| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(25.783703\) |
\(0.131550\) |
$[1932,87897,65765571,860544]$ |
$[483,6058,-161212,-28641190,6723]$ |
$[324526850403/83,25281736298/249,-4178776252/747]$ |
$y^2 + (x^3 + 1)y = -x^5 + x^3 + x^2 + 3x + 2$ |
| 256.a.512.1 |
256.a |
\( 2^{8} \) |
\( - 2^{9} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/10\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_4$ |
|
✓ |
|
$C_4$ |
$D_4$ |
$6$ |
$2$ |
2.180.3, 3.540.6 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(26.841829\) |
\(0.134209\) |
$[26,-2,40,2]$ |
$[52,118,-36,-3949,512]$ |
$[742586,129623/4,-1521/8]$ |
$y^2 + y = 2x^5 - 3x^4 + x^3 + x^2 - x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(19.798620\) |
\(0.197986\) |
$[16,100,1775,1556]$ |
$[8,-14,-159,-367,389]$ |
$[32768/389,-7168/389,-10176/389]$ |
$y^2 + (x + 1)y = x^5 + 2x^4 + 2x^3 + x^2$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(18.613176\) |
\(0.189930\) |
$[4564,-22439,-35962915,-382592]$ |
$[1141,55180,3641688,277583402,-2989]$ |
$[-39466820645749/61,-1672794336220/61,-96756008472/61]$ |
$y^2 + (x^3 + 1)y = x^5 - x^4 - 5x^3 + 4x^2 + 4x - 4$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(31.171156\) |
\(0.216466\) |
$[828,16635,5308452,56]$ |
$[828,17476,-853888,-253107460,448]$ |
$[6080953884912/7,155007628668/7,-1306723104]$ |
$y^2 + (x^3 + x)y = -2x^4 + 7$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(24.819904\) |
\(0.248199\) |
$[120,-540,-29169,-2092]$ |
$[60,240,2241,19215,-523]$ |
$[-777600000/523,-51840000/523,-8067600/523]$ |
$y^2 + (x + 1)y = x^5 - x^4 - x^3$ |
| 523.a.523.2 |
523.a |
\( 523 \) |
\( -523 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(0.992796\) |
\(0.248199\) |
$[332400,10084860,1107044456391,-2092]$ |
$[166200,1149254190,10581558955401,109467476288772525,-523]$ |
$[-126810465636208320000000000/523,-5276053055713522320000000/523,-292288477352026798440000/523]$ |
$y^2 + xy = x^5 - 31x^4 - 110x^3 + 21x^2 - x$ |
| 574.a.293888.1 |
574.a |
\( 2 \cdot 7 \cdot 41 \) |
\( - 2^{10} \cdot 7 \cdot 41 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$2$ |
2.180.3 |
✓ |
✓ |
$1$ |
\( 2 \cdot 5 \) |
\(1.000000\) |
\(11.546350\) |
\(0.288659\) |
$[68,-55823,-955895,-37617664]$ |
$[17,2338,2304,-1356769,-293888]$ |
$[-1419857/293888,-820471/20992,-2601/1148]$ |
$y^2 + (x^2 + x)y = x^5 - x^4 - 3x^2 + x + 1$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(26.910016\) |
\(0.269100\) |
$[176,148,7375,-2412]$ |
$[88,298,1361,7741,-603]$ |
$[-5277319168/603,-203078656/603,-10539584/603]$ |
$y^2 + (x^2 + 1)y = x^5 - x^3 + x$ |
| 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.a.659456.1 |
644.a |
\( 2^{2} \cdot 7 \cdot 23 \) |
\( 2^{12} \cdot 7 \cdot 23 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.90.3, 3.720.5 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(0.872985\) |
\(0.218246\) |
$[161796,1070662305,46065265919409,84410368]$ |
$[40449,23560804,14638854160,9253881697856,659456]$ |
$[108277681088425330677249/659456,389810454818831018649/164864,9297727292338785/256]$ |
