| 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 |
| 3200.e.819200.1 |
3200.e |
\( 2^{7} \cdot 5^{2} \) |
\( - 2^{15} \cdot 5^{2} \) |
$0$ |
$2$ |
$\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.5, 3.720.4 |
|
|
$2$ |
\( 3 \) |
\(1.000000\) |
\(4.252877\) |
\(0.708813\) |
$[520,1141,186367,100]$ |
$[2080,168096,17260544,1911416576,819200]$ |
$[47525504000,1846534560,91157248]$ |
$y^2 = -x^6 - 5x^4 - 7x^2 - 2$ |
| 3200.f.819200.1 |
3200.f |
\( 2^{7} \cdot 5^{2} \) |
\( 2^{15} \cdot 5^{2} \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$0$ |
2.180.7, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(0.717386\) |
\(15.397662\) |
\(0.460253\) |
$[520,1141,186367,100]$ |
$[2080,168096,17260544,1911416576,819200]$ |
$[47525504000,1846534560,91157248]$ |
$y^2 = x^6 - 5x^4 + 7x^2 - 2$ |
| 12800.g.819200.1 |
12800.g |
\( 2^{9} \cdot 5^{2} \) |
\( 2^{15} \cdot 5^{2} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.180.7, 3.360.2 |
|
|
$2$ |
\( 2 \) |
\(1.000000\) |
\(6.848768\) |
\(1.712192\) |
$[520,1141,186367,100]$ |
$[2080,168096,17260544,1911416576,819200]$ |
$[47525504000,1846534560,91157248]$ |
$y^2 = -x^6 + 5x^4 - 7x^2 + 2$ |
| 12800.i.819200.1 |
12800.i |
\( 2^{9} \cdot 5^{2} \) |
\( - 2^{15} \cdot 5^{2} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.90.5, 3.360.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.717386\) |
\(6.199040\) |
\(1.111776\) |
$[520,1141,186367,100]$ |
$[2080,168096,17260544,1911416576,819200]$ |
$[47525504000,1846534560,91157248]$ |
$y^2 = x^6 + 5x^4 + 7x^2 + 2$ |
