| 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 |
| 294.a.294.1 |
294.a |
\( 2 \cdot 3 \cdot 7^{2} \) |
\( - 2 \cdot 3 \cdot 7^{2} \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.45.1, 3.720.4 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(21.451533\) |
\(0.148969\) |
$[236,505,18451,37632]$ |
$[59,124,564,4475,294]$ |
$[714924299/294,12733498/147,327214/49]$ |
$y^2 + (x^3 + 1)y = x^4 + x^2$ |
| 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 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(7.150511\) |
\(0.148969\) |
$[7636,11785,29745701,1053696]$ |
$[1909,151354,15951264,1885732415,8232]$ |
$[25353016669288549/8232,75211396489919/588,49431027484/7]$ |
$y^2 + (x^3 + 1)y = -2x^4 + 4x^2 - 9x - 14$ |
| 448.a.448.2 |
448.a |
\( 2^{6} \cdot 7 \) |
\( - 2^{6} \cdot 7 \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.90.3, 3.2160.5 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(31.171156\) |
\(0.216466\) |
$[828,16635,5308452,56]$ |
$[828,17476,-853888,-253107460,448]$ |
$[6080953884912/7,155007628668/7,-1306723104]$ |
$y^2 + (x^3 + x)y = -2x^4 + 7$ |
| 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 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(13.910299\) |
\(0.289798\) |
$[228,705,135777,295936]$ |
$[57,106,-992,-16945,2312]$ |
$[601692057/2312,9815229/1156,-402876/289]$ |
$y^2 + (x^2 + x)y = x^5 - 2x^4 + 2x^3 - 2x^2 + x$ |
| 600.a.96000.1 |
600.a |
\( 2^{3} \cdot 3 \cdot 5^{2} \) |
\( 2^{8} \cdot 3 \cdot 5^{3} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.3, 3.640.2 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(9.467159\) |
\(0.262977\) |
$[92,4981,43947,-12000]$ |
$[92,-2968,47600,-1107456,-96000]$ |
$[-25745372/375,9027914/375,-62951/15]$ |
$y^2 + (x + 1)y = 4x^5 + 5x^4 + 3x^3 + 2x^2$ |
| 640.a.81920.1 |
640.a |
\( 2^{7} \cdot 5 \) |
\( - 2^{14} \cdot 5 \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.90.1, 3.2160.5 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(7.405674\) |
\(0.308570\) |
$[912,147,44562,10]$ |
$[3648,552928,111431680,25193348864,81920]$ |
$[39432490647552/5,1638374321664/5,18102076416]$ |
$y^2 + x^3y = 3x^4 + 13x^2 + 20$ |
| 640.a.81920.2 |
640.a |
\( 2^{7} \cdot 5 \) |
\( 2^{14} \cdot 5 \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.90.3, 3.2160.5 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(7.405674\) |
\(0.308570\) |
$[912,147,44562,10]$ |
$[3648,552928,111431680,25193348864,81920]$ |
$[39432490647552/5,1638374321664/5,18102076416]$ |
$y^2 + x^3y = -3x^4 + 13x^2 - 20$ |
| 704.a.45056.1 |
704.a |
\( 2^{6} \cdot 11 \) |
\( - 2^{12} \cdot 11 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(11.976027\) |
\(0.332667\) |
$[134,-464,-15328,-176]$ |
$[268,4230,61444,-356477,-45056]$ |
$[-1350125107/44,-636113745/352,-68955529/704]$ |
$y^2 + y = 4x^5 + 4x^4 - x^3 - 2x^2$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(20.793351\) |
\(0.288797\) |
$[792,120,15228,6272]$ |
$[396,6514,144256,3673295,1568]$ |
$[304316815968/49,12641055372/49,14427072]$ |
$y^2 + (x^3 + x)y = -2x^4 + 3x^2 - 2$ |
| 784.a.43904.1 |
784.a |
\( 2^{4} \cdot 7^{2} \) |
\( - 2^{7} \cdot 7^{3} \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.90.1, 3.2160.20 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(6.931117\) |
\(0.288797\) |
$[21288,3000,20891172,175616]$ |
$[10644,4720114,2790613504,1855953490895,43904]$ |
