| 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 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(7.150511\) |
\(0.148969\) |
$[7636,11785,29745701,1053696]$ |
$[1909,151354,15951264,1885732415,8232]$ |
$[25353016669288549/8232,75211396489919/588,49431027484/7]$ |
$y^2 + (x^3 + 1)y = -2x^4 + 4x^2 - 9x - 14$ |
| 353.a.353.1 |
353.a |
\( 353 \) |
\( -353 \) |
$0$ |
$0$ |
$\Z/11\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,11$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(22.495495\) |
\(0.185913\) |
$[188,817,30871,45184]$ |
$[47,58,256,2167,353]$ |
$[229345007/353,6021734/353,565504/353]$ |
$y^2 + (x^3 + x + 1)y = x^2$ |
| 389.a.389.1 |
389.a |
\( 389 \) |
\( 389 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(19.798620\) |
\(0.197986\) |
$[2440,51100,45041351,1556]$ |
$[1220,53500,2084961,-79649395,389]$ |
$[2702708163200000/389,97147868000000/389,3103255952400/389]$ |
$y^2 + (x^3 + x)y = x^5 - 2x^4 - 8x^3 + 16x + 7$ |
| 389.a.389.2 |
389.a |
\( 389 \) |
\( 389 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(19.798620\) |
\(0.197986\) |
$[16,100,1775,1556]$ |
$[8,-14,-159,-367,389]$ |
$[32768/389,-7168/389,-10176/389]$ |
$y^2 + (x + 1)y = x^5 + 2x^4 + 2x^3 + x^2$ |
| 400.a.409600.1 |
400.a |
\( 2^{4} \cdot 5^{2} \) |
\( - 2^{14} \cdot 5^{2} \) |
$0$ |
$1$ |
$\Z/3\Z\oplus\Z/6\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathrm{M}_2(\Q)\) |
|
$E_1$ |
|
|
|
$D_4$ |
$D_4$ |
$4$ |
$0$ |
2.180.4, 3.17280.4 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(7.977095\) |
\(0.221586\) |
$[248,181,14873,50]$ |
$[992,39072,1945600,100853504,409600]$ |
$[58632501248/25,2327987904/25,4674304]$ |
$y^2 = x^6 + 4x^4 + 4x^2 + 1$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(18.613176\) |
\(0.189930\) |
$[4564,-22439,-35962915,-382592]$ |
$[1141,55180,3641688,277583402,-2989]$ |
$[-39466820645749/61,-1672794336220/61,-96756008472/61]$ |
$y^2 + (x^3 + 1)y = x^5 - x^4 - 5x^3 + 4x^2 + 4x - 4$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(31.171156\) |
\(0.216466\) |
$[828,16635,5308452,56]$ |
$[828,17476,-853888,-253107460,448]$ |
$[6080953884912/7,155007628668/7,-1306723104]$ |
$y^2 + (x^3 + x)y = -2x^4 + 7$ |
| 450.a.36450.1 |
450.a |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2 \cdot 3^{6} \cdot 5^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/12\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.180.7, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(18.778996\) |
\(0.195615\) |
$[23444,212089,1627179821,4665600]$ |
$[5861,1422468,457836300,164990835819,36450]$ |
$[6916057684302385301/36450,5303516319500302/675,1294426477922/3]$ |
$y^2 + (x^3 + 1)y = x^5 - 4x^4 - 9x^3 + 28x^2 - 6x - 16$ |
| 476.a.952.1 |
476.a |
\( 2^{2} \cdot 7 \cdot 17 \) |
\( - 2^{3} \cdot 7 \cdot 17 \) |
$0$ |
$1$ |
$\Z/3\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.90.1, 3.5760.3 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(26.722339\) |
\(0.247429\) |
$[7340,1042345,2905273355,121856]$ |
$[1835,96870,-3910340,-4139817700,952]$ |
$[20805604708146875/952,299272981175625/476,-27661753375/2]$ |
$y^2 + (x^3 + 1)y = -5x^4 + 7x^3 + 25x^2 - 75x + 54$ |
| 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 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(15.318968\) |
\(0.204253\) |
$[184,37,721,242]$ |
$[184,1386,15040,211591,1936]$ |
$[13181630464/121,49057344/11,31824640/121]$ |
$y^2 + y = x^6 + 2x^4 + x^2$ |
| 523.a.523.1 |
523.a |
\( 523 \) |
\( -523 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(24.819904\) |
