| 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 |
| 169.a.169.1 |
169.a |
\( 13^{2} \) |
\( - 13^{2} \) |
$0$ |
$0$ |
$\Z/19\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$6$ |
$0$ |
2.40.3, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(32.667031\) |
\(0.090490\) |
$[4,793,3757,-21632]$ |
$[1,-33,-43,-283,-169]$ |
$[-1/169,33/169,43/169]$ |
$y^2 + (x^3 + x + 1)y = x^5 + x^4$ |
| 324.a.648.1 |
324.a |
\( 2^{2} \cdot 3^{4} \) |
\( - 2^{3} \cdot 3^{4} \) |
$0$ |
$0$ |
$\Z/21\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_3$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$6$ |
$0$ |
2.40.3, 3.1920.3 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(25.521769\) |
\(0.173617\) |
$[60,945,2295,82944]$ |
$[15,-30,140,300,648]$ |
$[9375/8,-625/4,875/18]$ |
$y^2 + (x^3 + x + 1)y = x^5 + 2x^4 + 2x^3 + x^2$ |
| 784.c.614656.1 |
784.c |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{4} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_3$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.5760.7 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(5.731485\) |
\(0.358218\) |
$[398,9016,912086,2401]$ |
$[796,2358,-2348,-1857293,614656]$ |
$[1248318403996/2401,9291226221/4802,-23245787/9604]$ |
$y^2 = x^5 - 4x^4 - 13x^3 - 9x^2 - x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(23.235042\) |
\(0.484063\) |
$[78,216,4806,81]$ |
$[156,438,-428,-64653,20736]$ |
$[4455516,160381/2,-18083/36]$ |
$y^2 = x^5 - x^4 - 3x^3 + 4x^2 - x$ |
| 2704.a.43264.1 |
2704.a |
\( 2^{4} \cdot 13^{2} \) |
\( 2^{8} \cdot 13^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.1440.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(11.781851\) |
\(0.736366\) |
$[110,520,15470,169]$ |
$[220,630,-620,-133325,43264]$ |
$[2013137500/169,52408125/338,-468875/676]$ |
$y^2 = x^5 - 5x^3 - 5x^2 - x$ |
| 3721.a.3721.1 |
3721.a |
\( 61^{2} \) |
\( - 61^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$12$ |
$0$ |
2.40.3, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.007315\) |
\(28.081352\) |
\(0.205420\) |
$[196,6649,304573,-476288]$ |
$[49,-177,-187,-10123,-3721]$ |
$[-282475249/3721,20823873/3721,448987/3721]$ |
$y^2 + (x^3 + x + 1)y = -x^4 + x^3 + 3x^2 + x$ |
| 3969.b.35721.1 |
3969.b |
\( 3^{4} \cdot 7^{2} \) |
\( 3^{6} \cdot 7^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$18$ |
$0$ |
2.80.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.003155\) |
\(23.234167\) |
\(0.219945\) |
$[268,2961,216951,18816]$ |
$[201,573,-563,-110373,35721]$ |
$[1350125107/147,57445733/441,-2527307/3969]$ |
$y^2 + (x^3 + x + 1)y = -2x^5 + 3x^4 - 3x^2$ |
| 3969.c.35721.1 |
3969.c |
\( 3^{4} \cdot 7^{2} \) |
\( 3^{6} \cdot 7^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(12.485061\) |
\(0.780316\) |
$[268,2961,216951,18816]$ |
$[201,573,-563,-110373,35721]$ |
$[1350125107/147,57445733/441,-2527307/3969]$ |
$y^2 + (x^2 + x)y = x^5 - 5x^4 + 4x^3 - x$ |
| 8281.b.405769.1 |
8281.b |
\( 7^{2} \cdot 13^{2} \) |
\( 7^{4} \cdot 13^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$12$ |
$0$ |
2.80.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.005669\) |
