| 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 |
| 1083.a.1083.1 |
1083.a |
\( 3 \cdot 19^{2} \) |
\( - 3 \cdot 19^{2} \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$0$ |
2.15.2, 3.720.4 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.075149\) |
\(22.662454\) |
\(0.189229\) |
$[56,244,928,4332]$ |
$[28,-8,264,1832,1083]$ |
$[17210368/1083,-175616/1083,68992/361]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^3$ |
| 1083.a.20577.1 |
1083.a |
\( 3 \cdot 19^{2} \) |
\( 3 \cdot 19^{3} \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.15.2, 3.2160.20 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.075149\) |
\(7.554151\) |
\(0.189229\) |
$[904,13684,4578992,82308]$ |
$[452,6232,-8664,-10688488,20577]$ |
$[18866536236032/20577,30289293824/1083,-1634432/19]$ |
$y^2 + x^3y = x^5 - 5x^4 + 11x^3 - 13x^2 + 9x - 3$ |
| 1083.b.87723.1 |
1083.b |
\( 3 \cdot 19^{2} \) |
\( - 3^{5} \cdot 19^{2} \) |
$0$ |
$1$ |
$\Z/15\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.15.2, 3.720.4 |
|
|
$2$ |
\( 5 \) |
\(1.000000\) |
\(5.981341\) |
\(0.265837\) |
$[5464,8692,15768656,350892]$ |
$[2732,309544,46549080,7838649656,87723]$ |
$[152196082896530432/87723,6311963449851392/87723,1429770125440/361]$ |
$y^2 + y = -x^6 - 3x^5 - 8x^4 - 11x^3 - 14x^2 - 9x - 6$ |
| 1083.b.390963.1 |
1083.b |
\( 3 \cdot 19^{2} \) |
\( - 3 \cdot 19^{4} \) |
$0$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.15.2, 3.720.5 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(0.132919\) |
\(0.265837\) |
$[150440,1945515892,68956865081488,-1563852]$ |
$[75220,-88500632,98386538568,-107931608328616,-390963]$ |
$[-2408056349828975363200000/390963,1982406707133537344000/20577,-27053302090985600/19]$ |
$y^2 + y = -x^6 + 3x^5 - 50x^4 + 95x^3 - 14x^2 - 33x - 6$ |