\(0.248199\) |
$[120,-540,-29169,-2092]$ |
$[60,240,2241,19215,-523]$ |
$[-777600000/523,-51840000/523,-8067600/523]$ |
$y^2 + (x + 1)y = x^5 - x^4 - x^3$ |
| 529.a.529.1 |
529.a |
\( 23^{2} \) |
\( 23^{2} \) |
$0$ |
$0$ |
$\Z/11\Z$ |
\(\mathsf{RM}\) |
\(\mathsf{RM}\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.120.2, 3.432.4 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(30.060256\) |
\(0.248432\) |
$[284,2401,246639,-67712]$ |
$[71,110,-624,-14101,-529]$ |
$[-1804229351/529,-39370210/529,3145584/529]$ |
$y^2 + (x^3 + x + 1)y = -x^5$ |
| 576.a.576.1 |
576.a |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{6} \cdot 3^{2} \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_2$ |
|
✓ |
|
$C_4$ |
$D_4$ |
$4$ |
$0$ |
2.180.4, 3.1080.16 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(22.396252\) |
\(0.223963\) |
$[68,124,2616,72]$ |
$[68,110,-36,-3637,576]$ |
$[22717712/9,540430/9,-289]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^3 - x$ |
| 576.b.147456.1 |
576.b |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{14} \cdot 3^{2} \) |
$0$ |
$2$ |
$\Z/4\Z\oplus\Z/4\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathrm{M}_2(\Q)\) |
|
$E_1$ |
|
|
|
$D_4$ |
$D_4$ |
$4$ |
$0$ |
2.180.7, 3.2160.25 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(9.301119\) |
\(0.290660\) |
$[152,109,5469,18]$ |
$[608,14240,405504,10942208,147456]$ |
$[5071050752/9,195344320/9,1016576]$ |
$y^2 = x^6 + 2x^4 + 2x^2 + 1$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(9.467159\) |
\(0.262977\) |
$[92,4981,43947,-12000]$ |
$[92,-2968,47600,-1107456,-96000]$ |
$[-25745372/375,9027914/375,-62951/15]$ |
$y^2 + (x + 1)y = 4x^5 + 5x^4 + 3x^3 + 2x^2$ |
| 600.b.30000.1 |
600.b |
\( 2^{3} \cdot 3 \cdot 5^{2} \) |
\( 2^{4} \cdot 3 \cdot 5^{4} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/8\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(8.316291\) |
\(0.259884\) |
$[600,18744,4690524,120000]$ |
$[300,626,-198336,-14973169,30000]$ |
$[81000000,563400,-595008]$ |
$y^2 + (x^3 + x)y = x^4 + x^2 - 3$ |
| 603.a.603.1 |
603.a |
\( 3^{2} \cdot 67 \) |
\( - 3^{2} \cdot 67 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(26.910016\) |
\(0.269100\) |
$[1672,75628,49887881,2412]$ |
$[836,16516,-1263521,-332270453,603]$ |
$[408348897330176/603,9649919856896/603,-883069772816/603]$ |
$y^2 + (x^2 + 1)y = x^5 + 8x^4 + 4x^3 + 4x^2 + 2x$ |
| 603.a.603.2 |
603.a |
\( 3^{2} \cdot 67 \) |
\( - 3^{2} \cdot 67 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(26.910016\) |
\(0.269100\) |
$[176,148,7375,-2412]$ |
$[88,298,1361,7741,-603]$ |
$[-5277319168/603,-203078656/603,-10539584/603]$ |
$y^2 + (x^2 + 1)y = x^5 - x^3 + x$ |
| 630.a.34020.1 |
630.a |
\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
\( 2^{2} \cdot 3^{5} \cdot 5 \cdot 7 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$4$ |
2.360.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(19.470889\) |
\(0.304233\) |
$[24100,969793,7474503265,4354560]$ |
$[6025,1472118,470090880,166291536519,34020]$ |
$[1587871127345703125/6804,10732293030978125/1134,13543327580000/27]$ |
$y^2 + (x^2 + x)y = 3x^5 + 10x^4 - 23x^2 - 6x + 15$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(7.405674\) |
\(0.308570\) |
$[912,147,44562,10]$ |
$[3648,552928,111431680,25193348864,81920]$ |
$[39432490647552/5,1638374321664/5,18102076416]$ |
$y^2 + x^3y = -3x^4 + 13x^2 - 20$ |
| 644.b.14812.1 |
644.b |
\( 2^{2} \cdot 7 \cdot 23 \) |
