| 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 |
| 1696.a.27136.1 |
1696.a |
\( 2^{5} \cdot 53 \) |
\( 2^{9} \cdot 53 \) |
$0$ |
$1$ |
$\Z/4\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(5.081240\) |
\(0.635155\) |
$[200,25297,3015545,3392]$ |
$[200,-15198,-1725040,-143996801,27136]$ |
$[625000000/53,-237468750/53,-134768750/53]$ |
$y^2 + (x + 1)y = 4x^5 + 7x^4 + 8x^3 + 3x^2 - 1$ |
| 1696.a.217088.1 |
1696.a |
\( 2^{5} \cdot 53 \) |
\( - 2^{12} \cdot 53 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(1.270310\) |
\(0.635155\) |
$[3746,232693,328269020,848]$ |
$[7492,1718238,-69556676,-868365110309,217088]$ |
$[23050953088040593/212,5645035221351423/1696,-61003448054801/3392]$ |
$y^2 + (x^2 + 1)y = x^5 - 24x^4 - 28x^3 - 22x^2 - 7x - 1$ |
| 1696.b.434176.1 |
1696.b |
\( 2^{5} \cdot 53 \) |
\( - 2^{13} \cdot 53 \) |
$0$ |
$0$ |
$\Z/9\Z$ |
\(\Q \times \Q\) |
\(\Q\) |
|
$N(\mathrm{SU}(2)\times\mathrm{SU}(2))$ |
|
✓ |
|
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.10.1, 3.2880.1 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(5.985343\) |
\(0.665038\) |
$[11236,7908289,22291799553,54272]$ |
$[11236,-11872,-76224768,-214150609408,434176]$ |
$[3299763591802133/8,-155150527903/4,-44328573381/2]$ |
$y^2 + xy = x^6 - 2x^5 + 2x^4 + 9x^3 - 12x^2 + 3x + 26$ |
