| 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 |
| 587.a.587.1 |
587.a |
\( 587 \) |
\( 587 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.003773\) |
\(29.510964\) |
\(0.111352\) |
$[60,1401,54147,-75136]$ |
$[15,-49,-501,-2479,-587]$ |
$[-759375/587,165375/587,112725/587]$ |
$y^2 + (x^3 + x + 1)y = -x^2 - x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.002250\) |
\(25.168364\) |
\(0.169871\) |
$[8,229,527,-466]$ |
$[8,-150,-128,-5881,-3728]$ |
$[-2048/233,4800/233,512/233]$ |
$y^2 + y = x^6 - 2x^5 + x^4 + x^2 - x$ |
| 1497.b.13473.1 |
1497.b |
\( 3 \cdot 499 \) |
\( 3^{3} \cdot 499 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.002757\) |
\(24.920459\) |
\(0.206128\) |
$[92,36025,3650051,-1724544]$ |
$[23,-1479,-41077,-783053,-13473]$ |
$[-6436343/13473,5998331/4491,21729733/13473]$ |
$y^2 + (x^3 + x + 1)y = -2x^5 + 3x^4 - x^2$ |
| 1503.a.4509.1 |
1503.a |
\( 3^{2} \cdot 167 \) |
\( - 3^{3} \cdot 167 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.002665\) |
\(25.832365\) |
\(0.206516\) |
$[676,11209,2364277,-577152]$ |
$[169,723,261,-119655,-4509]$ |
$[-137858491849/4509,-1163260969/1503,-828269/501]$ |
$y^2 + (x^3 + x + 1)y = x^5 - x^4 - 3x^3 + x$ |
| 1575.a.165375.1 |
1575.a |
\( 3^{2} \cdot 5^{2} \cdot 7 \) |
\( - 3^{3} \cdot 5^{3} \cdot 7^{2} \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$2$ |
2.180.3 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(0.027182\) |
\(17.779771\) |
\(0.241646\) |
$[12,19305,2541195,21168000]$ |
$[3,-804,-34624,-187572,165375]$ |
$[9/6125,-804/6125,-34624/18375]$ |
$y^2 + (x^2 + x + 1)y = -x^5 + 2x^4 + x^2 - 2x$ |
| 1854.a.11124.1 |
1854.a |
\( 2 \cdot 3^{2} \cdot 103 \) |
\( - 2^{2} \cdot 3^{3} \cdot 103 \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
2.10.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(0.016344\) |
\(25.054742\) |
\(0.273003\) |
$[44,19705,981779,1423872]$ |
$[11,-816,-11124,-197055,11124]$ |
$[161051/11124,-90508/927,-121]$ |
$y^2 + (x^3 + x^2 + x)y = -2x^3 - 2x^2 + x + 1$ |
| 2304.a.13824.1 |
2304.a |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{9} \cdot 3^{3} \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$2$ |
2.180.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.049602\) |
\(23.744931\) |
\(0.294447\) |
$[102,234,7128,54]$ |
$[204,1110,4324,-87501,13824]$ |
$[25557426,2726715/4,312409/24]$ |
$y^2 + y = 2x^5 + 3x^4 - x^3 - 2x^2$ |
| 2336.a.37376.1 |
2336.a |
\( 2^{5} \cdot 73 \) |
\( 2^{9} \cdot 73 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(0.002262\) |
\(21.598867\) |
\(0.390768\) |
$[84,825,13389,4672]$ |
$[84,-256,2304,32000,37376]$ |
$[8168202/73,-296352/73,31752/73]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^4 - 3x^3 + x$ |
| 2457.a.154791.1 |
2457.a |
\( 3^{3} \cdot 7 \cdot 13 \) |
\( - 3^{5} \cdot 7^{2} \cdot 13 \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$2$ |
2.180.3 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(0.033247\) |
\(18.983107\) |
\(0.315567\) |
$[780,63657,23411115,19813248]$ |
