| Label |
Class |
Conductor |
Discriminant |
Rank* |
2-Selmer rank |
Torsion |
$\textrm{End}^0(J_{\overline\Q})$ |
$\textrm{End}^0(J)$ |
$\GL_2\textsf{-type}$ |
Sato-Tate |
Nonmaximal primes |
$\Q$-simple |
\(\overline{\Q}\)-simple |
\(\Aut(X)\) |
\(\Aut(X_{\overline{\Q}})\) |
$\Q$-points |
$\Q$-Weierstrass points |
mod-$\ell$ images |
Locally solvable |
Square Ш* |
Analytic Ш* |
Tamagawa |
Regulator |
Real period |
Leading coefficient |
Igusa-Clebsch invariants |
Igusa invariants |
G2-invariants |
Equation |
| 249.a.6723.1 |
249.a |
\( 3 \cdot 83 \) |
\( - 3^{4} \cdot 83 \) |
$0$ |
$1$ |
$\Z/28\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(25.783703\) |
\(0.131550\) |
$[1932,87897,65765571,860544]$ |
$[483,6058,-161212,-28641190,6723]$ |
$[324526850403/83,25281736298/249,-4178776252/747]$ |
$y^2 + (x^3 + 1)y = -x^5 + x^3 + x^2 + 3x + 2$ |
| 294.a.8232.1 |
294.a |
\( 2 \cdot 3 \cdot 7^{2} \) |
\( 2^{3} \cdot 3 \cdot 7^{3} \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.45.1, 3.2160.20 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(7.150511\) |
\(0.148969\) |
$[7636,11785,29745701,1053696]$ |
$[1909,151354,15951264,1885732415,8232]$ |
$[25353016669288549/8232,75211396489919/588,49431027484/7]$ |
$y^2 + (x^3 + 1)y = -2x^4 + 4x^2 - 9x - 14$ |
| 360.a.6480.1 |
360.a |
\( 2^{3} \cdot 3^{2} \cdot 5 \) |
\( 2^{4} \cdot 3^{4} \cdot 5 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/8\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$4$ |
2.360.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(24.163379\) |
\(0.188776\) |
$[2360,11992,9047820,25920]$ |
$[1180,56018,3453120,234166319,6480]$ |
$[28596971960000/81,1150492082200/81,6677950400/9]$ |
$y^2 + (x^3 + x)y = -3x^4 + 7x^2 - 5$ |
| 394.a.3152.1 |
394.a |
\( 2 \cdot 197 \) |
\( 2^{4} \cdot 197 \) |
$0$ |
$1$ |
$\Z/20\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(20.078274\) |
\(0.200783\) |
$[80,-20,649,-12608]$ |
$[40,70,39,-835,-3152]$ |
$[-6400000/197,-280000/197,-3900/197]$ |
$y^2 + (x + 1)y = -x^5$ |
| 427.a.2989.1 |
427.a |
\( 7 \cdot 61 \) |
\( - 7^{2} \cdot 61 \) |
$0$ |
$1$ |
$\Z/14\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(18.613176\) |
\(0.189930\) |
$[4564,-22439,-35962915,-382592]$ |
$[1141,55180,3641688,277583402,-2989]$ |
$[-39466820645749/61,-1672794336220/61,-96756008472/61]$ |
$y^2 + (x^3 + 1)y = x^5 - x^4 - 5x^3 + 4x^2 + 4x - 4$ |
| 450.a.2700.1 |
450.a |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{2} \cdot 3^{3} \cdot 5^{2} \) |
$0$ |
$1$ |
$\Z/24\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$0$ |
2.180.4, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(18.778996\) |
\(0.195615\) |
$[364,3529,393211,345600]$ |
$[91,198,0,-9801,2700]$ |
$[6240321451/2700,8289281/150,0]$ |
$y^2 + (x^3 + 1)y = x^5 + 3x^4 + 3x^3 + 3x^2 + x$ |
| 484.a.1936.1 |
484.a |
\( 2^{2} \cdot 11^{2} \) |
\( - 2^{4} \cdot 11^{2} \) |
$0$ |
$0$ |
$\Z/15\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.60.2, 3.720.4 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(15.318968\) |
