2 - 498464*y^2 + 86485572*x*z + 85083716*z^2
; C4a (-8768547/673868 : 299715269/2695472 : 1)  C4b (-72981743/91555867 : -3523449263/366223468 : 1)
**u= 596/25 ;  -203966*x^2 - 29800*y^2 + 1012932*x*z - 407932*z^2
; C4a (1345/1698 : 50773/16980 : 1)  C4b (-177443/172629 : 935093/115086 : 1)
**u= 596/185 ;  7927234*x^2 - 220520*y^2 + 17275332*x*z + 15854468*z^2
; C4a (3824391/5858107 : -137813447/11716214 : 1)  C4b (-701653/1489823 : 21726259/2979646 : 1)
**u= 596/305 ;  22156834*x^2 - 363560*y^2 + 45734532*x*z + 44313668*z^2
; C4a (281159579/180126263 : 7782866625/360252526 : 1)  C4b (-448557/126146 : -5571435/252292 : 1)
**u= 596/353 ;  29800162*x^2 - 420776*y^2 + 61021188*x*z + 59600324*z^2
; C4a (-11543455/15300389 : -260635851/30600778 : 1)  C4b (-1440907/889290 : 6100429/592860 : 1)
**u= 596/433 ;  45017122*x^2 - 516136*y^2 + 91455108*x*z + 90034244*z^2
; C4a (-9090019/1790142 : -139749469/3580284 : 1)  C4b (-2536293/145027 : -45143379/290054 : 1)
**u= 596/521 ;  65333506*x^2 - 621032*y^2 + 132087876*x*z + 130667012*z^2
; C4a (77526225/16052398 : 1950590509/32104796 : 1)  C4b (-5649283/4182005 : -92582887/8364010 : 1)
**u= 596/577 ;  80213602*x^2 - 687784*y^2 + 161848068*x*z + 160427204*z^2
; C4a (21668831/1603626 : 504132023/3207252 : 1)  C4b (-27314671/26390454 : 192681717/17593636 : 1)
509
>

■これらのuについて、(3),(4a+),(4b+)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, Dを満たすように、A,B,C,Dの符号を変更して、Dの小さい順に並び替えると、以下のようになる。


[参考文献]


Last Update: 2026.05.10
H.Nakao

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