\(19.785401\) |
\(0.336475\) |
$[2596,375193,248614093,51938432]$ |
$[649,1917,-1907,-1228133,405769]$ |
$[115139273278249/405769,524030063733/405769,-803230307/405769]$ |
$y^2 + (x^3 + x + 1)y = -3x^5 + 9x^4 - 7x^3 - 2x^2 + x$ |
| 8281.c.405769.1 |
8281.c |
\( 7^{2} \cdot 13^{2} \) |
\( 7^{4} \cdot 13^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(19.785401\) |
\(1.236588\) |
$[2596,375193,248614093,51938432]$ |
$[649,1917,-1907,-1228133,405769]$ |
$[115139273278249/405769,524030063733/405769,-803230307/405769]$ |
$y^2 + (x^2 + x)y = x^5 + 8x^4 + 11x^3 + 3x^2 - x$ |
| 8649.b.700569.1 |
8649.b |
\( 3^{2} \cdot 31^{2} \) |
\( 3^{6} \cdot 31^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(5.541100\) |
\(1.385275\) |
$[1132,73377,21088959,369024]$ |
$[849,2517,-2507,-2115933,700569]$ |
$[1815232161643/2883,19016091893/8649,-200783123/77841]$ |
$y^2 + (x^2 + x)y = 9x^5 + 2x^4 - 21x^3 - 22x^2 - 8x - 1$ |
| 8649.c.700569.1 |
8649.c |
\( 3^{2} \cdot 31^{2} \) |
\( 3^{6} \cdot 31^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(18.772889\) |
\(1.173306\) |
$[1132,73377,21088959,369024]$ |
$[849,2517,-2507,-2115933,700569]$ |
$[1815232161643/2883,19016091893/8649,-200783123/77841]$ |
$y^2 + (x^2 + x)y = x^5 + 9x^4 + 13x^3 + 4x^2 - x$ |
| 11881.a.11881.1 |
11881.a |
\( 109^{2} \) |
\( 109^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(19.585813\) |
\(1.224113\) |
$[484,6649,988957,1520768]$ |
$[121,333,-323,-37493,11881]$ |
$[25937424601/11881,589929813/11881,-4729043/11881]$ |
$y^2 + (x^2 + x)y = x^5 - 3x^4 + 2x^2 - x$ |
| 12321.a.36963.1 |
12321.a |
\( 3^{2} \cdot 37^{2} \) |
\( - 3^{3} \cdot 37^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$12$ |
$0$ |
2.40.3, 3.480.12 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.007338\) |
\(18.952746\) |
\(0.417205\) |
$[4,6697,85285,-4731264]$ |
$[1,-279,-1107,-19737,-36963]$ |
$[-1/36963,31/4107,41/1369]$ |
$y^2 + (x^3 + x + 1)y = x^5 + 3x^4 + 4x^3 + 2x^2$ |
| 12544.a.12544.1 |
12544.a |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(18.675725\) |
\(1.167233\) |
$[62,112,2114,49]$ |
$[124,342,-332,-39533,12544]$ |
$[114516604/49,5094261/98,-79763/196]$ |
$y^2 = x^5 + 2x^4 - x^3 - 3x^2 - x$ |
| 12544.c.12544.1 |
12544.c |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(21.839889\) |
\(1.364993\) |
$[62,112,2114,49]$ |
$[124,342,-332,-39533,12544]$ |
$[114516604/49,5094261/98,-79763/196]$ |
$y^2 = x^5 - 2x^4 - x^3 + 3x^2 - x$ |
| 12544.i.614656.1 |
12544.i |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{4} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_3$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.2880.16 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(19.017610\) |
\(1.188601\) |
$[398,9016,912086,2401]$ |
$[796,2358,-2348,-1857293,614656]$ |
$[1248318403996/2401,9291226221/4802,-23245787/9604]$ |
$y^2 = x^5 + 4x^4 - 13x^3 + 9x^2 - x$ |
| 13689.a.13689.1 |
13689.a |
\( 3^{4} \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$12$ |
$0$ |
2.80.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.017079\) |
\(22.369055\) |
\(0.382039\) |