\(0.204253\) |
$[184,37,721,242]$ |
$[184,1386,15040,211591,1936]$ |
$[13181630464/121,49057344/11,31824640/121]$ |
$y^2 + y = x^6 + 2x^4 + x^2$ |
| 555.a.8325.1 |
555.a |
\( 3 \cdot 5 \cdot 37 \) |
\( 3^{2} \cdot 5^{2} \cdot 37 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(25.692472\) |
\(0.256925\) |
$[1264,18124,6869487,33300]$ |
$[632,13622,351361,9125317,8325]$ |
$[100828984082432/8325,3438682756096/8325,140342016064/8325]$ |
$y^2 + (x + 1)y = 3x^5 - 2x^4 - 4x^3 + x^2 + x$ |
| 578.a.2312.1 |
578.a |
\( 2 \cdot 17^{2} \) |
\( 2^{3} \cdot 17^{2} \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.90.3, 3.2160.21 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(13.910299\) |
\(0.289798\) |
$[228,705,135777,295936]$ |
$[57,106,-992,-16945,2312]$ |
$[601692057/2312,9815229/1156,-402876/289]$ |
$y^2 + (x^2 + x)y = x^5 - 2x^4 + 2x^3 - 2x^2 + x$ |
| 604.a.9664.1 |
604.a |
\( 2^{2} \cdot 151 \) |
\( 2^{6} \cdot 151 \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1, 3.720.5 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(0.291788\) |
\(0.291788\) |
$[49556,-797087975,-23996873337603,1236992]$ |
$[12389,39607304,223396249616,299729401586052,9664]$ |
$[291864493641401980949/9664,9414430497536890397/1208,2143030742187944921/604]$ |
$y^2 + (x^2 + x + 1)y = 4x^5 + 9x^4 + 48x^3 - 4x^2 - 53x - 21$ |
| 604.a.9664.2 |
604.a |
\( 2^{2} \cdot 151 \) |
\( 2^{6} \cdot 151 \) |
$0$ |
$0$ |
$\Z/27\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(23.634831\) |
\(0.291788\) |
$[116,6265,95277,1236992]$ |
$[29,-226,836,-6708,9664]$ |
$[20511149/9664,-2755957/4832,175769/2416]$ |
$y^2 + (x^3 + 1)y = -x^4 + x^3 + x^2 - x$ |
| 644.a.2576.1 |
644.a |
\( 2^{2} \cdot 7 \cdot 23 \) |
\( - 2^{4} \cdot 7 \cdot 23 \) |
$0$ |
$2$ |
$\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.720.4 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(3.928431\) |
\(0.218246\) |
$[39036,4124865,50880984159,329728]$ |
$[9759,3796384,1910683600,1058457444236,2576]$ |
$[88516980336138032799/2576,220529201888022246/161,70640465629725]$ |
$y^2 + (x^2 + x)y = -5x^6 + 11x^5 - 20x^4 + 20x^3 - 20x^2 + 11x - 5$ |
| 676.a.5408.1 |
676.a |
\( 2^{2} \cdot 13^{2} \) |
\( - 2^{5} \cdot 13^{2} \) |
$0$ |
$0$ |
$\Z/21\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$0$ |
2.60.2, 3.2160.21 |
✓ |
✓ |
$1$ |
\( 7 \) |
\(1.000000\) |
\(20.169780\) |
\(0.320155\) |
$[204,3273,161211,692224]$ |
$[51,-28,0,-196,5408]$ |
$[345025251/5408,-928557/1352,0]$ |
$y^2 + (x^3 + x^2 + x)y = x^3 + 3x^2 + 3x + 1$ |
| 688.a.2752.1 |
688.a |
\( 2^{4} \cdot 43 \) |
\( - 2^{6} \cdot 43 \) |
$0$ |
$1$ |
$\Z/20\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(1.000000\) |
\(25.707298\) |
\(0.321341\) |
$[32,112,-680,-344]$ |
$[32,-32,1344,10496,-2752]$ |
$[-524288/43,16384/43,-21504/43]$ |
$y^2 + y = 2x^5 - 5x^4 + 4x^3 - x$ |
| 708.a.2832.1 |
708.a |
\( 2^{2} \cdot 3 \cdot 59 \) |
\( 2^{4} \cdot 3 \cdot 59 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(16.267181\) |
