| 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 |
| 8649.a.77841.1 |
8649.a |
\( 3^{2} \cdot 31^{2} \) |
\( 3^{4} \cdot 31^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\mathsf{RM}\) |
\(\mathsf{RM}\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$14$ |
$0$ |
2.120.2, 3.432.4 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.004685\) |
\(18.142300\) |
\(0.339965\) |
$[92,17689,603507,-9963648]$ |
$[23,-715,-3645,-148765,-77841]$ |
$[-\frac{6436343}{77841},\frac{8699405}{77841},\frac{23805}{961}]$ |
$y^2 + (x^3 + x + 1)y = x^3 + x^2 - 2x$ |
| 8649.a.233523.1 |
8649.a |
\( 3^{2} \cdot 31^{2} \) |
\( 3^{5} \cdot 31^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\mathsf{RM}\) |
\(\mathsf{RM}\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
2.15.2, 3.432.4 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.018739\) |
\(9.071150\) |
\(0.339965\) |
$[36388,-1141271,-13820841051,29890944]$ |
$[9097,3495695,1814445117,1071530924081,233523]$ |
$[\frac{62300419867534985257}{233523},\frac{2631649929116327735}{233523},\frac{1853767256362813}{2883}]$ |
$y^2 + (x^3 + x + 1)y = -3x^4 + 3x^3 + 7x^2 - 47x - 70$ |
| 8649.b.700569.1 |
8649.b |
\( 3^{2} \cdot 31^{2} \) |
\( 3^{6} \cdot 31^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(5.541100\) |
\(1.385275\) |
$[1132,73377,21088959,369024]$ |
$[849,2517,-2507,-2115933,700569]$ |
$[\frac{1815232161643}{2883},\frac{19016091893}{8649},-\frac{200783123}{77841}]$ |
$y^2 + (x^2 + x)y = 9x^5 + 2x^4 - 21x^3 - 22x^2 - 8x - 1$ |
| 8649.c.700569.1 |
8649.c |
\( 3^{2} \cdot 31^{2} \) |
\( 3^{6} \cdot 31^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(18.772889\) |
\(1.173306\) |
$[1132,73377,21088959,369024]$ |
$[849,2517,-2507,-2115933,700569]$ |
$[\frac{1815232161643}{2883},\frac{19016091893}{8649},-\frac{200783123}{77841}]$ |
$y^2 + (x^2 + x)y = x^5 + 9x^4 + 13x^3 + 4x^2 - x$ |
