| 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 |
| 3969.a.3969.1 |
3969.a |
\( 3^{4} \cdot 7^{2} \) |
\( 3^{4} \cdot 7^{2} \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.80.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.021040\) |
\(22.638195\) |
\(0.476310\) |
$[2628,11025,9519993,508032]$ |
$[657,17526,608080,23086971,3969]$ |
$[\frac{1511269191297}{49},\frac{61361207478}{49},\frac{3240458320}{49}]$ |
$y^2 + (x^3 + x + 1)y = 2x^5 - 6x^3 + 2x^2 + x - 1$ |
| 3969.b.35721.1 |
3969.b |
\( 3^{4} \cdot 7^{2} \) |
\( 3^{6} \cdot 7^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$18$ |
$0$ |
2.80.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.003155\) |
\(23.234167\) |
\(0.219945\) |
$[268,2961,216951,18816]$ |
$[201,573,-563,-110373,35721]$ |
$[\frac{1350125107}{147},\frac{57445733}{441},-\frac{2527307}{3969}]$ |
$y^2 + (x^3 + x + 1)y = -2x^5 + 3x^4 - 3x^2$ |
| 3969.c.35721.1 |
3969.c |
\( 3^{4} \cdot 7^{2} \) |
\( 3^{6} \cdot 7^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(12.485061\) |
\(0.780316\) |
$[268,2961,216951,18816]$ |
$[201,573,-563,-110373,35721]$ |
$[\frac{1350125107}{147},\frac{57445733}{441},-\frac{2527307}{3969}]$ |
$y^2 + (x^2 + x)y = x^5 - 5x^4 + 4x^3 - x$ |
| 3969.d.250047.1 |
3969.d |
\( 3^{4} \cdot 7^{2} \) |
\( - 3^{6} \cdot 7^{3} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{RM}\) |
✓ |
$J(E_1)$ |
|
✓ |
|
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.3, 3.1920.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(13.559050\) |
\(0.753281\) |
$[452,-15543,-660459,131712]$ |
$[339,10617,-211009,-46063185,250047]$ |
$[\frac{18424351793}{1029},\frac{5106412483}{3087},-\frac{2694373921}{27783}]$ |
$y^2 + (x^2 + x + 1)y = -3x^5 + 5x^4 - 4x^3 + x$ |