\(0.325344\) |
$[148,2065,76361,362496]$ |
$[37,-29,-59,-756,2832]$ |
$[69343957/2832,-1468937/2832,-1369/48]$ |
$y^2 + (x^2 + x + 1)y = x^5$ |
| 720.a.6480.1 |
720.a |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( - 2^{4} \cdot 3^{4} \cdot 5 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.180.7, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(9.444268\) |
\(0.295133\) |
$[2360,11992,9047820,25920]$ |
$[1180,56018,3453120,234166319,6480]$ |
$[28596971960000/81,1150492082200/81,6677950400/9]$ |
$y^2 + (x^3 + x)y = 2x^4 + 7x^2 + 5$ |
| 726.a.1452.1 |
726.a |
\( 2 \cdot 3 \cdot 11^{2} \) |
\( - 2^{2} \cdot 3 \cdot 11^{2} \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(15.124086\) |
\(0.302482\) |
$[760,-69236,-16142609,-5808]$ |
$[380,17556,702601,-10306189,-1452]$ |
$[-1980879200000/363,-7297976000/11,-25363896100/363]$ |
$y^2 + (x^2 + 1)y = 2x^5 + 2x^4 + 6x^3 - 2x^2 - x$ |
| 762.a.3048.1 |
762.a |
\( 2 \cdot 3 \cdot 127 \) |
\( - 2^{3} \cdot 3 \cdot 127 \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.15.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(16.733449\) |
\(0.348614\) |
$[428,3169,355487,390144]$ |
$[107,345,1823,19009,3048]$ |
$[14025517307/3048,140879945/1016,20871527/3048]$ |
$y^2 + (x^3 + x^2 + x)y = x^2 + x + 1$ |
| 768.a.1536.1 |
768.a |
\( 2^{8} \cdot 3 \) |
\( 2^{9} \cdot 3 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(25.146749\) |
\(0.349260\) |
$[134,82,3600,6]$ |
$[268,2774,35236,437043,1536]$ |
$[2700250214/3,417158281/12,39543601/24]$ |
$y^2 + y = 2x^5 - x^4 - 3x^3 + x$ |
| 768.a.4608.1 |
768.a |
\( 2^{8} \cdot 3 \) |
\( 2^{9} \cdot 3^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(12.573375\) |
\(0.349260\) |
$[38,22,384,18]$ |
$[76,182,-476,-17325,4608]$ |
$[4952198/9,624169/36,-42959/72]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^3 - x^2 - x - 1$ |
| 784.a.1568.1 |
784.a |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{5} \cdot 7^{2} \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.90.3, 3.2160.21 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(20.793351\) |
\(0.288797\) |
$[792,120,15228,6272]$ |
$[396,6514,144256,3673295,1568]$ |
$[304316815968/49,12641055372/49,14427072]$ |
$y^2 + (x^3 + x)y = -2x^4 + 3x^2 - 2$ |
| 800.a.1600.1 |
800.a |
\( 2^{5} \cdot 5^{2} \) |
\( 2^{6} \cdot 5^{2} \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.90.2, 3.2160.21 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(16.770151\) |
\(0.349378\) |
$[0,84,936,200]$ |
$[0,-56,832,-784,-1600]$ |
$[0,-134456/625,728/25]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^4 - x^2$ |
| 800.a.8000.1 |
800.a |
\( 2^{5} \cdot 5^{2} \) |
\( 2^{6} \cdot 5^{3} \) |
$0$ |
$1$ |
$\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.4, 3.720.5 |
|
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(5.590050\) |
\(0.349378\) |
$[192,11604,322392,-1000]$ |
$[192,-6200,142400,-2774800,-8000]$ |
$[-4076863488/125,27426816/5,-3280896/5]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^6 + 2x^4 + 4x^3 + 2x^2 - 1$ |
