| Label |
Cremona label |
Class |
Cremona class |
Class size |
Class degree |
Conductor |
Discriminant |
Rank |
Torsion |
$\textrm{End}^0(E_{\overline\Q})$ |
CM |
Sato-Tate |
Semistable |
Potentially good |
Nonmax $\ell$ |
$\ell$-adic images |
mod-$\ell$ images |
Adelic level |
Adelic index |
Adelic genus |
Regulator |
$Ш_{\textrm{an}}$ |
Ш primes |
Integral points |
Modular degree |
Faltings height |
j-invariant |
$abc$ quality |
Szpiro ratio |
Weierstrass coefficients |
Weierstrass equation |
mod-$m$ images |
MW-generators |
| 56.a1 |
56a4 |
56.a |
56a |
$4$ |
$4$ |
\( 2^{3} \cdot 7 \) |
\( 2^{11} \cdot 7 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.103 |
2B |
$56$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$8$ |
$-0.002033$ |
$1443468546/7$ |
$1.04654$ |
$7.13352$ |
$[0, 0, 0, -299, 1990]$ |
\(y^2=x^3-299x+1990\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.p.1.7, 28.12.0-4.c.1.1, 56.48.0-56.bp.1.3 |
$[]$ |
| 56.a2 |
56a3 |
56.a |
56a |
$4$ |
$4$ |
\( 2^{3} \cdot 7 \) |
\( 2^{11} \cdot 7^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.58 |
2B |
$56$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$8$ |
$-0.002033$ |
$11090466/2401$ |
$1.11706$ |
$5.92401$ |
$[0, 0, 0, -59, -138]$ |
\(y^2=x^3-59x-138\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.k.1.1, 56.48.0-56.v.1.8 |
$[]$ |
| 56.a3 |
56a2 |
56.a |
56a |
$4$ |
$4$ |
\( 2^{3} \cdot 7 \) |
\( 2^{10} \cdot 7^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.1 |
2Cs |
$56$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$3$ |
$4$ |
$-0.348607$ |
$740772/49$ |
$1.06534$ |
$5.07954$ |
$[0, 0, 0, -19, 30]$ |
\(y^2=x^3-19x+30\) |
2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.a.1.2, 28.24.0-28.b.1.1, 56.48.0-56.d.1.3 |
$[]$ |
| 56.a4 |
56a1 |
56.a |
56a |
$4$ |
$4$ |
\( 2^{3} \cdot 7 \) |
\( - 2^{8} \cdot 7 \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.50 |
2B |
$56$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$3$ |
$2$ |
$-0.695180$ |
$432/7$ |
$0.89152$ |
$3.70389$ |
$[0, 0, 0, 1, 2]$ |
\(y^2=x^3+x+2\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.p.1.1, 14.6.0.b.1, 28.24.0-28.g.1.2, $\ldots$ |
$[]$ |
| 56.b1 |
56b2 |
56.b |
56b |
$2$ |
$2$ |
\( 2^{3} \cdot 7 \) |
\( 2^{11} \cdot 7^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.6 |
2B |
$56$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$8$ |
$-0.234669$ |
$3543122/49$ |
$1.08036$ |
$5.64054$ |
$[0, -1, 0, -40, -84]$ |
\(y^2=x^3-x^2-40x-84\) |
2.3.0.a.1, 8.6.0.b.1, 28.6.0.c.1, 56.12.0.k.1 |
$[]$ |
| 56.b2 |
56b1 |
56.b |
56b |
$2$ |
$2$ |
\( 2^{3} \cdot 7 \) |
\( - 2^{10} \cdot 7 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.1 |
2B |
$56$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$4$ |
$-0.581243$ |
$-4/7$ |
$1.03482$ |
$4.05739$ |
$[0, -1, 0, 0, -4]$ |
\(y^2=x^3-x^2-4\) |
2.3.0.a.1, 8.6.0.c.1, 14.6.0.b.1, 56.12.0.n.1 |
$[]$ |
