| 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 |
| 7680.a.46080.1 |
7680.a |
\( 2^{9} \cdot 3 \cdot 5 \) |
\( 2^{10} \cdot 3^{2} \cdot 5 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$4$ |
2.360.2 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(14.167858\) |
\(0.885491\) |
$[200,472,32580,180]$ |
$[400,5408,56320,-1679616,46080]$ |
$[2000000000/9,67600000/9,1760000/9]$ |
$y^2 = x^5 - 3x^4 + 5x^2 - x - 2$ |
| 7680.b.46080.1 |
7680.b |
\( 2^{9} \cdot 3 \cdot 5 \) |
\( 2^{10} \cdot 3^{2} \cdot 5 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$4$ |
2.360.2 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(17.497219\) |
\(1.093576\) |
$[200,472,32580,180]$ |
$[400,5408,56320,-1679616,46080]$ |
$[2000000000/9,67600000/9,1760000/9]$ |
$y^2 = x^5 + 3x^4 - 5x^2 - x + 2$ |
| 7680.c.61440.1 |
7680.c |
\( 2^{9} \cdot 3 \cdot 5 \) |
\( 2^{12} \cdot 3 \cdot 5 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.180.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(9.065227\) |
\(1.133153\) |
$[390,1680,206664,240]$ |
$[780,20870,599556,8024195,61440]$ |
$[18796708125/4,5158281375/32,379968615/64]$ |
$y^2 = x^5 - 5x^3 + x^2 + 6x - 3$ |
| 7680.d.245760.1 |
7680.d |
\( 2^{9} \cdot 3 \cdot 5 \) |
\( - 2^{14} \cdot 3 \cdot 5 \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.90.1 |
|
✓ |
$1$ |
\( 2 \) |
\(1.351604\) |
\(4.918269\) |
\(0.830944\) |
$[2976,573,566004,30]$ |
$[11904,5898272,3892776960,2887501086464,245760]$ |
$[4863214183514112/5,202424165167104/5,2244575195136]$ |
$y^2 + y = -20x^6 - 21x^4 - 7x^2 - 1$ |
| 7680.e.245760.1 |
7680.e |
\( 2^{9} \cdot 3 \cdot 5 \) |
\( 2^{14} \cdot 3 \cdot 5 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(8.406152\) |
\(1.050769\) |
$[2976,573,566004,30]$ |
$[11904,5898272,3892776960,2887501086464,245760]$ |
$[4863214183514112/5,202424165167104/5,2244575195136]$ |
$y^2 + y = 20x^6 - 21x^4 + 7x^2 - 1$ |