| 807.a.2421.1 |
807.a |
\( 3 \cdot 269 \) |
\( 3^{2} \cdot 269 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(9.761140\) |
\(0.305036\) |
$[680,640,153059,9684]$ |
$[340,4710,84049,1598140,2421]$ |
$[4543542400000/2421,61707280000/807,9716064400/2421]$ |
$y^2 + (x^3 + x)y = x^5 - 2x^3 - x^2 + 2x - 1$ |
| 830.a.6640.1 |
830.a |
\( 2 \cdot 5 \cdot 83 \) |
\( - 2^{4} \cdot 5 \cdot 83 \) |
$0$ |
$1$ |
$\Z/16\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(23.474917\) |
\(0.366796\) |
$[652,4273,1339719,849920]$ |
$[163,929,-521,-236991,6640]$ |
$[115063617043/6640,4023263963/6640,-13842449/6640]$ |
$y^2 + (x^3 + 1)y = -x^5 + x^4 - 2x^2 + x + 1$ |
| 834.a.1668.1 |
834.a |
\( 2 \cdot 3 \cdot 139 \) |
\( 2^{2} \cdot 3 \cdot 139 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(11.763516\) |
\(0.367610\) |
$[372,3345,401289,213504]$ |
$[93,221,-111,-14791,1668]$ |
$[2318961231/556,59254299/556,-320013/556]$ |
$y^2 + (x^3 + 1)y = -x^2 + x - 1$ |
| 847.b.9317.1 |
847.b |
\( 7 \cdot 11^{2} \) |
\( 7 \cdot 11^{3} \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1, 3.80.4 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(16.827271\) |
\(0.336545\) |
$[304,5932,452465,-37268]$ |
$[152,-26,-401,-15407,-9317]$ |
$[-81136812032/9317,91307008/9317,9264704/9317]$ |
$y^2 + (x^2 + 1)y = x^5 + 2x^4 - 3x^3 + 2x^2 - x$ |
| 847.c.9317.1 |
847.c |
\( 7 \cdot 11^{2} \) |
\( 7 \cdot 11^{3} \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(9.983400\) |
\(0.311981\) |
$[424,3520,581427,37268]$ |
$[212,1286,-7999,-837396,9317]$ |
$[428232184832/9317,12253172608/9317,-359507056/9317]$ |
$y^2 + (x^3 + x^2)y = x^4 + x^3 - x - 2$ |
| 856.a.1712.1 |
856.a |
\( 2^{3} \cdot 107 \) |
\( - 2^{4} \cdot 107 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(22.653846\) |
\(0.314637\) |
$[32,-368,-11044,-6848]$ |
$[16,72,964,2560,-1712]$ |
$[-65536/107,-18432/107,-15424/107]$ |
$y^2 + (x^3 + x)y = -x^4 - x^3 + x$ |
| 862.a.6896.1 |
862.a |
\( 2 \cdot 431 \) |
\( - 2^{4} \cdot 431 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(23.926605\) |
\(0.373853\) |
$[932,12385,3688145,-882688]$ |
$[233,1746,11456,-94817,-6896]$ |
$[-686719856393/6896,-11042871201/3448,-38870924/431]$ |
$y^2 + (x^2 + x)y = 4x^5 + 6x^4 - 3x^2 - x$ |
| 864.a.1728.1 |
864.a |
\( 2^{5} \cdot 3^{3} \) |
\( - 2^{6} \cdot 3^{3} \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.90.4, 3.720.4 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(18.142966\) |
\(0.377978\) |
$[96,180,5256,216]$ |
$[96,264,576,-3600,1728]$ |
$[4718592,135168,3072]$ |
$y^2 + (x^3 + x^2 + x + 1)y = x^4 + x^2$ |
| 886.a.3544.1 |
886.a |
\( 2 \cdot 443 \) |
\( 2^{3} \cdot 443 \) |
$0$ |
$0$ |
$\Z/15\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(24.085472\) |
\(0.321140\) |
$[232,1180,93881,-14176]$ |
$[116,364,-481,-47073,-3544]$ |
$[-2625427072/443,-71020768/443,809042/443]$ |
$y^2 + (x^3 + x)y = -x^4 - x + 1$ |
| 909.a.8181.1 |
909.a |
\( 3^{2} \cdot 101 \) |