$[195,-1068,-164320,-8295756,154791]$ |
$[89253125/49,-7520500/147,-53404000/1323]$ |
$y^2 + (x^3 + 1)y = x^5 - 3x^3 - x^2 + 2$ |
| 2556.a.30672.1 |
2556.a |
\( 2^{2} \cdot 3^{2} \cdot 71 \) |
\( - 2^{4} \cdot 3^{3} \cdot 71 \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
2.10.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(0.015776\) |
\(20.515105\) |
\(0.323646\) |
$[8,373,7913,3834]$ |
$[8,-246,-6480,-28089,30672]$ |
$[2048/1917,-2624/639,-960/71]$ |
$y^2 + x^3y = -2x^4 - 2x^3 + x^2 + 2x + 1$ |
| 2588.a.82816.1 |
2588.a |
\( 2^{2} \cdot 647 \) |
\( - 2^{7} \cdot 647 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 11 \) |
\(0.002169\) |
\(17.413917\) |
\(0.415511\) |
$[12,9465,-98157,10600448]$ |
$[3,-394,1692,-37540,82816]$ |
$[243/82816,-5319/41408,3807/20704]$ |
$y^2 + (x^3 + 1)y = x^3 + 2x^2$ |
| 2672.a.342016.1 |
2672.a |
\( 2^{4} \cdot 167 \) |
\( - 2^{11} \cdot 167 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(0.002591\) |
\(18.074641\) |
\(0.421450\) |
$[276,3129,227757,-42752]$ |
$[276,1088,6144,128000,-342016]$ |
$[-1564031349/334,-11169306/167,-228528/167]$ |
$y^2 + y = x^6 - 6x^4 - 7x^3 - x^2 + x$ |
| 2848.a.45568.1 |
2848.a |
\( 2^{5} \cdot 89 \) |
\( 2^{9} \cdot 89 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(0.002857\) |
\(19.026989\) |
\(0.434815\) |
$[20,601,1373,5696]$ |
$[20,-384,1024,-31744,45568]$ |
$[6250/89,-6000/89,800/89]$ |
$y^2 + y = x^6 - 2x^5 - 7x^4 - 5x^3 + x$ |
| 2952.a.283392.1 |
2952.a |
\( 2^{3} \cdot 3^{2} \cdot 41 \) |
\( - 2^{8} \cdot 3^{3} \cdot 41 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(0.009021\) |
\(18.180414\) |
\(0.328006\) |
$[138,2232,142443,1107]$ |
$[276,-2778,-507940,-36977181,283392]$ |
$[231708348/41,-16899963/82,-67175065/492]$ |
$y^2 + x^3y = -2x^4 - x^3 + 3x^2 + 4x + 4$ |
| 2980.a.381440.1 |
2980.a |
\( 2^{2} \cdot 5 \cdot 149 \) |
\( - 2^{9} \cdot 5 \cdot 149 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(0.010301\) |
\(14.543823\) |
\(0.449451\) |
$[364,1081,1867603,48824320]$ |
$[91,300,-23056,-547024,381440]$ |
$[6240321451/381440,11303565/19072,-11932921/23840]$ |
$y^2 + (x^3 + 1)y = 2x^5 + 3x^4 - x^2 - x$ |
| 3092.a.98944.1 |
3092.a |
\( 2^{2} \cdot 773 \) |
\( - 2^{7} \cdot 773 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 11 \) |
\(0.002124\) |
\(19.591064\) |
\(0.457655\) |
$[276,19545,1278813,-12664832]$ |
$[69,-616,-1392,-118876,-98944]$ |
$[-1564031349/98944,25295193/12368,414207/6184]$ |
$y^2 + (x^3 + 1)y = -x^4 + 3x^2 + x$ |
| 3138.a.301248.1 |
3138.a |
\( 2 \cdot 3 \cdot 523 \) |
\( - 2^{6} \cdot 3^{2} \cdot 523 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(0.009642\) |
\(13.716170\) |
\(0.396771\) |
$[296,-1820,-2495,1204992]$ |
$[148,1216,-4689,-543157,301248]$ |
$[1109503312/4707,61594048/4707,-713249/2092]$ |
$y^2 + (x^3 + x)y = -x^4 - 2x^2 - x + 1$ |
| 3462.a.560844.1 |
3462.a |
\( 2 \cdot 3 \cdot 577 \) |
\( - 2^{2} \cdot 3^{5} \cdot 577 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \cdot 5 \) |
