| 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 |
| 262144.a.262144.1 |
262144.a |
\( 2^{18} \) |
\( - 2^{18} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_2)$ |
|
✓ |
|
$C_2$ |
$D_4$ |
$2$ |
$2$ |
2.90.3, 3.3240.5 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.123513\) |
\(10.883805\) |
\(3.057023\) |
$[4,-14,2,1]$ |
$[32,640,-6144,-151552,262144]$ |
$[128,80,-24]$ |
$y^2 = x^5 - 2x^3 - x$ |
| 262144.b.524288.1 |
262144.b |
\( 2^{18} \) |
\( 2^{19} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_4)$ |
|
✓ |
|
$C_2$ |
$D_4$ |
$2$ |
$2$ |
2.90.3, 3.270.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.970077\) |
\(7.048011\) |
\(3.418555\) |
$[26,-2,40,2]$ |
$[208,1888,-2304,-1010944,524288]$ |
$[742586,129623/4,-1521/8]$ |
$y^2 = x^5 + 2x^3 + 2x$ |
| 262144.c.524288.1 |
262144.c |
\( 2^{18} \) |
\( 2^{19} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_4)$ |
|
✓ |
|
$C_2$ |
$D_4$ |
$4$ |
$2$ |
2.90.3, 3.270.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.759196\) |
\(7.048011\) |
\(2.675411\) |
$[26,-2,40,2]$ |
$[208,1888,-2304,-1010944,524288]$ |
$[742586,129623/4,-1521/8]$ |
$y^2 = x^5 - 2x^3 + 2x$ |
| 262144.d.524288.1 |
262144.d |
\( 2^{18} \) |
\( 2^{19} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\mathsf{QM}\) |
\(\Q\) |
|
$J(E_2)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.90.3, 3.360.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.658241\) |
\(3.857919\) |
\(3.198681\) |
$[42,-18,-324,2]$ |
$[336,5472,163584,6255360,524288]$ |
$[8168202,1583631/4,281799/8]$ |
$y^2 = x^5 - x^4 + 4x^3 - 8x^2 + 5x - 1$ |
| 262144.d.524288.2 |
262144.d |
\( 2^{18} \) |
\( 2^{19} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\mathsf{QM}\) |
\(\Q\) |
|
$J(E_2)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.90.3, 3.360.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.552747\) |
\(11.573758\) |
\(3.198681\) |
$[42,-18,-324,2]$ |
$[336,5472,163584,6255360,524288]$ |
$[8168202,1583631/4,281799/8]$ |
$y^2 = x^5 + x^4 + 4x^3 + 8x^2 + 5x + 1$ |