\( 3^{4} \cdot 101 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(21.805548\) |
\(0.340712\) |
$[1384,44560,19431635,32724]$ |
$[692,12526,35569,-33071732,8181]$ |
$[158683025503232/8181,4150789321088/8181,17032713616/8181]$ |
$y^2 + xy = 3x^5 - 7x^4 + x^3 + 6x^2 - 3x$ |
| 932.a.3728.1 |
932.a |
\( 2^{2} \cdot 233 \) |
\( - 2^{4} \cdot 233 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.002250\) |
\(25.168364\) |
\(0.169871\) |
$[8,229,527,-466]$ |
$[8,-150,-128,-5881,-3728]$ |
$[-2048/233,4800/233,512/233]$ |
$y^2 + y = x^6 - 2x^5 + x^4 + x^2 - x$ |
| 936.a.1872.1 |
936.a |
\( 2^{3} \cdot 3^{2} \cdot 13 \) |
\( - 2^{4} \cdot 3^{2} \cdot 13 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.90.1 |
|
|
$2$ |
\( 2 \) |
\(1.000000\) |
\(7.131061\) |
\(0.445691\) |
$[45352,11224,169415364,7488]$ |
$[22676,21423170,26983749312,38232821637503,1872]$ |
$[374724646811252438336/117,15612163699641478120/117,7411896491650496]$ |
$y^2 + (x^3 + x)y = -x^6 - 9x^4 - 32x^2 - 39$ |
| 968.a.1936.1 |
968.a |
\( 2^{3} \cdot 11^{2} \) |
\( - 2^{4} \cdot 11^{2} \) |
$1$ |
$1$ |
$\Z/5\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$8$ |
$0$ |
2.60.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.080529\) |
\(26.986750\) |
\(0.173857\) |
$[120,357,14937,242]$ |
$[120,362,-1344,-73081,1936]$ |
$[1555200000/121,39096000/121,-1209600/121]$ |
$y^2 + y = x^6 - x^4$ |
| 970.a.1940.1 |
970.a |
\( 2 \cdot 5 \cdot 97 \) |
\( 2^{2} \cdot 5 \cdot 97 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(17.375772\) |
\(0.347515\) |
$[24,684,4887,7760]$ |
$[12,-108,-159,-3393,1940]$ |
$[62208/485,-46656/485,-5724/485]$ |
$y^2 + (x + 1)y = x^5 + x^4 + x^3 + x^2$ |
| 980.a.7840.1 |
980.a |
\( 2^{2} \cdot 5 \cdot 7^{2} \) |
\( 2^{5} \cdot 5 \cdot 7^{2} \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.45.1, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(14.031519\) |
\(0.389764\) |
$[276,3945,280149,1003520]$ |
$[69,34,20,56,7840]$ |
$[1564031349/7840,5584653/3920,4761/392]$ |
$y^2 + (x^2 + x + 1)y = -x^6 + 3x^5 - 3x^4 - x$ |
| 990.a.8910.1 |
990.a |
\( 2 \cdot 3^{2} \cdot 5 \cdot 11 \) |
\( 2 \cdot 3^{4} \cdot 5 \cdot 11 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(6.174937\) |
\(0.385934\) |
$[3268,252577,318023313,1140480]$ |
$[817,17288,-766260,-231227341,8910]$ |
$[364007458703857/8910,4713906106372/4455,-57404054]$ |
$y^2 + (x^2 + x)y = 3x^5 + 4x^4 + 7x^3 + 4x^2 + 3x$ |
| 1012.a.4048.1 |
1012.a |
\( 2^{2} \cdot 11 \cdot 23 \) |
\( 2^{4} \cdot 11 \cdot 23 \) |
$0$ |
$0$ |
$\Z/15\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(1.000000\) |
\(18.518969\) |
\(0.411533\) |
$[140,2425,78163,-518144]$ |
$[35,-50,-4,-660,-4048]$ |
$[-52521875/4048,1071875/2024,1225/1012]$ |
$y^2 + (x^3 + 1)y = x^4 + x^3 + x^2 + x$ |
| 1038.a.1038.2 |
1038.a |
\( 2 \cdot 3 \cdot 173 \) |
\( - 2 \cdot 3 \cdot 173 \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.15.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(15.397347\) |
\(0.427704\) |
$[844,4129,1133983,132864]$ |
$[211,1683,16079,140045,1038]$ |