\(0.015776\) |
\(11.411347\) |
\(0.450053\) |
$[184,-5456,-146259,2243376]$ |
$[92,1262,-5185,-517416,560844]$ |
$[1647703808/140211,245676064/140211,-10971460/140211]$ |
$y^2 + (x + 1)y = x^5 - 3x^3 + 4x^2 - 3x$ |
| 3528.b.338688.1 |
3528.b |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{8} \cdot 3^{3} \cdot 7^{2} \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
2.40.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(0.002339\) |
\(13.499787\) |
\(0.378882\) |
$[58,280,4018,1323]$ |
$[116,-186,-900,-34749,338688]$ |
$[82044596/1323,-756059/882,-21025/588]$ |
$y^2 + (x^3 + x^2 + x + 1)y = 2x^4 - x^3 - x$ |
| 3564.b.705672.1 |
3564.b |
\( 2^{2} \cdot 3^{4} \cdot 11 \) |
\( - 2^{3} \cdot 3^{6} \cdot 11^{2} \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
2.40.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3^{2} \) |
\(0.017792\) |
\(12.922605\) |
\(0.459848\) |
$[404,6537,761861,371712]$ |
$[303,1374,-14980,-1606704,705672]$ |
$[10510100501/2904,235938929/4356,-38202745/19602]$ |
$y^2 + (x^3 + x + 1)y = 2x^2 + 4x + 2$ |
| 3798.a.729216.1 |
3798.a |
\( 2 \cdot 3^{2} \cdot 211 \) |
\( 2^{7} \cdot 3^{3} \cdot 211 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 3 \cdot 7 \) |
\(0.001682\) |
\(13.562243\) |
\(0.479182\) |
$[64,6052,193561,-2916864]$ |
$[32,-966,-12465,-333009,-729216]$ |
$[-262144/5697,82432/1899,11080/633]$ |
$y^2 + (x + 1)y = x^6 + x^5 + 2x^4 - x^2$ |
| 3812.a.243968.1 |
3812.a |
\( 2^{2} \cdot 953 \) |
\( 2^{8} \cdot 953 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 13 \) |
\(0.002640\) |
\(14.802103\) |
\(0.508099\) |
$[108,12633,795555,-31227904]$ |
$[27,-496,-7056,-109132,-243968]$ |
$[-14348907/243968,610173/15248,321489/15248]$ |
$y^2 + (x^3 + 1)y = 2x^2 - 2x$ |
| 4128.b.594432.1 |
4128.b |
\( 2^{5} \cdot 3 \cdot 43 \) |
\( - 2^{9} \cdot 3^{3} \cdot 43 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \cdot 3 \) |
\(0.001730\) |
\(13.796533\) |
\(0.572872\) |
$[108,1641,49131,74304]$ |
$[108,-608,-7936,-306688,594432]$ |
$[1062882/43,-55404/43,-6696/43]$ |
$y^2 + y = x^6 - x^3 + x^2 + x$ |
| 4388.a.140416.1 |
4388.a |
\( 2^{2} \cdot 1097 \) |
\( 2^{7} \cdot 1097 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 11 \) |
\(0.002816\) |
\(17.459324\) |
\(0.540853\) |
$[212,14185,450581,17973248]$ |
$[53,-474,2788,-19228,140416]$ |
$[418195493/140416,-35283849/70208,1957873/35104]$ |
$y^2 + (x^3 + 1)y = -x^5 + 2x^2 - x$ |
| 4400.b.352000.1 |
4400.b |
\( 2^{4} \cdot 5^{2} \cdot 11 \) |
\( - 2^{8} \cdot 5^{3} \cdot 11 \) |
$1$ |
$2$ |
$\Z/3\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$10$ |
$0$ |
2.90.1, 3.5760.3 |
✓ |
✓ |
$1$ |
\( 3^{3} \) |
\(0.365679\) |
\(17.627207\) |
\(0.537158\) |
$[154,1876,128326,1375]$ |
$[308,-1050,-416900,-32376925,352000]$ |
$[984285148/125,-871563/10,-2247091/20]$ |
$y^2 = x^6 - 2x^4 - 3x^3 + x^2 + 3x + 1$ |
| 4428.a.239112.1 |
4428.a |
\( 2^{2} \cdot 3^{3} \cdot 41 \) |
\( 2^{3} \cdot 3^{6} \cdot 41 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
