| 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 |
| 40000.a.160000.1 |
40000.a |
\( 2^{6} \cdot 5^{4} \) |
\( 2^{8} \cdot 5^{4} \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.120.2, 3.360.2 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(1.000000\) |
\(6.649769\) |
\(1.329954\) |
$[508,4375,808450,20000]$ |
$[508,7836,-3584,-15805892,160000]$ |
$[\frac{132153477628}{625},\frac{4012782297}{625},-\frac{3612896}{625}]$ |
$y^2 + (x^3 + x)y = -2x^2 - 4$ |
| 40000.b.160000.1 |
40000.b |
\( 2^{6} \cdot 5^{4} \) |
\( - 2^{8} \cdot 5^{4} \) |
$1$ |
$1$ |
$\Z/5\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.60.2, 3.360.2 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(0.636945\) |
\(18.309356\) |
\(2.332409\) |
$[508,4375,808450,20000]$ |
$[508,7836,-3584,-15805892,160000]$ |
$[\frac{132153477628}{625},\frac{4012782297}{625},-\frac{3612896}{625}]$ |
$y^2 + (x^3 + x)y = -x^4 - 2x^2 + 4$ |
| 40000.c.200000.1 |
40000.c |
\( 2^{6} \cdot 5^{4} \) |
\( - 2^{6} \cdot 5^{5} \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.60.2, 3.720.4 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.636945\) |
\(8.188193\) |
\(1.738475\) |
$[220,55,3610,8]$ |
$[1100,49500,2960000,201437500,200000]$ |
$[8052550000,329422500,17908000]$ |
$y^2 + (x^3 + x)y = 2x^4 + 6x^2 + 5$ |
| 40000.d.200000.1 |
40000.d |
\( 2^{6} \cdot 5^{4} \) |
\( 2^{6} \cdot 5^{5} \) |
$0$ |
$0$ |
$\Z/3\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.60.2, 3.720.4 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(2.973867\) |
\(0.991289\) |
$[220,55,3610,8]$ |
$[1100,49500,2960000,201437500,200000]$ |
$[8052550000,329422500,17908000]$ |
$y^2 + (x^3 + x)y = -3x^4 + 6x^2 - 5$ |
| 40000.e.200000.1 |
40000.e |
\( 2^{6} \cdot 5^{4} \) |
\( - 2^{6} \cdot 5^{5} \) |
$2$ |
$3$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\mathsf{CM})\) |
\(\mathsf{CM}\) |
✓ |
$J(C_4)$ |
|
✓ |
|
$C_4$ |
$GL(2,3)$ |
$8$ |
$0$ |
2.90.7, 3.3240.15 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.126734\) |
\(11.350269\) |
\(0.719235\) |
$[20,-20,-40,8]$ |
$[100,750,-2500,-203125,200000]$ |
$[50000,3750,-125]$ |
$y^2 + x^3y = x^5 - 5x^3 - 10x^2 - 8x - 2$ |