$[1067368445729034408/343,6352710665144931/49,50408453477952/7]$ |
$y^2 + (x^3 + x)y = 4x^4 + 27x^2 + 56$ |
| 784.b.12544.1 |
784.b |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.360.1, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(11.270100\) |
\(0.313058\) |
$[116,445,16259,1568]$ |
$[116,264,-1280,-54544,12544]$ |
$[82044596/49,1609674/49,-67280/49]$ |
$y^2 + (x^3 + x)y = -1$ |
| 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 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(16.770151\) |
\(0.349378\) |
$[0,84,936,200]$ |
$[0,-56,832,-784,-1600]$ |
$[0,-134456/625,728/25]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^4 - x^2$ |
| 816.a.13872.1 |
816.a |
\( 2^{4} \cdot 3 \cdot 17 \) |
\( - 2^{4} \cdot 3 \cdot 17^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(22.166697\) |
\(0.307871\) |
$[688,9592,2944404,55488]$ |
$[344,3332,-80164,-9669660,13872]$ |
$[301073291264/867,498667904/51,-592892944/867]$ |
$y^2 + (x^3 + x^2)y = -2x^4 + 6x^2 - 8x + 3$ |
| 826.a.11564.1 |
826.a |
\( 2 \cdot 7 \cdot 59 \) |
\( - 2^{2} \cdot 7^{2} \cdot 59 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(13.174483\) |
\(0.365958\) |
$[92,-554591,-3126961,1480192]$ |
$[23,23130,-104176,-134348237,11564]$ |
$[6436343/11564,140711355/5782,-13777276/2891]$ |
$y^2 + (x^2 + x)y = x^5 + x^4 + 3x^3 - 4x^2 - 4x + 3$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(22.653846\) |
\(0.314637\) |
$[32,-368,-11044,-6848]$ |
$[16,72,964,2560,-1712]$ |
$[-65536/107,-18432/107,-15424/107]$ |
$y^2 + (x^3 + x)y = -x^4 - x^3 + x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(18.142966\) |
\(0.377978\) |
$[96,180,5256,216]$ |
$[96,264,576,-3600,1728]$ |
$[4718592,135168,3072]$ |
$y^2 + (x^3 + x^2 + x + 1)y = x^4 + x^2$ |
| 864.a.221184.1 |
864.a |
\( 2^{5} \cdot 3^{3} \) |
\( - 2^{13} \cdot 3^{3} \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.45.1, 3.720.4 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(18.142966\) |
\(0.377978\) |
$[168,34560,-211428,-864]$ |
$[336,-87456,10192896,-1055934720,-221184]$ |
$[-19361664,14998704,-5202624]$ |
$y^2 + x^3y = x^5 - 4x^4 - 6x^3 + 33x^2 - 36x + 12$ |
| 864.a.442368.1 |
864.a |
\( 2^{5} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{3} \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.90.3, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(9.071483\) |
\(0.377978\) |
$[552,45,7083,54]$ |
$[2208,202656,24809472,3427464960,442368]$ |
$[118634674176,4931431104,273421056]$ |
$y^2 = x^6 - 4x^4 + 6x^2 - 3$ |
| 975.a.63375.1 |
975.a |
\( 3 \cdot 5^{2} \cdot 13 \) |
\( - 3 \cdot 5^{3} \cdot 13^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(14.356290\) |
\(0.398786\) |
$[148,-48575,-4076175,-8112000]$ |
$[37,2081,35929,-750297,-63375]$ |
$[-69343957/63375,-105408893/63375,-49186801/63375]$ |
$y^2 + (x^3 + 1)y = -x^5 + x^3 + 2x^2 + x - 1$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(14.031519\) |
\(0.389764\) |
$[276,3945,280149,1003520]$ |
$[69,34,20,56,7840]$ |
$[1564031349/7840,5584653/3920,4761/392]$ |
$y^2 + (x^2 + x + 1)y = -x^6 + 3x^5 - 3x^4 - x$ |
| 980.a.878080.1 |
980.a |
\( 2^{2} \cdot 5 \cdot 7^{2} \) |
\( - 2^{9} \cdot 5 \cdot 7^{3} \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.2160.20 |
|
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(1.000000\) |
\(4.677173\) |
\(0.389764\) |