$y^2 + (x^2 + x)y = -3x^6 - 13x^5 + 4x^4 + 51x^3 + 4x^2 - 13x - 3$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(15.435107\) |
\(0.308702\) |
$[1268,-40511,-17688719,-1895936]$ |
$[317,5875,170781,4905488,-14812]$ |
$[-3201078401357/14812,-187148201375/14812,-17161611909/14812]$ |
$y^2 + (x^3 + 1)y = x^5 - x^4 - 4x^3 + 5x^2 - x - 1$ |
| 686.a.686.1 |
686.a |
\( 2 \cdot 7^{3} \) |
\( 2 \cdot 7^{3} \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.90.3, 3.2160.5 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(11.491655\) |
\(0.319213\) |
$[420,4305,640185,87808]$ |
$[105,280,-980,-45325,686]$ |
$[37209375/2,472500,-15750]$ |
$y^2 + (x^2 + x)y = x^5 + x^4 + 2x^3 + x^2 + x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(1.000000\) |
\(25.707298\) |
\(0.321341\) |
$[32,112,-680,-344]$ |
$[32,-32,1344,10496,-2752]$ |
$[-524288/43,16384/43,-21504/43]$ |
$y^2 + y = 2x^5 - 5x^4 + 4x^3 - x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(18.361162\) |
\(0.286893\) |
$[160,-1280,-42089,2836]$ |
$[80,480,1121,-35180,709]$ |
$[3276800000/709,245760000/709,7174400/709]$ |
$y^2 + xy = x^5 - 2x^2 + x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(14.926779\) |
\(0.298536\) |
$[480,-21564,-3373785,-49708]$ |
$[240,5994,167265,1053891,-12427]$ |
$[-796262400000/12427,-82861056000/12427,-9634464000/12427]$ |
$y^2 + (x^3 + x^2)y = x^5 + 2x^4 - x - 3$ |
| 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.409600.1 |
800.a |
\( 2^{5} \cdot 5^{2} \) |
\( - 2^{14} \cdot 5^{2} \) |
$0$ |
$1$ |
$\Z/24\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$2$ |
2.90.3, 3.2160.21 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(1.000000\) |
\(16.770151\) |
\(0.349378\) |
$[120,309,14889,50]$ |
$[480,6304,-151552,-28121344,409600]$ |
$[62208000,1702080,-85248]$ |
$y^2 = x^6 - 2x^2 + 1$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(9.761140\) |
\(0.305036\) |
$[680,640,153059,9684]$ |
$[340,4710,84049,1598140,2421]$ |
$[4543542400000/2421,61707280000/807,9716064400/2421]$ |
$y^2 + (x^3 + x)y = x^5 - 2x^3 - x^2 + 2x - 1$ |
| 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.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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(20.878934\) |
\(0.326233\) |
$[40,-944,-14117,3700]$ |
$[20,174,713,-4004,925]$ |
$[128000/37,55680/37,11408/37]$ |
$y^2 + (x + 1)y = -x^5 + 2x^4 - x^3 - x^2$ |
| 930.a.930.1 |
930.a |
\( 2 \cdot 3 \cdot 5 \cdot 31 \) |
\( 2 \cdot 3 \cdot 5 \cdot 31 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(24.846489\) |
\(0.388226\) |
$[46596,239073,3674852529,119040]$ |
$[11649,5644172,3640360380,2637470125259,930]$ |
$[71502622649365111083/310,1487013548016809538/155,531176338621566]$ |
$y^2 + (x^2 + x)y = -x^5 - 7x^4 + 37x^2 - 45x + 15$ |
| 960.a.245760.1 |
960.a |
\( 2^{6} \cdot 3 \cdot 5 \) |
\( 2^{14} \cdot 3 \cdot 5 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(6.402317\) |
\(0.400145\) |
$[120,213,10095,30]$ |
$[480,7328,-15360,-15268096,245760]$ |