$[516,8073,1250613,1752192]$ |
$[129,357,-347,-43053,13689]$ |
$[441025329/169,9461333/169,-641603/1521]$ |
$y^2 + (x^3 + x + 1)y = x^5 - x^4 - 4x^3 - 2x^2$ |
| 13689.b.13689.1 |
13689.b |
\( 3^{4} \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(22.369055\) |
\(1.398066\) |
$[516,8073,1250613,1752192]$ |
$[129,357,-347,-43053,13689]$ |
$[441025329/169,9461333/169,-641603/1521]$ |
$y^2 + (x^2 + x)y = x^5 + 3x^4 + x^3 - 2x^2 - x$ |
| 15876.b.222264.1 |
15876.b |
\( 2^{2} \cdot 3^{4} \cdot 7^{2} \) |
\( - 2^{3} \cdot 3^{4} \cdot 7^{3} \) |
$0$ |
$0$ |
$\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_3$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$0$ |
$0$ |
2.40.3, 3.1920.3 |
|
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(5.070237\) |
\(1.690079\) |
$[636,6129,310743,28449792]$ |
$[159,798,16268,487452,222264]$ |
$[1254586479/2744,2828663/196,233147/126]$ |
$y^2 + (x^3 + x + 1)y = -x^6 + 2x^5 - 4x^4 + 4x^3 - 5x^2 + 2x - 1$ |
| 17689.a.17689.1 |
17689.a |
\( 7^{2} \cdot 19^{2} \) |
\( 7^{2} \cdot 19^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(15.833414\) |
\(0.989588\) |
$[580,11305,1902565,2264192]$ |
$[145,405,-395,-55325,17689]$ |
$[64097340625/17689,1234693125/17689,-8304875/17689]$ |
$y^2 + (x^2 + x)y = x^5 - 4x^4 + 2x^3 + x^2 - x$ |
| 17689.b.17689.1 |
17689.b |
\( 7^{2} \cdot 19^{2} \) |
\( 7^{2} \cdot 19^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$12$ |
$0$ |
2.80.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.020782\) |
\(23.059848\) |
\(0.479221\) |
$[580,11305,1902565,2264192]$ |
$[145,405,-395,-55325,17689]$ |
$[64097340625/17689,1234693125/17689,-8304875/17689]$ |
$y^2 + (x^3 + x + 1)y = -3x^4 - 3x^3 + x^2 + x$ |
| 20736.a.20736.1 |
20736.a |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{4} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_3$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.960.8 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(14.923707\) |
\(0.932732\) |
$[78,216,4806,81]$ |
$[156,438,-428,-64653,20736]$ |
$[4455516,160381/2,-18083/36]$ |
$y^2 = x^5 + x^4 - 3x^3 - 4x^2 - x$ |
| 20736.f.186624.1 |
20736.f |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{6} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(7.834469\) |
\(1.468963\) |
$[74,288,5502,3]$ |
$[444,1302,-1292,-567213,186624]$ |
$[277375828/3,10991701/18,-442187/324]$ |
$y^2 = x^5 - 2x^4 - 9x^3 - 7x^2 - x$ |
| 20736.g.186624.1 |
20736.g |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{6} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(21.153445\) |
\(1.322090\) |
$[74,288,5502,3]$ |
$[444,1302,-1292,-567213,186624]$ |
$[277375828/3,10991701/18,-442187/324]$ |
$y^2 = x^5 + 2x^4 - 9x^3 + 7x^2 - x$ |
| 21316.a.42632.1 |
21316.a |
\( 2^{2} \cdot 73^{2} \) |
\( - 2^{3} \cdot 73^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$12$ |
$0$ |
2.40.3, 3.480.12 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.012306\) |
\(20.941659\) |
\(0.773095\) |
$[196,12337,588745,-5456896]$ |
$[49,-414,-908,-53972,-42632]$ |
$[-282475249/42632,24353343/21316,545027/10658]$ |