$[2508,50745,41700723,112394240]$ |
$[627,14266,359660,5497016,878080]$ |
$[96903107471907/878080,251175228777/62720,144278343/896]$ |
$y^2 + (x^3 + 1)y = -x^6 + x^5 - 4x^4 + 2x^3 - 4x^2 + x - 1$ |
| 1088.b.2176.2 |
1088.b |
\( 2^{6} \cdot 17 \) |
\( 2^{7} \cdot 17 \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.90.1, 3.2160.5 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(23.575776\) |
\(0.491162\) |
$[7572,68115,166006308,272]$ |
$[7572,2343556,952909568,430794130940,2176]$ |
$[194465720403941544/17,7948719687495546/17,25108109106912]$ |
$y^2 + (x^3 + x)y = -5x^4 + 24x^2 - 34$ |
| 1122.b.2244.1 |
1122.b |
\( 2 \cdot 3 \cdot 11 \cdot 17 \) |
\( 2^{2} \cdot 3 \cdot 11 \cdot 17 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(30.724131\) |
\(0.426724\) |
$[1828,153793,73850145,287232]$ |
$[457,2294,8704,-321177,2244]$ |
$[19933382494057/2244,109474259971/1122,26732672/33]$ |
$y^2 + (x^2 + x)y = x^5 + 7x^4 + 5x^3 - x^2 - x$ |
| 1142.b.9136.1 |
1142.b |
\( 2 \cdot 571 \) |
\( - 2^{4} \cdot 571 \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(17.757282\) |
\(0.493258\) |
$[864,-4488,-1442025,-36544]$ |
$[432,8524,257089,9600968,-9136]$ |
$[-940369969152/571,-42951140352/571,-2998686096/571]$ |
$y^2 + (x + 1)y = -x^5 + 3x^4 - 6x^2 + x + 3$ |
| 1170.a.10530.1 |
1170.a |
\( 2 \cdot 3^{2} \cdot 5 \cdot 13 \) |
\( - 2 \cdot 3^{4} \cdot 5 \cdot 13 \) |
$0$ |
$4$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.720.4 |
✓ |
✓ |
$4$ |
\( 3 \) |
\(1.000000\) |
\(5.542030\) |
\(0.461836\) |
$[507196,192673,32552199279,1347840]$ |
$[126799,669908072,4718980180980,37396285759331459,10530]$ |
$[32777750301275239538233999/10530,682861614668954802420364/5265,7205289570406928666]$ |
$y^2 + (x^2 + x)y = 15x^6 + 28x^5 + 62x^4 + 59x^3 + 62x^2 + 28x + 15$ |
| 1176.b.16464.1 |
1176.b |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( 2^{4} \cdot 3 \cdot 7^{3} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.3, 3.640.2 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(13.019302\) |
\(0.361647\) |
$[160,4720,130020,-65856]$ |
$[80,-520,4220,16800,-16464]$ |
$[-204800000/1029,16640000/1029,-1688000/1029]$ |
$y^2 + (x + 1)y = -2x^5 + x^2$ |
| 1272.a.122112.1 |
1272.a |
\( 2^{3} \cdot 3 \cdot 53 \) |
\( - 2^{8} \cdot 3^{2} \cdot 53 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(14.397916\) |
\(0.399942\) |
$[124,-5027,-35457,15264]$ |
$[124,3992,-79504,-6448640,122112]$ |
$[114516604/477,29731418/477,-4775209/477]$ |
$y^2 + (x^2 + 1)y = 3x^5 + 4x^4 + 2x^3 - x^2 - x$ |
| 1280.a.12800.1 |
1280.a |
\( 2^{8} \cdot 5 \) |
\( - 2^{9} \cdot 5^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(17.070788\) |
\(0.474189\) |
$[22,-170,-1832,-50]$ |
$[44,534,7684,13235,-12800]$ |
$[-322102/25,-355377/100,-232441/200]$ |
$y^2 + y = 2x^5 + x^4 - x^3 - x^2$ |
| 1296.a.20736.1 |
1296.a |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{4} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_3$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.1920.3 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(23.235042\) |
\(0.484063\) |
$[78,216,4806,81]$ |
$[156,438,-428,-64653,20736]$ |
$[4455516,160381/2,-18083/36]$ |
$y^2 = x^5 - x^4 - 3x^3 + 4x^2 - x$ |
| 1312.b.10496.1 |
1312.b |
\( 2^{5} \cdot 41 \) |
\( - 2^{8} \cdot 41 \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.90.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(14.584701\) |
