| 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 |
| 285.a1 |
285a2 |
285.a |
285a |
$2$ |
$2$ |
\( 3 \cdot 5 \cdot 19 \) |
\( 3^{10} \cdot 5^{2} \cdot 19 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
2.3.0.1 |
2B |
$1140$ |
$12$ |
$0$ |
$0.134827177$ |
$1$ |
|
$14$ |
$80$ |
$0.118643$ |
$48587168449/28048275$ |
$1.03180$ |
$4.35324$ |
$[1, 0, 0, -76, -19]$ |
\(y^2+xy=x^3-76x-19\) |
2.3.0.a.1, 60.6.0.c.1, 76.6.0.?, 1140.12.0.? |
$[(-7, 17)]$ |
| 285.a2 |
285a1 |
285.a |
285a |
$2$ |
$2$ |
\( 3 \cdot 5 \cdot 19 \) |
\( - 3^{5} \cdot 5 \cdot 19^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
2.3.0.1 |
2B |
$1140$ |
$12$ |
$0$ |
$0.269654355$ |
$1$ |
|
$11$ |
$40$ |
$-0.227931$ |
$756058031/438615$ |
$1.00322$ |
$3.61675$ |
$[1, 0, 0, 19, 0]$ |
\(y^2+xy=x^3+19x\) |
2.3.0.a.1, 30.6.0.a.1, 76.6.0.?, 1140.12.0.? |
$[(1, 4)]$ |
| 285.b1 |
285b2 |
285.b |
285b |
$2$ |
$2$ |
\( 3 \cdot 5 \cdot 19 \) |
\( 3^{2} \cdot 5^{6} \cdot 19 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
2.3.0.1 |
2B |
$1140$ |
$12$ |
$0$ |
$1.050691831$ |
$1$ |
|
$4$ |
$48$ |
$0.010340$ |
$90458382169/2671875$ |
$1.09032$ |
$4.46319$ |
$[1, 1, 0, -93, -378]$ |
\(y^2+xy=x^3+x^2-93x-378\) |
2.3.0.a.1, 60.6.0.c.1, 76.6.0.?, 1140.12.0.? |
$[(-6, 6)]$ |
| 285.b2 |
285b1 |
285.b |
285b |
$2$ |
$2$ |
\( 3 \cdot 5 \cdot 19 \) |
\( - 3 \cdot 5^{3} \cdot 19^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
2.3.0.1 |
2B |
$1140$ |
$12$ |
$0$ |
$2.101383662$ |
$1$ |
|
$3$ |
$24$ |
$-0.336234$ |
$357911/135375$ |
$0.95197$ |
$3.40894$ |
$[1, 1, 0, 2, -17]$ |
\(y^2+xy=x^3+x^2+2x-17\) |
2.3.0.a.1, 30.6.0.a.1, 76.6.0.?, 1140.12.0.? |
$[(6, 13)]$ |
| 285.c1 |
285c3 |
285.c |
285c |
$4$ |
$4$ |
\( 3 \cdot 5 \cdot 19 \) |
\( 3^{2} \cdot 5^{3} \cdot 19^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
4.12.0.8 |
2B |
$760$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$288$ |
$0.754139$ |
$23977812996389881/146611125$ |
$1.09826$ |
$6.67244$ |
$[1, 1, 0, -6007, -181724]$ |
\(y^2+xy=x^3+x^2-6007x-181724\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 10.6.0.a.1, 20.24.0-20.g.1.1, 152.24.0.?, $\ldots$ |
$[]$ |
| 285.c2 |
285c4 |
285.c |
285c |
$4$ |
$4$ |
\( 3 \cdot 5 \cdot 19 \) |
\( 3^{2} \cdot 5^{12} \cdot 19 \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
4.12.0.7 |
2B |
$760$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$288$ |
$0.754139$ |
$209595169258201/41748046875$ |
$0.98100$ |
$5.83393$ |
$[1, 1, 0, -1237, 13054]$ |
\(y^2+xy=x^3+x^2-1237x+13054\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 40.24.0-40.z.1.4, 76.24.0.?, 760.48.0.? |
$[]$ |
| 285.c3 |
285c2 |
285.c |
285c |
$4$ |
$4$ |
\( 3 \cdot 5 \cdot 19 \) |
\( 3^{4} \cdot 5^{6} \cdot 19^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
4.12.0.1 |
2Cs |
$380$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$144$ |
$0.407565$ |
$6189976379881/456890625$ |
$0.95560$ |
$5.21079$ |
$[1, 1, 0, -382, -2849]$ |
\(y^2+xy=x^3+x^2-382x-2849\) |
2.6.0.a.1, 4.12.0-2.a.1.1, 20.24.0-20.b.1.2, 76.24.0.?, 380.48.0.? |
$[]$ |
| 285.c4 |
285c1 |
285.c |
285c |
$4$ |
$4$ |
\( 3 \cdot 5 \cdot 19 \) |
\( - 3^{8} \cdot 5^{3} \cdot 19 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.12.0.6 |
2B |
$760$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$72$ |
$0.060992$ |
$1256216039/15582375$ |
$0.94875$ |
$4.24036$ |
$[1, 1, 0, 23, -176]$ |
\(y^2+xy=x^3+x^2+23x-176\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 20.12.0-4.c.1.2, 40.24.0-40.z.1.10, $\ldots$ |
$[]$ |
