| 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 |
| 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 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.005669\) |
\(19.785401\) |
\(0.336475\) |
$[2596,375193,248614093,51938432]$ |
$[649,1917,-1907,-1228133,405769]$ |
$[\frac{115139273278249}{405769},\frac{524030063733}{405769},-\frac{803230307}{405769}]$ |
$y^2 + (x^3 + x + 1)y = -3x^5 + 9x^4 - 7x^3 - 2x^2 + x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(19.785401\) |
\(1.236588\) |
$[2596,375193,248614093,51938432]$ |
$[649,1917,-1907,-1228133,405769]$ |
$[\frac{115139273278249}{405769},\frac{524030063733}{405769},-\frac{803230307}{405769}]$ |
$y^2 + (x^2 + x)y = x^5 + 8x^4 + 11x^3 + 3x^2 - x$ |
| 405769.b.405769.1 |
405769.b |
\( 7^{4} \cdot 13^{2} \) |
\( 7^{4} \cdot 13^{2} \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$0$ |
$0$ |
2.80.1, 3.480.12 |
|
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(6.383879\) |
\(6.383879\) |
$[2596,375193,248614093,51938432]$ |
$[649,1917,-1907,-1228133,405769]$ |
$[\frac{115139273278249}{405769},\frac{524030063733}{405769},-\frac{803230307}{405769}]$ |
$y^2 + (x^3 + x + 1)y = -x^6 + 4x^5 - 5x^4 - 4x^3 + 4x^2 - 1$ |