\(0.405131\) |
$[148,373,15335,1312]$ |
$[148,664,4096,41328,10496]$ |
$[277375828/41,8408398/41,350464/41]$ |
$y^2 + (x + 1)y = x^6 + x^4 + x^3 + x^2$ |
| 1312.b.83968.1 |
1312.b |
\( 2^{5} \cdot 41 \) |
\( 2^{11} \cdot 41 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(14.584701\) |
\(0.405131\) |
$[1556,36553,20209667,10496]$ |
$[1556,76512,1289104,-962060080,83968]$ |
$[8907339520949/82,140743510779/41,12191781649/328]$ |
$y^2 + xy = 8x^5 - 21x^4 + 15x^3 - x^2 - x$ |
| 1338.b.72252.1 |
1338.b |
\( 2 \cdot 3 \cdot 223 \) |
\( 2^{2} \cdot 3^{4} \cdot 223 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(17.653207\) |
\(0.490367\) |
$[9956,4983313,12890442777,9248256]$ |
$[2489,50492,218356,-501488495,72252]$ |
$[95526635745351449/72252,194642319821287/18063,338185460269/18063]$ |
$y^2 + (x^2 + x)y = x^5 + 7x^4 + 4x^3 - 12x^2 - 6x + 5$ |
| 1350.a.5400.1 |
1350.a |
\( 2 \cdot 3^{3} \cdot 5^{2} \) |
\( 2^{3} \cdot 3^{3} \cdot 5^{2} \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.90.3, 3.720.4 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(22.247707\) |
\(0.463494\) |
$[1380,3969,1536129,691200]$ |
$[345,4794,89568,1979631,5400]$ |
$[7240885875/8,145821495/4,1974228]$ |
$y^2 + (x^2 + x)y = x^5 + 4x^4 + 4x^3 - x^2 + 3$ |
| 1350.b.6750.1 |
1350.b |
\( 2 \cdot 3^{3} \cdot 5^{2} \) |
\( 2 \cdot 3^{3} \cdot 5^{3} \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.45.1, 3.720.4 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(13.781572\) |
\(0.287116\) |
$[1236,3321,1171629,864000]$ |
$[309,3840,63900,1249875,6750]$ |
$[104334666687/250,419607168/25,4519434/5]$ |
$y^2 + (x^3 + x^2 + x)y = -2x^3 - 2x^2 + 3x - 1$ |
| 1350.c.656100.1 |
1350.c |
\( 2 \cdot 3^{3} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{8} \cdot 5^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.360.1, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(1.000000\) |
\(6.178250\) |
\(0.514854\) |
$[364,3529,393211,345600]$ |
$[273,1782,0,-793881,656100]$ |
$[6240321451/2700,8289281/150,0]$ |
$y^2 + (x^2 + x)y = x^5 + x^4 + 4x^3 + x^2 + x$ |
| 1377.a.37179.1 |
1377.a |
\( 3^{4} \cdot 17 \) |
\( - 3^{7} \cdot 17 \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3, 3.640.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(18.604798\) |
\(0.516800\) |
$[2484,1110609,457848297,-4758912]$ |
$[621,-30207,2177857,109996587,-37179]$ |
$[-42228846423/17,3307757121/17,-1152086353/51]$ |
$y^2 + (x^2 + x + 1)y = -x^5 + 5x^4 + x^3 - 5x^2 + x + 2$ |
| 1416.a.8496.1 |
1416.a |
\( 2^{3} \cdot 3 \cdot 59 \) |
\( - 2^{4} \cdot 3^{2} \cdot 59 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(14.958620\) |
\(0.415517\) |
$[256,-2144,-178692,-33984]$ |
$[128,1040,12004,113728,-8496]$ |
$[-2147483648/531,-136314880/531,-12292096/531]$ |
$y^2 + (x^3 + x)y = x^5 - x^3 - 1$ |
| 1440.a.116640.1 |
1440.a |
\( 2^{5} \cdot 3^{2} \cdot 5 \) |
\( - 2^{5} \cdot 3^{6} \cdot 5 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.90.6, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(1.000000\) |
\(5.650548\) |
\(0.470879\) |
$[35416,45688,537039964,466560]$ |
$[17708,13057938,12831384960,14177105014959,116640]$ |
$[54412363190235229024/3645,251762275020280012/405,310461362928064/9]$ |
$y^2 + (x^3 + x)y = 5x^4 + 39x^2 + 90$ |
| 1488.a.71424.1 |
1488.a |
\( 2^{4} \cdot 3 \cdot 31 \) |