$y^2 + (x^3 + x + 1)y = 3x^3 + 4x^2 + x$ |
| 21904.e.350464.1 |
21904.e |
\( 2^{4} \cdot 37^{2} \) |
\( 2^{8} \cdot 37^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(20.051730\) |
\(1.253233\) |
$[302,5032,388574,1369]$ |
$[604,1782,-1772,-1061453,350464]$ |
$[314010903004/1369,3067669341/2738,-10100843/5476]$ |
$y^2 = x^5 + 3x^4 - 11x^3 + 8x^2 - x$ |
| 24649.a.24649.1 |
24649.a |
\( 157^{2} \) |
\( 157^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(23.312929\) |
\(1.457058\) |
$[676,17113,3248173,3155072]$ |
$[169,477,-467,-76613,24649]$ |
$[137858491849/24649,2302387893/24649,-13337987/24649]$ |
$y^2 + (x^2 + x)y = x^5 + 4x^4 + 3x^3 - x^2 - x$ |
| 32761.a.32761.1 |
32761.a |
\( 181^{2} \) |
\( - 181^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$12$ |
$0$ |
2.40.3, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.020993\) |
\(24.533253\) |
\(0.515025\) |
$[676,41449,6681253,-4193408]$ |
$[169,-537,-547,-95203,-32761]$ |
$[-137858491849/32761,2591996433/32761,15622867/32761]$ |
$y^2 + (x^3 + x + 1)y = x^5 + 10x^2 + 19x + 10$ |
| 37636.a.602176.1 |
37636.a |
\( 2^{2} \cdot 97^{2} \) |
\( - 2^{6} \cdot 97^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$12$ |
$0$ |
2.40.3, 3.480.12 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.021512\) |
\(15.407337\) |
\(0.994336\) |
$[196,28033,1517953,-77078528]$ |
$[49,-1068,-4912,-345328,-602176]$ |
$[-282475249/602176,31412283/150544,737107/37636]$ |
$y^2 + (x^3 + x + 1)y = x^5 + 4x^4 + 6x^3 + 3x^2$ |
| 43264.c.43264.1 |
43264.c |
\( 2^{8} \cdot 13^{2} \) |
\( 2^{8} \cdot 13^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.1440.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(23.105046\) |
\(1.444065\) |
$[110,520,15470,169]$ |
$[220,630,-620,-133325,43264]$ |
$[2013137500/169,52408125/338,-468875/676]$ |
$y^2 = x^5 - 5x^3 + 5x^2 - x$ |
| 48841.b.830297.1 |
48841.b |
\( 13^{2} \cdot 17^{2} \) |
\( - 13^{2} \cdot 17^{3} \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$0$ |
$0$ |
2.40.3, 3.480.12 |
|
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(4.401272\) |
\(4.401272\) |
$[764,10777,650195,106278016]$ |
$[191,1071,30923,1189813,830297]$ |
$[254194901951/830297,438975873/48841,3903467/2873]$ |
$y^2 + (x^3 + x + 1)y = -x^6 + 2x^5 - 5x^4 + 6x^3 - 6x^2 + 2x - 1$ |
| 52441.a.52441.1 |
52441.a |
\( 229^{2} \) |
\( 229^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(22.932231\) |
\(1.433264\) |
$[964,41449,10706437,6712448]$ |
$[241,693,-683,-161213,52441]$ |
$[812990017201/52441,9700282053/52441,-39669323/52441]$ |
$y^2 + (x^2 + x)y = x^5 + 5x^4 + 5x^3 - x$ |
| 76729.a.76729.1 |
76729.a |
\( 277^{2} \) |
\( 277^{2} \) |
$0$ |
$4$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$4$ |
\( 1 \) |
\(1.000000\) |
\(9.986430\) |
\(2.496608\) |
$[1156,63433,19359253,9821312]$ |
$[289,837,-827,-234893,76729]$ |
$[2015993900449/76729,20203145253/76729,-69071867/76729]$ |
$y^2 + (x^2 + x)y = x^5 - 6x^4 + 6x^3 - x^2 - x$ |
| 92416.a.92416.1 |
92416.a |
\( 2^{8} \cdot 19^{2} \) |
\( 2^{8} \cdot 19^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(9.481728\) |
\(0.592608\) |
