| 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 |
| 1380.a1 |
1380b1 |
1380.a |
1380b |
$1$ |
$1$ |
\( 2^{2} \cdot 3 \cdot 5 \cdot 23 \) |
\( - 2^{8} \cdot 3^{14} \cdot 5^{13} \cdot 23 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$230$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$43680$ |
$2.437252$ |
$194879272239195815936/134287459716796875$ |
$1.17188$ |
$7.22894$ |
$[0, -1, 0, 766939, 112645761]$ |
\(y^2=x^3-x^2+766939x+112645761\) |
230.2.0.? |
$[]$ |
| 1380.b1 |
1380a1 |
1380.b |
1380a |
$2$ |
$2$ |
\( 2^{2} \cdot 3 \cdot 5 \cdot 23 \) |
\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 23 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$1380$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$120$ |
$-0.365673$ |
$67108864/1725$ |
$1.03105$ |
$2.87619$ |
$[0, -1, 0, -21, -30]$ |
\(y^2=x^3-x^2-21x-30\) |
2.3.0.a.1, 20.6.0.b.1, 138.6.0.?, 1380.12.0.? |
$[]$ |
| 1380.b2 |
1380a2 |
1380.b |
1380a |
$2$ |
$2$ |
\( 2^{2} \cdot 3 \cdot 5 \cdot 23 \) |
\( - 2^{8} \cdot 3^{2} \cdot 5 \cdot 23^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$1380$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$240$ |
$-0.019099$ |
$21296/23805$ |
$0.90472$ |
$3.19191$ |
$[0, -1, 0, 4, -120]$ |
\(y^2=x^3-x^2+4x-120\) |
2.3.0.a.1, 20.6.0.a.1, 276.6.0.?, 1380.12.0.? |
$[]$ |
| 1380.c1 |
1380c2 |
1380.c |
1380c |
$2$ |
$3$ |
\( 2^{2} \cdot 3 \cdot 5 \cdot 23 \) |
\( - 2^{8} \cdot 3^{2} \cdot 5^{3} \cdot 23^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.2 |
3B.1.2 |
$690$ |
$16$ |
$0$ |
$3.725124435$ |
$1$ |
|
$2$ |
$864$ |
$0.643212$ |
$-1138621087744/13687875$ |
$0.98819$ |
$4.60959$ |
$[0, 1, 0, -1381, -20425]$ |
\(y^2=x^3+x^2-1381x-20425\) |
3.8.0-3.a.1.1, 230.2.0.?, 690.16.0.? |
$[(50, 195)]$ |
| 1380.c2 |
1380c1 |
1380.c |
1380c |
$2$ |
$3$ |
\( 2^{2} \cdot 3 \cdot 5 \cdot 23 \) |
\( - 2^{8} \cdot 3^{6} \cdot 5 \cdot 23 \) |
$1$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.1 |
3B.1.1 |
$690$ |
$16$ |
$0$ |
$1.241708145$ |
$1$ |
|
$8$ |
$288$ |
$0.093906$ |
$87228416/83835$ |
$0.92669$ |
$3.29595$ |
$[0, 1, 0, 59, -121]$ |
\(y^2=x^3+x^2+59x-121\) |
3.8.0-3.a.1.2, 230.2.0.?, 690.16.0.? |
$[(2, 3)]$ |
| 1380.d1 |
1380d3 |
1380.d |
1380d |
$4$ |
$6$ |
\( 2^{2} \cdot 3 \cdot 5 \cdot 23 \) |
\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 23^{3} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.8.0.2 |
2B, 3B.1.2 |
$1380$ |
$96$ |
$1$ |
$1$ |
$9$ |
$3$ |
$1$ |
$1512$ |
$0.825448$ |
$12444451776495616/912525$ |
$1.07101$ |
$5.50948$ |
$[0, 1, 0, -12165, -520512]$ |
\(y^2=x^3+x^2-12165x-520512\) |
2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 20.6.0.b.1, 60.48.0-60.p.1.15, $\ldots$ |
$[]$ |
| 1380.d2 |
1380d4 |
1380.d |
1380d |
$4$ |
$6$ |
\( 2^{2} \cdot 3 \cdot 5 \cdot 23 \) |
\( - 2^{8} \cdot 3^{2} \cdot 5 \cdot 23^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.8.0.2 |
2B, 3B.1.2 |
$1380$ |
$96$ |
$1$ |
$1$ |
$9$ |
$3$ |
$1$ |
$3024$ |
$1.172022$ |
$-772993034343376/6661615005$ |
$1.03684$ |
$5.51067$ |
$[0, 1, 0, -12140, -522732]$ |
\(y^2=x^3+x^2-12140x-522732\) |
2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 20.6.0.a.1, 60.48.0-60.o.1.15, $\ldots$ |
$[]$ |
| 1380.d3 |
1380d1 |
1380.d |
1380d |
$4$ |
$6$ |
\( 2^{2} \cdot 3 \cdot 5 \cdot 23 \) |
\( 2^{4} \cdot 3^{3} \cdot 5^{6} \cdot 23 \) |
$0$ |
$\Z/6\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.8.0.1 |
2B, 3B.1.1 |
$1380$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$5$ |
$504$ |
$0.276142$ |
$31238127616/9703125$ |
$1.02129$ |
$3.72588$ |
$[0, 1, 0, -165, -612]$ |
\(y^2=x^3+x^2-165x-612\) |
2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 20.6.0.b.1, 60.48.0-60.p.1.16, $\ldots$ |
$[]$ |
| 1380.d4 |
1380d2 |
1380.d |
1380d |
$4$ |
$6$ |
\( 2^{2} \cdot 3 \cdot 5 \cdot 23 \) |
\( - 2^{8} \cdot 3^{6} \cdot 5^{3} \cdot 23^{2} \) |
$0$ |
$\Z/6\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.8.0.1 |
2B, 3B.1.1 |
$1380$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$5$ |
$1008$ |
$0.622715$ |
$41957807024/48205125$ |
$0.90940$ |
$4.15018$ |
$[0, 1, 0, 460, -3612]$ |
\(y^2=x^3+x^2+460x-3612\) |
2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 20.6.0.a.1, 60.48.0-60.o.1.16, $\ldots$ |
$[]$ |
| 1380.e1 |
1380e1 |
1380.e |
1380e |
$1$ |
$1$ |
\( 2^{2} \cdot 3 \cdot 5 \cdot 23 \) |
\( - 2^{8} \cdot 3^{4} \cdot 5^{7} \cdot 23 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$230$ |
$2$ |
$0$ |
$0.033717503$ |
$1$ |
|
$16$ |
$1344$ |
$0.731775$ |
$-260956266496/145546875$ |
$0.96228$ |
$4.49632$ |
$[0, 1, 0, -845, 12975]$ |
\(y^2=x^3+x^2-845x+12975\) |
230.2.0.? |
$[(85, 750)]$ |