\( - 2^{8} \cdot 3^{2} \cdot 31 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(11.909626\) |
\(0.496234\) |
$[34,-104,-438,279]$ |
$[68,470,-1396,-78957,71424]$ |
$[5679428/279,1154555/558,-100861/1116]$ |
$y^2 = x^5 - x^3 - x^2 - x$ |
| 1536.a.12288.1 |
1536.a |
\( 2^{9} \cdot 3 \) |
\( 2^{12} \cdot 3 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(12.002671\) |
\(0.500111\) |
$[38,112,1704,48]$ |
$[76,-58,-4796,-91965,12288]$ |
$[2476099/12,-198911/96,-432839/192]$ |
$y^2 = x^5 - 3x^4 + 5x^3 - 4x^2 + 2x$ |
| 1600.b.409600.1 |
1600.b |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{14} \cdot 5^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_4$ |
$4$ |
$2$ |
2.360.1, 3.8640.8 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(12.846191\) |
\(0.535258\) |
$[248,181,14873,50]$ |
$[992,39072,1945600,100853504,409600]$ |
$[58632501248/25,2327987904/25,4674304]$ |
$y^2 = x^6 - 4x^4 + 4x^2 - 1$ |
| 1632.a.52224.1 |
1632.a |
\( 2^{5} \cdot 3 \cdot 17 \) |
\( 2^{10} \cdot 3 \cdot 17 \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.45.1, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(15.157132\) |
\(0.631547\) |
$[15964,2380825,11444690699,6528]$ |
$[15964,9031504,6282991104,4683401370560,52224]$ |
$[1012531723491160951/51,35882713644370099/51,30660536527816]$ |
$y^2 + (x^3 + x)y = -x^6 + 11x^4 - 27x^2 + 17$ |
| 1650.a.371250.1 |
1650.a |
\( 2 \cdot 3 \cdot 5^{2} \cdot 11 \) |
\( 2 \cdot 3^{3} \cdot 5^{4} \cdot 11 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(13.792193\) |
\(0.574675\) |
$[30180,172689,1721884569,47520000]$ |
$[7545,2364764,985411548,460705338491,371250]$ |
$[1448946796623435/22,150474103581314/55,3777545308302/25]$ |
$y^2 + (x^2 + x)y = x^5 - 11x^4 + 30x^3 - 11x^2 + x$ |
| 1680.c.241920.1 |
1680.c |
\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
\( 2^{8} \cdot 3^{3} \cdot 5 \cdot 7 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(11.725763\) |
\(0.488573\) |
$[182340,50613,3073006935,30240]$ |
$[182340,1385294408,14032351630080,159904599848179184,241920]$ |
$[5832248478791381977500/7,243004434356588125950/7,1928513067842084400]$ |
$y^2 + (x^2 + 1)y = 135x^6 - 96x^4 + 22x^2 - 2$ |
| 1740.a.104400.1 |
1740.a |
\( 2^{2} \cdot 3 \cdot 5 \cdot 29 \) |
\( - 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{4} \) |
\(1.000000\) |
\(5.116047\) |
\(0.568450\) |
$[28100,7231657,99549877317,-13363200]$ |
$[7025,1754957,7872289,-756142810406,-104400]$ |
$[-684371056797265625/4176,-24336911168273125/4176,-15540095293225/4176]$ |
$y^2 + (x^2 + x)y = 2x^5 - 14x^3 - 5x^2 + 30x$ |
| 1746.a.10476.1 |
1746.a |
\( 2 \cdot 3^{2} \cdot 97 \) |
\( - 2^{2} \cdot 3^{3} \cdot 97 \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.90.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(13.248981\) |
\(0.552041\) |
$[844,21553,4894663,1340928]$ |
$[211,957,6399,108585,10476]$ |
$[418227202051/10476,2996663989/3492,10551477/388]$ |
$y^2 + (x^2 + x + 1)y = x^6 + x^5 + 2x^4 - x$ |
| 1770.a.26550.1 |
1770.a |
\( 2 \cdot 3 \cdot 5 \cdot 59 \) |
\( - 2 \cdot 3^{2} \cdot 5^{2} \cdot 59 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(18.809597\) |
\(0.522489\) |
$[8740,87985,236184393,-3398400]$ |
$[2185,195260,23092156,3082473315,-26550]$ |
$[-1992127808244625/1062,-40737803081950/531,-2204942969582/531]$ |
$y^2 + (x^2 + x)y = 3x^5 - 7x^3 + 7x + 3$ |