$[103680000,3297600,-14400]$ |
$y^2 = 2x^5 + x^4 + 4x^3 + x^2 + 2x$ |
| 960.a.368640.1 |
960.a |
\( 2^{6} \cdot 3 \cdot 5 \) |
\( 2^{13} \cdot 3^{2} \cdot 5 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(6.402317\) |
\(0.400145\) |
$[8952,6072,17987052,1440]$ |
$[17904,13340192,13237770240,14762078945024,368640]$ |
$[24952719973569408/5,1038436236963696/5,11510985848256]$ |
$y^2 = x^5 + 13x^4 + 44x^3 + 13x^2 + x$ |
| 960.a.983040.1 |
960.a |
\( 2^{6} \cdot 3 \cdot 5 \) |
\( - 2^{16} \cdot 3 \cdot 5 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(6.402317\) |
\(0.400145\) |
$[9,33,666,120]$ |
$[36,-298,-34260,-330541,983040]$ |
$[19683/320,-36207/2560,-46251/1024]$ |
$y^2 = x^5 - 2x^4 - x^3 - 2x^2 + x$ |
| 966.a.834624.1 |
966.a |
\( 2 \cdot 3 \cdot 7 \cdot 23 \) |
\( 2^{6} \cdot 3^{4} \cdot 7 \cdot 23 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/12\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$2$ |
2.180.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \cdot 3 \) |
\(1.000000\) |
\(9.526771\) |
\(0.396949\) |
$[92,24673,-557265,-106831872]$ |
$[23,-1006,14336,-170577,-834624]$ |
$[-279841/36288,266087/18144,-736/81]$ |
$y^2 + (x^2 + x)y = x^5 - x^4 + x^3 + x^2 - x + 1$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(14.356290\) |
\(0.398786\) |
$[148,-48575,-4076175,-8112000]$ |
$[37,2081,35929,-750297,-63375]$ |
$[-69343957/63375,-105408893/63375,-49186801/63375]$ |
$y^2 + (x^3 + 1)y = -x^5 + x^3 + 2x^2 + x - 1$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(6.174937\) |
\(0.385934\) |
$[3268,252577,318023313,1140480]$ |
$[817,17288,-766260,-231227341,8910]$ |
$[364007458703857/8910,4713906106372/4455,-57404054]$ |
$y^2 + (x^2 + x)y = 3x^5 + 4x^4 + 7x^3 + 4x^2 + 3x$ |
| 990.a.240570.1 |
990.a |
\( 2 \cdot 3^{2} \cdot 5 \cdot 11 \) |
\( 2 \cdot 3^{7} \cdot 5 \cdot 11 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(3.087468\) |
\(0.385934\) |
$[153028,6848257,343366646113,30792960]$ |
$[38257,60697908,127876480380,301983618580299,240570]$ |
$[81951056110393451083057/240570,188813894774599018858/13365,7001861848004294/9]$ |
$y^2 + (x^2 + x)y = 3x^5 + 28x^4 + 72x^3 + 28x^2 + 3x$ |
| 997.a.997.2 |
997.a |
\( 997 \) |
\( 997 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(21.589621\) |
\(0.337338\) |
$[64,184,391,3988]$ |
$[32,12,305,2404,997]$ |
$[33554432/997,393216/997,312320/997]$ |
$y^2 + (x + 1)y = x^5 + x^4$ |
| 1008.a.27216.1 |
1008.a |
\( 2^{4} \cdot 3^{2} \cdot 7 \) |
\( 2^{4} \cdot 3^{5} \cdot 7 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/8\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(12.167487\) |
\(0.380234\) |
$[8456,9496,26675348,108864]$ |
$[4228,743250,173847744,45651924783,27216]$ |
$[12063042849801664/243,167186257609000/81,3083035208512/27]$ |
$y^2 + (x^3 + x)y = -4x^4 + 15x^2 - 21$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(17.821680\) |
\(0.356434\) |
$[8,604,1017,-12564]$ |
$[4,-100,-1,-2501,-3141]$ |
$[-1024/3141,6400/3141,16/3141]$ |
$y^2 + (x^3 + x)y = x$ |
