| 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.a.8281.1 |
8281.a |
\( 7^{2} \cdot 13^{2} \) |
\( 7^{2} \cdot 13^{2} \) |
$2$ |
$2$ |
$\Z/3\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$10$ |
$0$ |
2.30.2, 3.2160.21 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.150828\) |
\(23.537474\) |
\(0.394457\) |
$[72,1236,15984,33124]$ |
$[36,-152,392,-2248,8281]$ |
$[\frac{60466176}{8281},-\frac{7091712}{8281},\frac{10368}{169}]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^4 - 3x^3 - x^2$ |
| 8281.a.753571.1 |
8281.a |
\( 7^{2} \cdot 13^{2} \) |
\( - 7^{3} \cdot 13^{3} \) |
$2$ |
$2$ |
$\Z/3\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$10$ |
$0$ |
2.30.4, 3.2160.20 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(0.050276\) |
\(7.845825\) |
\(0.394457\) |
$[1752,12756,7332144,3014284]$ |
$[876,29848,1258712,52932152,753571]$ |
$[\frac{515846550629376}{753571},\frac{220488611328}{8281},\frac{116641152}{91}]$ |
$y^2 + y = x^6 - 3x^5 + 6x^4 - 7x^3 + 7x^2 - 4x + 2$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(19.785401\) |
\(1.236588\) |
$[2596,375193,248614093,51938432]$ |
$[649,1917,-1907,-1228133,405769]$ |
$[\frac{115139273278249}{405769},\frac{524030063733}{405769},-\frac{803230307}{405769}]$ |
$y^2 + (x^2 + x)y = x^5 + 8x^4 + 11x^3 + 3x^2 - x$ |
