| 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 |
| 73728.c.884736.1 |
73728.c |
\( 2^{13} \cdot 3^{2} \) |
\( 2^{15} \cdot 3^{3} \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_4)$ |
|
✓ |
|
$C_2$ |
$D_4$ |
$2$ |
$2$ |
2.180.3, 3.270.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(0.793842\) |
\(5.583154\) |
\(2.216071\) |
$[195,630,44910,108]$ |
$[780,18630,-380,-86843325,884736]$ |
$[\frac{10442615625}{32},\frac{2558131875}{256},-\frac{401375}{1536}]$ |
$y^2 = x^5 + 5x^3 + 6x$ |
| 73728.d.884736.1 |
73728.d |
\( 2^{13} \cdot 3^{2} \) |
\( 2^{15} \cdot 3^{3} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_4)$ |
|
✓ |
|
$C_2$ |
$D_4$ |
$4$ |
$4$ |
2.360.2, 3.270.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(11.166308\) |
\(1.395789\) |
$[195,630,44910,108]$ |
$[780,18630,-380,-86843325,884736]$ |
$[\frac{10442615625}{32},\frac{2558131875}{256},-\frac{401375}{1536}]$ |
$y^2 = 2x^5 - 5x^3 + 3x$ |
| 147456.c.884736.1 |
147456.c |
\( 2^{14} \cdot 3^{2} \) |
\( 2^{15} \cdot 3^{3} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_4)$ |
|
✓ |
|
$C_2$ |
$D_4$ |
$2$ |
$2$ |
2.180.3, 3.270.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(5.583154\) |
\(1.395789\) |
$[195,630,44910,108]$ |
$[780,18630,-380,-86843325,884736]$ |
$[\frac{10442615625}{32},\frac{2558131875}{256},-\frac{401375}{1536}]$ |
$y^2 = 2x^5 + 5x^3 + 3x$ |
| 147456.e.884736.1 |
147456.e |
\( 2^{14} \cdot 3^{2} \) |
\( 2^{15} \cdot 3^{3} \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_4)$ |
|
✓ |
|
$C_2$ |
$D_4$ |
$4$ |
$2$ |
2.180.3, 3.270.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.970167\) |
\(11.166308\) |
\(2.708295\) |
$[195,630,44910,108]$ |
$[780,18630,-380,-86843325,884736]$ |
$[\frac{10442615625}{32},\frac{2558131875}{256},-\frac{401375}{1536}]$ |
$y^2 = x^5 - 5x^3 + 6x$ |