\( - 2^{2} \cdot 7 \cdot 23^{2} \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.90.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(15.435107\) |
\(0.308702\) |
$[1268,-40511,-17688719,-1895936]$ |
$[317,5875,170781,4905488,-14812]$ |
$[-3201078401357/14812,-187148201375/14812,-17161611909/14812]$ |
$y^2 + (x^3 + 1)y = x^5 - x^4 - 4x^3 + 5x^2 - x - 1$ |
| 676.a.562432.1 |
676.a |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 13^{3} \) |
$0$ |
$0$ |
$\Z/21\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.60.2, 3.2160.20 |
✓ |
✓ |
$1$ |
\( 3 \cdot 7 \) |
\(1.000000\) |
\(6.723260\) |
\(0.320155\) |
$[1620,52953,29527389,71991296]$ |
$[405,4628,-8112,-6175936,562432]$ |
$[10896201253125/562432,5912281125/10816,-492075/208]$ |
$y^2 + (x^3 + 1)y = 2x^5 + 2x^4 + 4x^3 + 2x^2 + 2x$ |
| 688.a.704512.2 |
688.a |
\( 2^{4} \cdot 43 \) |
\( - 2^{14} \cdot 43 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(1.000000\) |
\(6.426825\) |
\(0.321341\) |
$[464,-248,-39602,-86]$ |
$[1856,146176,15688704,1937702912,-704512]$ |
$[-1344218660864/43,-57041383424/43,-3298550016/43]$ |
$y^2 = 2x^5 - 7x^4 - 8x^3 + 2x^2 + 4x + 1$ |
| 691.a.691.1 |
691.a |
\( 691 \) |
\( -691 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(18.812569\) |
\(0.293946\) |
$[104,-824,-20333,-2764]$ |
$[52,250,601,-7812,-691]$ |
$[-380204032/691,-35152000/691,-1625104/691]$ |
$y^2 + (x + 1)y = x^5 - x^3 - x^2$ |
| 708.a.19116.1 |
708.a |
\( 2^{2} \cdot 3 \cdot 59 \) |
\( - 2^{2} \cdot 3^{4} \cdot 59 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(16.267181\) |
\(0.325344\) |
$[908,-132815,8426215,2446848]$ |
$[227,7681,-438901,-39657072,19116]$ |
$[602738989907/19116,89845294523/19116,-383324231/324]$ |
$y^2 + (x^3 + 1)y = -x^5 + 4x^2 + 4x - 1$ |
| 709.a.709.1 |
709.a |
\( 709 \) |
\( 709 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(18.361162\) |
\(0.286893\) |
$[160,-1280,-42089,2836]$ |
$[80,480,1121,-35180,709]$ |
$[3276800000/709,245760000/709,7174400/709]$ |
$y^2 + xy = x^5 - 2x^2 + x$ |
| 713.b.713.1 |
713.b |
\( 23 \cdot 31 \) |
\( 23 \cdot 31 \) |
$0$ |
$0$ |
$\Z/9\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.20.2, 3.80.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(23.149881\) |
\(0.285801\) |
$[92,73,6379,-91264]$ |
$[23,19,-41,-326,-713]$ |
$[-279841/31,-10051/31,943/31]$ |
$y^2 + (x^3 + x + 1)y = -x^4$ |
| 720.b.116640.1 |
720.b |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{5} \cdot 3^{6} \cdot 5 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/12\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.180.3, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(1.000000\) |
\(14.457058\) |
\(0.301189\) |
$[35416,45688,537039964,466560]$ |
$[17708,13057938,12831384960,14177105014959,116640]$ |
$[54412363190235229024/3645,251762275020280012/405,310461362928064/9]$ |
$y^2 + (x^3 + x)y = -6x^4 + 39x^2 - 90$ |
| 731.a.12427.1 |
731.a |
\( 17 \cdot 43 \) |
\( - 17^{2} \cdot 43 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(14.926779\) |
\(0.298536\) |
$[480,-21564,-3373785,-49708]$ |
$[240,5994,167265,1053891,-12427]$ |
$[-796262400000/12427,-82861056000/12427,-9634464000/12427]$ |
$y^2 + (x^3 + x^2)y = x^5 + 2x^4 - x - 3$ |
| 745.a.745.1 |
745.a |
\( 5 \cdot 149 \) |
\( - 5 \cdot 149 \) |
$0$ |
$0$ |
$\Z/9\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.10.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(24.572840\) |
\(0.303368\) |
$[124,1417,38763,95360]$ |
$[31,-19,39,212,745]$ |
$[28629151/745,-566029/745,37479/745]$ |
