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 |
578.a1 |
578a4 |
578.a |
578a |
$4$ |
$6$ |
\( 2 \cdot 17^{2} \) |
\( 2 \cdot 17^{12} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.6, 3.4.0.1 |
2B, 3B |
$408$ |
$96$ |
$1$ |
$1$ |
$9$ |
$3$ |
$0$ |
$3456$ |
$1.596094$ |
$159661140625/48275138$ |
$1.06848$ |
$6.72932$ |
$[1, 1, 1, -32663, -1583717]$ |
\(y^2+xy+y=x^3+x^2-32663x-1583717\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.b.1, 12.24.0-6.a.1.5, $\ldots$ |
$[]$ |
578.a2 |
578a3 |
578.a |
578a |
$4$ |
$6$ |
\( 2 \cdot 17^{2} \) |
\( 2^{2} \cdot 17^{9} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.1, 3.4.0.1 |
2B, 3B |
$408$ |
$96$ |
$1$ |
$1$ |
$9$ |
$3$ |
$1$ |
$1728$ |
$1.249521$ |
$120920208625/19652$ |
$0.98564$ |
$6.68562$ |
$[1, 1, 1, -29773, -1989473]$ |
\(y^2+xy+y=x^3+x^2-29773x-1989473\) |
2.3.0.a.1, 3.4.0.a.1, 6.24.0-6.a.1.3, 8.6.0.c.1, 24.48.0-24.bw.1.6, $\ldots$ |
$[]$ |
578.a3 |
578a2 |
578.a |
578a |
$4$ |
$6$ |
\( 2 \cdot 17^{2} \) |
\( 2^{3} \cdot 17^{8} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.6, 3.4.0.1 |
2B, 3B |
$408$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$1152$ |
$1.046787$ |
$8805624625/2312$ |
$0.96590$ |
$6.27368$ |
$[1, 1, 1, -12433, 528295]$ |
\(y^2+xy+y=x^3+x^2-12433x+528295\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.b.1, 12.24.0-6.a.1.11, $\ldots$ |
$[]$ |
578.a4 |
578a1 |
578.a |
578a |
$4$ |
$6$ |
\( 2 \cdot 17^{2} \) |
\( 2^{6} \cdot 17^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.1, 3.4.0.1 |
2B, 3B |
$408$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$576$ |
$0.700214$ |
$3048625/1088$ |
$0.90010$ |
$5.02070$ |
$[1, 1, 1, -873, 5783]$ |
\(y^2+xy+y=x^3+x^2-873x+5783\) |
2.3.0.a.1, 3.4.0.a.1, 6.24.0-6.a.1.1, 8.6.0.c.1, 24.48.0-24.bw.1.2, $\ldots$ |
$[]$ |