| 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 |
$\Q$-simple |
\(\overline{\Q}\)-simple |
\(\Aut(X)\) |
\(\Aut(X_{\overline{\Q}})\) |
$\Q$-points |
$\Q$-Weierstrass points |
Locally solvable |
Square Ш* |
Analytic Ш* |
Tamagawa |
Regulator |
Real period |
Leading coefficient |
Igusa-Clebsch invariants |
Igusa invariants |
G2-invariants |
Equation |
| 2156.a.17248.1 |
2156.a |
\( 2^{2} \cdot 7^{2} \cdot 11 \) |
\( 2^{5} \cdot 7^{2} \cdot 11 \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(7.251618\) |
\(0.402868\) |
$[452,24145,4532153,2207744]$ |
$[113,-474,-28028,-847960,17248]$ |
$[18424351793/17248,-341966589/8624,-165997/8]$ |
$y^2 + (x^2 + x)y = 2x^5 + 5x^4 + 7x^3 + 5x^2 + 2x$ |
| 2156.b.34496.1 |
2156.b |
\( 2^{2} \cdot 7^{2} \cdot 11 \) |
\( 2^{6} \cdot 7^{2} \cdot 11 \) |
$1$ |
$2$ |
$\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
$C_2^2$ |
$C_2^2$ |
$8$ |
$2$ |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.123039\) |
\(21.055838\) |
\(0.287853\) |
$[2916,41745,37024569,4415488]$ |
$[729,20404,734800,29836496,34496]$ |
$[205891132094649/34496,1976231914389/8624,2218766175/196]$ |
$y^2 + (x^2 + x)y = 2x^5 - x^4 - 5x^3 + 3x + 1$ |
| 2156.c.275968.1 |
2156.c |
\( 2^{2} \cdot 7^{2} \cdot 11 \) |
\( - 2^{9} \cdot 7^{2} \cdot 11 \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(1.000000\) |
\(6.695303\) |
\(0.557942\) |
$[17292,11145,58172763,35323904]$ |
$[4323,778216,186762752,50438808560,275968]$ |
$[137256680839210713/25088,714452219992269/3136,619723677969/49]$ |
$y^2 + (x^2 + x + 1)y = x^6 + 3x^5 + 9x^4 + 13x^3 + 18x^2 + 12x + 8$ |
