| 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 |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(22.369055\) |
\(1.398066\) |
$[516,8073,1250613,1752192]$ |
$[129,357,-347,-43053,13689]$ |
$[441025329/169,9461333/169,-641603/1521]$ |
$y^2 + (x^2 + x)y = x^5 + 3x^4 + x^3 - 2x^2 - x$ |
| 13689.c.41067.1 |
13689.c |
\( 3^{4} \cdot 13^{2} \) |
\( 3^{5} \cdot 13^{2} \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.20.2 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.056212\) |
\(7.243718\) |
\(0.814362\) |
$[616,31720,4631783,-676]$ |
$[924,-12006,142983,-3006936,-41067]$ |
$[-2771746976768/169,38976961408/169,-1507104368/507]$ |
$y^2 + (x^3 + x)y = x^5 - 6x^3 - 13x^2 - 6x + 9$ |
