| 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 |
| 2520.a.408240.1 |
2520.a |
\( 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \) |
\( 2^{4} \cdot 3^{6} \cdot 5 \cdot 7 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/8\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(13.006052\) |
\(0.406439\) |
$[124376,729208,30027691484,1632960]$ |
$[62188,161017938,555482007360,2154384678982959,408240]$ |
$[8304527484794625120064/3645,38417889080153290792/405,47359829493022144/9]$ |
$y^2 + (x^2 + 1)y = 5x^6 - 23x^4 + 33x^2 - 16$ |
| 2520.b.635040.1 |
2520.b |
\( 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \) |
\( 2^{5} \cdot 3^{4} \cdot 5 \cdot 7^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 5 \) |
\(1.000000\) |
\(16.306226\) |
\(0.815311\) |
$[3296,104464,104578588,2540160]$ |
$[1648,95752,6711044,472838752,635040]$ |
$[379870928666624/19845,13392741850112/19845,569579726368/19845]$ |
$y^2 + xy = 2x^5 + 6x^4 - 16x^3 + 8x^2 + x - 1$ |
| 2520.c.680400.1 |
2520.c |
\( 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \) |
\( - 2^{4} \cdot 3^{5} \cdot 5^{2} \cdot 7 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.90.1 |
|
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(4.065285\) |
\(0.508161\) |
$[202664,70648,4771785956,2721600]$ |
$[101332,427828818,2408353617600,15251447816841519,680400]$ |
$[95392679863974687468736/6075,1324861868713610149384/2025,981325180099899712/27]$ |
$y^2 + (x^2 + 1)y = -75x^6 - 65x^4 - 19x^2 - 2$ |