2.10.1, 3.80.2 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(0.003691\) |
\(11.609152\) |
\(0.514253\) |
$[76,-311,-17605,125952]$ |
$[57,252,5184,57996,239112]$ |
$[2476099/984,48013/246,2888/41]$ |
$y^2 + (x^3 + x + 1)y = -2x^5 - x^4 - x$ |
| 4489.a.4489.1 |
4489.a |
\( 67^{2} \) |
\( 67^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\mathsf{RM}\) |
\(\mathsf{RM}\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
2.12.2, 3.2160.18 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.011439\) |
\(20.465113\) |
\(0.234100\) |
$[284,1369,127187,-574592]$ |
$[71,153,187,-2533,-4489]$ |
$[-1804229351/4489,-54760383/4489,-942667/4489]$ |
$y^2 + (x^3 + x + 1)y = x^5 - x$ |
| 5008.a.641024.1 |
5008.a |
\( 2^{4} \cdot 313 \) |
\( 2^{11} \cdot 313 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 17 \) |
\(0.002839\) |
\(14.512519\) |
\(0.700367\) |
$[12,1005,-33069,80128]$ |
$[12,-664,31632,-15328,641024]$ |
$[243/626,-2241/1252,17793/2504]$ |
$y^2 + (x^3 + x)y = x^5 - x^4 - 2x^3 + x + 1$ |
| 5026.a.35182.1 |
5026.a |
\( 2 \cdot 7 \cdot 359 \) |
\( 2 \cdot 7^{2} \cdot 359 \) |
$2$ |
$3$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.031070\) |
\(18.252991\) |
\(0.283562\) |
$[31220,278329,2852760749,4503296]$ |
$[7805,2526654,1086135208,523326215681,35182]$ |
$[591110204777028125/718,12258530733232875/359,675155221982900/359]$ |
$y^2 + (x^3 + 1)y = 4x^5 + 22x^4 + 46x^3 + 28x^2 + 5x$ |
| 5280.a.633600.1 |
5280.a |
\( 2^{5} \cdot 3 \cdot 5 \cdot 11 \) |
\( - 2^{8} \cdot 3^{2} \cdot 5^{2} \cdot 11 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2^{4} \) |
\(0.008232\) |
\(16.181823\) |
\(0.532826\) |
$[1304,57976,30026254,79200]$ |
$[1304,32200,-7557136,-2722836336,633600]$ |
$[14728142981504/2475,11156004272/99,-50196386596/2475]$ |
$y^2 + (x^2 + 1)y = x^5 + 12x^4 + 5x^3 + 4x^2 + 2x$ |
| 5329.b.5329.1 |
5329.b |
\( 73^{2} \) |
\( 73^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\mathsf{RM}\) |
\(\mathsf{RM}\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
2.12.2, 3.2160.18 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.010713\) |
\(24.093314\) |
\(0.258121\) |
$[188,3721,413963,-682112]$ |
$[47,-63,-3485,-41941,-5329]$ |
$[-229345007/5329,6540849/5329,7698365/5329]$ |
$y^2 + (x^3 + x^2 + 1)y = x^3 - x$ |
| 5360.a.686080.1 |
5360.a |
\( 2^{4} \cdot 5 \cdot 67 \) |
\( - 2^{11} \cdot 5 \cdot 67 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 17 \) |
\(0.002765\) |
\(15.306043\) |
\(0.719345\) |
$[24,2796,33618,85760]$ |
$[24,-1840,-17424,-950944,686080]$ |
$[3888/335,-2484/67,-9801/670]$ |
$y^2 + (x^3 + x)y = x^4 - x^3 - 2x^2 + x + 1$ |
| 5364.a.193104.1 |
5364.a |
\( 2^{2} \cdot 3^{2} \cdot 149 \) |
\( - 2^{4} \cdot 3^{4} \cdot 149 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 3 \cdot 5 \) |
\(0.003006\) |
\(12.930610\) |
\(0.583063\) |
$[248,3232,161348,772416]$ |
$[124,102,5040,153639,193104]$ |
$[1832265664/12069,4051576/4023,538160/1341]$ |
$y^2 + (x^3 + x)y = 2x^3 + 3x^2 + 2x + 1$ |
| 5464.a.349696.1 |
5464.a |