$[158,1216,50426,361]$ |
$[316,918,-908,-282413,92416]$ |
$[12308225596/361,226304901/722,-1416707/1444]$ |
$y^2 = x^5 - x^4 - 7x^3 - 6x^2 - x$ |
| 92416.b.92416.1 |
92416.b |
\( 2^{8} \cdot 19^{2} \) |
\( 2^{8} \cdot 19^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(22.243716\) |
\(1.390232\) |
$[158,1216,50426,361]$ |
$[316,918,-908,-282413,92416]$ |
$[12308225596/361,226304901/722,-1416707/1444]$ |
$y^2 = x^5 + x^4 - 7x^3 + 6x^2 - x$ |
| 110889.a.110889.1 |
110889.a |
\( 3^{4} \cdot 37^{2} \) |
\( 3^{4} \cdot 37^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$6$ |
$0$ |
2.80.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.039046\) |
\(21.980563\) |
\(0.858248\) |
$[1380,94905,34200765,14193792]$ |
$[345,1005,-995,-338325,110889]$ |
$[60340715625/1369,509493125/1369,-13158875/12321]$ |
$y^2 + (x^3 + x + 1)y = x^5 - 3x^4 - 3x^3 + 6x^2 - 3x$ |
| 110889.b.110889.1 |
110889.b |
\( 3^{4} \cdot 37^{2} \) |
\( 3^{4} \cdot 37^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(21.980563\) |
\(1.373785\) |
$[1380,94905,34200765,14193792]$ |
$[345,1005,-995,-338325,110889]$ |
$[60340715625/1369,509493125/1369,-13158875/12321]$ |
$y^2 + (x^2 + x)y = x^5 + 6x^4 + 7x^3 + x^2 - x$ |
| 123201.c.369603.1 |
123201.c |
\( 3^{6} \cdot 13^{2} \) |
\( - 3^{7} \cdot 13^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$12$ |
$0$ |
2.40.3, 3.480.12 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.021919\) |
\(16.986079\) |
\(1.116945\) |
$[108,3393,88335,-194688]$ |
$[81,-999,-3267,-315657,-369603]$ |
$[-1594323/169,242757/169,9801/169]$ |
$y^2 + (x^3 + x + 1)y = x^4 + 5x^3 + 5x^2 + x$ |
| 157609.a.157609.1 |
157609.a |
\( 397^{2} \) |
\( 397^{2} \) |
$0$ |
$4$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$4$ |
\( 1 \) |
\(1.000000\) |
\(8.197399\) |
\(2.049350\) |
$[1636,138553,58711933,20173952]$ |
$[409,1197,-1187,-479573,157609]$ |
$[11445019581049/157609,81896261013/157609,-198562547/157609]$ |
$y^2 + (x^2 + x)y = x^5 - 7x^4 + 8x^3 - 2x^2 - x$ |
| 177241.a.177241.1 |
177241.a |
\( 421^{2} \) |
\( - 421^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$12$ |
$0$ |
2.40.3, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.035352\) |
\(21.437650\) |
\(0.757868\) |
$[1636,197449,78791413,-22686848]$ |
$[409,-1257,-1267,-524563,-177241]$ |
$[-11445019581049/177241,86001336753/177241,211945027/177241]$ |
$y^2 + (x^3 + x + 1)y = x^5 - x^4 - 7x^3 + 8x^2 - 3x$ |
| 188356.a.376712.1 |
188356.a |
\( 2^{2} \cdot 7^{2} \cdot 31^{2} \) |
\( 2^{3} \cdot 7^{2} \cdot 31^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$12$ |
$0$ |
2.40.3, 3.480.12 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.032521\) |
\(14.030104\) |
\(1.368801\) |
$[964,26257,7791385,48219136]$ |
$[241,1326,-2572,-594532,376712]$ |
$[812990017201/376712,9280356423/188356,-37346083/94178]$ |
$y^2 + (x^3 + x + 1)y = x^5 - 2x^4 - 6x^3 - 3x^2$ |
| 188356.b.376712.1 |
188356.b |
\( 2^{2} \cdot 7^{2} \cdot 31^{2} \) |
\( 2^{3} \cdot 7^{2} \cdot 31^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$6$ |
$0$ |
2.40.3, 3.480.12 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.035403\) |
