| 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 |
| 10040.a.20080.1 |
10040.a |
\( 2^{3} \cdot 5 \cdot 251 \) |
\( - 2^{4} \cdot 5 \cdot 251 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.079534\) |
\(19.409052\) |
\(0.771844\) |
$[272,-620,-181772,-80320]$ |
$[136,874,22116,560975,-20080]$ |
$[-2907867136/1255,-137406784/1255,-25566096/1255]$ |
$y^2 + (x + 1)y = 2x^5 - x^4 - 2x^3$ |
| 10040.b.321280.1 |
10040.b |
\( 2^{3} \cdot 5 \cdot 251 \) |
\( - 2^{8} \cdot 5 \cdot 251 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \cdot 7 \) |
\(0.018737\) |
\(16.510273\) |
\(1.082736\) |
$[776,8044,1792988,-1285120]$ |
$[388,4932,80484,1725792,-321280]$ |
$[-34349361028/1255,-1125325809/1255,-189318489/5020]$ |
$y^2 + (x + 1)y = 2x^5 - x^4 - 3x^3 + x^2 + x$ |
| 10040.c.502000.1 |
10040.c |
\( 2^{3} \cdot 5 \cdot 251 \) |
\( - 2^{4} \cdot 5^{3} \cdot 251 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(0.045172\) |
\(11.060477\) |
\(0.749431\) |
$[16,-4076,38588,2008000]$ |
$[8,682,-5796,-127873,502000]$ |
$[2048/31375,21824/31375,-23184/31375]$ |
$y^2 + (x^2 + 1)y = x^5 - 3x^4 + 3x^3 - 2x$ |