\( 2^{3} \cdot 683 \) |
\( - 2^{9} \cdot 683 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 17 \) |
\(0.002969\) |
\(14.473471\) |
\(0.730561\) |
$[72,4092,31572,1398784]$ |
$[36,-628,3420,-67816,349696]$ |
$[118098/683,-114453/1366,69255/5464]$ |
$y^2 + (x + 1)y = x^6 + 2x^5 + x^4 - x^3$ |
| 5580.a.33480.1 |
5580.a |
\( 2^{2} \cdot 3^{2} \cdot 5 \cdot 31 \) |
\( 2^{3} \cdot 3^{3} \cdot 5 \cdot 31 \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
3.80.1 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(0.027041\) |
\(20.905602\) |
\(0.565312\) |
$[388,10417,421321,4285440]$ |
$[97,-42,7956,192492,33480]$ |
$[8587340257/33480,-6388711/5580,2079389/930]$ |
$y^2 + (x^3 + x + 1)y = x^5 - 2x^4 - 2x^3 + x^2$ |
| 5904.a.70848.1 |
5904.a |
\( 2^{4} \cdot 3^{2} \cdot 41 \) |
\( - 2^{6} \cdot 3^{3} \cdot 41 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \cdot 5 \) |
\(0.016345\) |
\(16.826010\) |
\(0.687546\) |
$[48,0,6840,8856]$ |
$[48,96,-5824,-72192,70848]$ |
$[147456/41,6144/41,-23296/123]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -2x^2 - 2x$ |
| 6210.c.894240.1 |
6210.c |
\( 2 \cdot 3^{3} \cdot 5 \cdot 23 \) |
\( - 2^{5} \cdot 3^{5} \cdot 5 \cdot 23 \) |
$1$ |
$1$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 3 \cdot 5 \) |
\(0.080655\) |
\(15.022669\) |
\(0.726996\) |
$[2604,204561,190462743,114462720]$ |
$[651,9135,-465361,-96599559,894240]$ |
$[481170140857/3680,2074317539/736,-21913384129/99360]$ |
$y^2 + (x^3 + 1)y = x^5 + x^4 + x^3 + 4x^2 - 5x + 1$ |
| 6336.a.152064.1 |
6336.a |
\( 2^{6} \cdot 3^{2} \cdot 11 \) |
\( 2^{9} \cdot 3^{3} \cdot 11 \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
2.10.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(0.027391\) |
\(16.866005\) |
\(0.615972\) |
$[68,1369,33335,-19008]$ |
$[68,-720,-11664,-327888,-152064]$ |
$[-2839714/297,49130/33,7803/22]$ |
$y^2 + (x^3 + x)y = -x^4 - 2x^3 + 2x + 1$ |
| 6437.a.6437.1 |
6437.a |
\( 41 \cdot 157 \) |
\( 41 \cdot 157 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.013054\) |
\(25.574626\) |
\(0.333856\) |
$[120,2772,168912,-25748]$ |
$[60,-312,-10568,-182856,-6437]$ |
$[-777600000/6437,67392000/6437,38044800/6437]$ |
$y^2 + (x^3 + x^2 + x + 1)y = x^3 - 2x$ |
| 6845.a.6845.1 |
6845.a |
\( 5 \cdot 37^{2} \) |
\( 5 \cdot 37^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$10$ |
$0$ |
2.15.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.022546\) |
\(14.663073\) |
\(0.330594\) |
$[24,852,-14064,-27380]$ |
$[12,-136,2040,1496,-6845]$ |
$[-248832/6845,235008/6845,-58752/1369]$ |
$y^2 + x^3y = x^5 - 7x^3 - 16x^2 - 15x - 5$ |
| 7200.d.345600.1 |
7200.d |
\( 2^{5} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{9} \cdot 3^{3} \cdot 5^{2} \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
2.20.3 |
✓ |
✓ |
$1$ |
\( 2^{3} \cdot 3 \) |
\(0.001910\) |
\(17.244566\) |
\(0.790323\) |
$[148,1945,58045,43200]$ |
$[148,-384,9216,304128,345600]$ |
$[138687914/675,-810448/225,43808/75]$ |
$y^2 + y = x^6 - 2x^4 - x^3 + 4x^2 - 2x$ |
| 7440.b.89280.1 |