$[418227202051/1038,5269995291/346,715853159/1038]$ |
$y^2 + (x^3 + 1)y = x^4 + 2x^2 + x + 1$ |
| 1038.a.1038.1 |
1038.a |
\( 2 \cdot 3 \cdot 173 \) |
\( 2 \cdot 3 \cdot 173 \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.60.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(15.397347\) |
\(0.427704\) |
$[109988,334849,12332566337,132864]$ |
$[27497,31489590,48060441688,82480921681709,1038]$ |
$[15719059879327073637257/1038,109111794064913809345/173,18168889743107727596/519]$ |
$y^2 + (x^2 + x)y = x^5 - 12x^4 + 26x^3 + 46x^2 + 21x + 3$ |
| 1042.a.1042.1 |
1042.a |
\( 2 \cdot 521 \) |
\( 2 \cdot 521 \) |
$0$ |
$0$ |
$\Z/9\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(30.423017\) |
\(0.375593\) |
$[480,3912,728889,-4168]$ |
$[240,1748,-5521,-1095136,-1042]$ |
$[-398131200000/521,-12082176000/521,159004800/521]$ |
$y^2 + (x^3 + x)y = -x^4 - x^3 - x^2 + 2x + 2$ |
| 1047.a.3141.1 |
1047.a |
\( 3 \cdot 349 \) |
\( 3^{2} \cdot 349 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(17.821680\) |
\(0.356434\) |
$[8,604,1017,-12564]$ |
$[4,-100,-1,-2501,-3141]$ |
$[-1024/3141,6400/3141,16/3141]$ |
$y^2 + (x^3 + x)y = x$ |
| 1051.a.1051.1 |
1051.a |
\( 1051 \) |
\( -1051 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.007925\) |
\(23.437821\) |
\(0.185743\) |
$[96,-144,144,4204]$ |
$[48,120,-80,-4560,1051]$ |
$[254803968/1051,13271040/1051,-184320/1051]$ |
$y^2 + y = x^5 - x^4 + x^2 - x$ |
| 1051.b.1051.1 |
1051.b |
\( 1051 \) |
\( -1051 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(23.331720\) |
\(0.364558\) |
$[64,-200,185,4204]$ |
$[32,76,-241,-3372,1051]$ |
$[33554432/1051,2490368/1051,-246784/1051]$ |
$y^2 + (x + 1)y = -x^5 - x^4$ |
| 1051.b.1051.2 |
1051.b |
\( 1051 \) |
\( -1051 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(5.832930\) |
\(0.364558\) |
$[6176,-50240,-103225225,-4204]$ |
$[3088,405696,72449921,14784027908,-1051]$ |
$[-280793117300359168/1051,-11946277554880512/1051,-690863899476224/1051]$ |
$y^2 + xy = x^5 + 8x^4 + 16x^3 + x$ |
| 1055.a.1055.1 |
1055.a |
\( 5 \cdot 211 \) |
\( - 5 \cdot 211 \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(15.577626\) |
\(0.432712\) |
$[500,-3023,-525127,-135040]$ |
$[125,777,7441,81599,-1055]$ |
$[-6103515625/211,-303515625/211,-23253125/211]$ |
$y^2 + (x^3 + 1)y = -x^4 + x^2 - x - 1$ |
| 1062.a.6372.1 |
1062.a |
\( 2 \cdot 3^{2} \cdot 59 \) |
\( 2^{2} \cdot 3^{3} \cdot 59 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$11$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.008698\) |
\(21.575863\) |
\(0.187677\) |
$[300,2601,306603,-815616]$ |
$[75,126,-1024,-23169,-6372]$ |
$[-87890625/236,-984375/118,160000/177]$ |
$y^2 + (x^3 + 1)y = x^5 - x^4 + x^2 - x$ |
| 1069.a.1069.1 |
1069.a |
\( 1069 \) |
\( 1069 \) |
$0$ |
$0$ |
$\Z/7\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(14.937046\) |
\(0.304838\) |
$[244,3193,263789,136832]$ |
$[61,22,-884,-13602,1069]$ |
$[844596301/1069,4993582/1069,-3289364/1069]$ |
$y^2 + (x^2 + x + 1)y = x^5 + x^3$ |