\(14.834309\) |
\(1.575556\) |
$[964,26257,7791385,48219136]$ |
$[241,1326,-2572,-594532,376712]$ |
$[812990017201/376712,9280356423/188356,-37346083/94178]$ |
$y^2 + (x^3 + x + 1)y = -4x^4 - 5x^3 + x$ |
| 202500.a.405000.1 |
202500.a |
\( 2^{2} \cdot 3^{4} \cdot 5^{4} \) |
\( - 2^{3} \cdot 3^{4} \cdot 5^{4} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_3$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$12$ |
$0$ |
2.40.3, 3.960.8 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.029866\) |
\(18.488720\) |
\(1.656551\) |
$[804,72225,13647825,-51840000]$ |
$[201,-1326,-2732,-576852,-405000]$ |
$[-4050375321/5000,66468623/2500,3065987/11250]$ |
$y^2 + (x^3 + x + 1)y = -2x^5 + 6x^4 - 6x^3$ |
| 219961.a.219961.1 |
219961.a |
\( 7^{2} \cdot 67^{2} \) |
\( 7^{2} \cdot 67^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(20.874496\) |
\(1.304656\) |
$[1924,197449,97792597,28155008]$ |
$[481,1413,-1403,-667853,219961]$ |
$[25746925826401/219961,157245197733/219961,-324599483/219961]$ |
$y^2 + (x^2 + x)y = x^5 + 7x^4 + 9x^3 + 2x^2 - x$ |
| 219961.b.219961.1 |
219961.b |
\( 7^{2} \cdot 67^{2} \) |
\( 7^{2} \cdot 67^{2} \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$0$ |
$0$ |
2.80.1, 3.480.12 |
|
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(7.499062\) |
\(7.499062\) |
$[1924,197449,97792597,28155008]$ |
$[481,1413,-1403,-667853,219961]$ |
$[25746925826401/219961,157245197733/219961,-324599483/219961]$ |
$y^2 + (x^3 + x + 1)y = -x^6 - 2x^5 + x^4 + 5x^3 - 3x - 1$ |
| 232324.a.464648.1 |
232324.a |
\( 2^{2} \cdot 241^{2} \) |
\( 2^{3} \cdot 241^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$6$ |
$0$ |
2.40.3, 3.480.12 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.041763\) |
\(15.981619\) |
\(2.002332\) |
$[1060,34945,11024545,59474944]$ |
$[265,1470,-2860,-729700,464648]$ |
$[1306860915625/464648,13678074375/232324,-50210875/116162]$ |
$y^2 + (x^3 + x + 1)y = -2x^5 + 2x^4 + 2x^3 - 4x^2$ |
| 301401.a.301401.1 |
301401.a |
\( 3^{4} \cdot 61^{2} \) |
\( 3^{4} \cdot 61^{2} \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$0$ |
$0$ |
2.80.1, 3.480.12 |
|
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(6.900558\) |
\(6.900558\) |
$[2244,275049,158130117,38579328]$ |
$[561,1653,-1643,-913533,301401]$ |
$[686008169121/3721,3603100853/3721,-57454067/33489]$ |
$y^2 + (x^3 + x + 1)y = -x^6 - x^5 + 3x^4 + 4x^3 - 3x^2 - 4x - 1$ |
| 301401.b.301401.1 |
301401.b |
\( 3^{4} \cdot 61^{2} \) |
\( 3^{4} \cdot 61^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(6.900558\) |
\(0.431285\) |
$[2244,275049,158130117,38579328]$ |
$[561,1653,-1643,-913533,301401]$ |
$[686008169121/3721,3603100853/3721,-57454067/33489]$ |
$y^2 + (x^2 + x)y = x^5 - 8x^4 + 10x^3 - 3x^2 - x$ |
| 350464.a.350464.1 |
350464.a |
\( 2^{8} \cdot 37^{2} \) |
\( 2^{8} \cdot 37^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$9$ |
\( 1 \) |
\(1.000000\) |
\(6.632969\) |
\(3.731045\) |
$[302,5032,388574,1369]$ |
$[604,1782,-1772,-1061453,350464]$ |
$[314010903004/1369,3067669341/2738,-10100843/5476]$ |
$y^2 = x^5 - 3x^4 - 11x^3 - 8x^2 - x$ |