7440.b |
\( 2^{4} \cdot 3 \cdot 5 \cdot 31 \) |
\( - 2^{6} \cdot 3^{2} \cdot 5 \cdot 31 \) |
$1$ |
$2$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \cdot 5 \) |
\(0.410806\) |
\(18.323085\) |
\(0.752724\) |
$[208,736,40136,-11160]$ |
$[208,1312,13504,271872,-89280]$ |
$[-6083264512/1395,-184477696/1395,-9128704/1395]$ |
$y^2 + y = 2x^5 + x^4 - 2x^3 + x$ |
| 7529.a.7529.1 |
7529.a |
\( 7529 \) |
\( -7529 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.018195\) |
\(19.214379\) |
\(0.349605\) |
$[268,4201,296203,963712]$ |
$[67,12,-160,-2716,7529]$ |
$[1350125107/7529,3609156/7529,-718240/7529]$ |
$y^2 + (x^3 + x^2 + x)y = x^2 + 2x + 1$ |
| 7549.a.7549.1 |
7549.a |
\( 7549 \) |
\( -7549 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.016682\) |
\(19.319746\) |
\(0.322300\) |
$[1476,345,34893,-966272]$ |
$[369,5659,117293,2814209,-7549]$ |
$[-6841192812849/7549,-284327451531/7549,-15970732173/7549]$ |
$y^2 + (x^3 + x + 1)y = -2x^4 + 3x^2 - x - 2$ |
| 7609.a.7609.1 |
7609.a |
\( 7 \cdot 1087 \) |
\( - 7 \cdot 1087 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.017112\) |
\(18.664433\) |
\(0.319377\) |
$[188,2713,74963,973952]$ |
$[47,-21,675,7821,7609]$ |
$[229345007/7609,-311469/1087,1491075/7609]$ |
$y^2 + (x^3 + x + 1)y = x^2 - x$ |
| 7643.a.7643.1 |
7643.a |
\( 7643 \) |
\( -7643 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.015846\) |
\(23.292205\) |
\(0.369100\) |
$[44,6601,93275,978304]$ |
$[11,-270,-452,-19468,7643]$ |
$[161051/7643,-359370/7643,-54692/7643]$ |
$y^2 + (x^3 + 1)y = x^5 + x^4 + 2x^2 + x$ |
| 7697.a.7697.1 |
7697.a |
\( 43 \cdot 179 \) |
\( 43 \cdot 179 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.018544\) |
\(19.064654\) |
\(0.353535\) |
$[12,2553,50451,-985216]$ |
$[3,-106,-612,-3268,-7697]$ |
$[-243/7697,2862/7697,5508/7697]$ |
$y^2 + (x^3 + 1)y = x^3 - x^2$ |
| 7848.a.188352.1 |
7848.a |
\( 2^{3} \cdot 3^{2} \cdot 109 \) |
\( 2^{6} \cdot 3^{3} \cdot 109 \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
2.10.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3^{2} \) |
\(0.022215\) |
\(15.203596\) |
\(0.675481\) |
$[376,304,163540,-753408]$ |
$[188,1422,-144,-512289,-188352]$ |
$[-3669520112/2943,-16404034/327,8836/327]$ |
$y^2 + (x^3 + x)y = x^5 - x^2 - x + 1$ |
| 7927.b.7927.1 |
7927.b |
\( 7927 \) |
\( -7927 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.018265\) |
\(21.118080\) |
\(0.385723\) |
$[648,2388,522000,-31708]$ |
$[324,3976,56552,628568,-7927]$ |
$[-3570467226624/7927,-135232602624/7927,-5936602752/7927]$ |
$y^2 + x^3y = -2x^4 - x^3 + 3x^2 + x - 1$ |
| 8100.a.145800.1 |
8100.a |
\( 2^{2} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{3} \cdot 3^{6} \cdot 5^{2} \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
3.2880.4 |
✓ |
✓ |
$1$ |
\( 3 \cdot 5 \) |
\(0.021279\) |
\(19.908545\) |
\(0.706041\) |
$[84,16425,1153845,-76800]$ |
$[63,-5994,-324324,-14090112,-145800]$ |
$[-1361367/200,1027971/100,441441/50]$ |
$y^2 + (x^3 + x + 1)y = x^4 + x^3 - 4x^2 - 2x + 2$ |
