| 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 |
| 520.a1 |
520a3 |
520.a |
520a |
$4$ |
$4$ |
\( 2^{3} \cdot 5 \cdot 13 \) |
\( 2^{11} \cdot 5^{4} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.7 |
2B |
$520$ |
$48$ |
$0$ |
$3.801262636$ |
$1$ |
|
$1$ |
$128$ |
$0.313121$ |
$9636491538/8125$ |
$0.94289$ |
$4.89515$ |
$[0, 0, 0, -563, -5138]$ |
\(y^2=x^3-563x-5138\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 40.24.0-40.y.1.6, 52.12.0-4.c.1.1, $\ldots$ |
$[(169/2, 1725/2)]$ |
| 520.a2 |
520a2 |
520.a |
520a |
$4$ |
$4$ |
\( 2^{3} \cdot 5 \cdot 13 \) |
\( 2^{10} \cdot 5^{2} \cdot 13^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.1 |
2Cs |
$520$ |
$48$ |
$0$ |
$1.900631318$ |
$1$ |
|
$7$ |
$64$ |
$-0.033453$ |
$8586756/4225$ |
$0.96662$ |
$3.66131$ |
$[0, 0, 0, -43, -42]$ |
\(y^2=x^3-43x-42\) |
2.6.0.a.1, 8.12.0-2.a.1.1, 20.12.0-2.a.1.1, 40.24.0-40.b.1.3, 52.12.0-2.a.1.1, $\ldots$ |
$[(-2, 6)]$ |
| 520.a3 |
520a1 |
520.a |
520a |
$4$ |
$4$ |
\( 2^{3} \cdot 5 \cdot 13 \) |
\( 2^{8} \cdot 5 \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.12 |
2B |
$520$ |
$48$ |
$0$ |
$0.950315659$ |
$1$ |
|
$5$ |
$32$ |
$-0.380026$ |
$5256144/65$ |
$0.85145$ |
$3.36115$ |
$[0, 0, 0, -23, 42]$ |
\(y^2=x^3-23x+42\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 20.12.0-4.c.1.2, 40.24.0-40.y.1.9, $\ldots$ |
$[(2, 2)]$ |
| 520.a4 |
520a4 |
520.a |
520a |
$4$ |
$4$ |
\( 2^{3} \cdot 5 \cdot 13 \) |
\( - 2^{11} \cdot 5 \cdot 13^{4} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.8 |
2B |
$520$ |
$48$ |
$0$ |
$3.801262636$ |
$1$ |
|
$3$ |
$128$ |
$0.313121$ |
$208974222/142805$ |
$0.95226$ |
$4.28255$ |
$[0, 0, 0, 157, -322]$ |
\(y^2=x^3+157x-322\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 20.12.0-4.c.1.1, 40.24.0-40.s.1.4, $\ldots$ |
$[(38, 246)]$ |
| 520.b1 |
520b1 |
520.b |
520b |
$2$ |
$2$ |
\( 2^{3} \cdot 5 \cdot 13 \) |
\( 2^{8} \cdot 5 \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.21 |
2B |
$520$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$32$ |
$-0.394336$ |
$3631696/65$ |
$0.75998$ |
$3.30204$ |
$[0, -1, 0, -20, -28]$ |
\(y^2=x^3-x^2-20x-28\) |
2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.3, 130.6.0.?, 260.24.0.?, $\ldots$ |
$[]$ |
| 520.b2 |
520b2 |
520.b |
520b |
$2$ |
$2$ |
\( 2^{3} \cdot 5 \cdot 13 \) |
\( - 2^{10} \cdot 5^{2} \cdot 13^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.12 |
2B |
$520$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$64$ |
$-0.047762$ |
$-4/4225$ |
$1.09431$ |
$3.63537$ |
$[0, -1, 0, 0, -100]$ |
\(y^2=x^3-x^2-100\) |
2.3.0.a.1, 4.12.0-4.a.1.1, 260.24.0.?, 520.48.0.? |
$[]$ |