$y^2 + (x^3 + x + 1)y = -x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(16.733449\) |
\(0.348614\) |
$[428,3169,355487,390144]$ |
$[107,345,1823,19009,3048]$ |
$[14025517307/3048,140879945/1016,20871527/3048]$ |
$y^2 + (x^3 + x^2 + x)y = x^2 + x + 1$ |
| 763.a.763.1 |
763.a |
\( 7 \cdot 109 \) |
\( - 7 \cdot 109 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(30.485750\) |
\(0.304858\) |
$[216,1116,75735,-3052]$ |
$[108,300,81,-20313,-763]$ |
$[-14693280768/763,-377913600/763,-944784/763]$ |
$y^2 + (x^3 + x)y = -2x^4 + 2x^2 - x$ |
| 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.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 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(16.770151\) |
\(0.349378\) |
$[0,84,936,200]$ |
$[0,-56,832,-784,-1600]$ |
$[0,-134456/625,728/25]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^4 - x^2$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(9.761140\) |
\(0.305036\) |
$[680,640,153059,9684]$ |
$[340,4710,84049,1598140,2421]$ |
$[4543542400000/2421,61707280000/807,9716064400/2421]$ |
$y^2 + (x^3 + x)y = x^5 - 2x^3 - x^2 + 2x - 1$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(22.166697\) |
\(0.307871\) |
$[688,9592,2944404,55488]$ |
$[344,3332,-80164,-9669660,13872]$ |
$[301073291264/867,498667904/51,-592892944/867]$ |
$y^2 + (x^3 + x^2)y = -2x^4 + 6x^2 - 8x + 3$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(9.071483\) |
\(0.377978\) |
$[552,45,7083,54]$ |
$[2208,202656,24809472,3427464960,442368]$ |
$[118634674176,4931431104,273421056]$ |
$y^2 = x^6 - 4x^4 + 6x^2 - 3$ |
| 882.a.63504.1 |
882.a |
\( 2 \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 7^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/8\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.360.1, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(12.542623\) |
\(0.391957\) |
$[548,6049,662961,8128512]$ |
$[137,530,6336,146783,63504]$ |
$[48261724457/63504,681408545/31752,825836/441]$ |
$y^2 + (x^2 + x)y = x^5 + x^4 + x^3 + 3x^2 + 3x + 1$ |
| 909.a.909.1 |
909.a |
\( 3^{2} \cdot 101 \) |
\( 3^{2} \cdot 101 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(21.805548\) |
\(0.340712\) |
$[40,-200,-5469,3636]$ |
$[20,50,441,1580,909]$ |
$[3200000/909,400000/909,19600/101]$ |
$y^2 + (x^3 + x)y = -x^4 + x^2 - x$ |
| 925.a.925.1 |
925.a |
\( 5^{2} \cdot 37 \) |
\( 5^{2} \cdot 37 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(20.878934\) |
\(0.326233\) |
$[40,-944,-14117,3700]$ |
$[20,174,713,-4004,925]$ |
$[128000/37,55680/37,11408/37]$ |
$y^2 + (x + 1)y = -x^5 + 2x^4 - x^3 - x^2$ |
| 968.a.234256.1 |
968.a |
\( 2^{3} \cdot 11^{2} \) |
\( - 2^{4} \cdot 11^{4} \) |
$1$ |
$1$ |
$\Z/5\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.60.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 5 \) |
\(0.080529\) |
\(5.397350\) |
\(0.173857\) |
$[23544,6117,47655081,29282]$ |
$[23544,23092586,30194746560,44409396210311,234256]$ |
$[452148675314325387264/14641,1712381980706754624/1331,785948064456960/11]$ |
$y^2 + x^3y = 6x^4 + 47x^2 + 121$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(17.375772\) |
\(0.347515\) |
$[24,684,4887,7760]$ |
$[12,-108,-159,-3393,1940]$ |
$[62208/485,-46656/485,-5724/485]$ |
$y^2 + (x + 1)y = x^5 + x^4 + x^3 + x^2$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(14.356290\) |
\(0.398786\) |
$[148,-48575,-4076175,-8112000]$ |
$[37,2081,35929,-750297,-63375]$ |
$[-69343957/63375,-105408893/63375,-49186801/63375]$ |
$y^2 + (x^3 + 1)y = -x^5 + x^3 + 2x^2 + x - 1$ |
