| 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 |
| 275.a1 |
275a4 |
275.a |
275a |
$4$ |
$4$ |
\( 5^{2} \cdot 11 \) |
\( 5^{10} \cdot 11 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.6 |
2B |
$440$ |
$48$ |
$0$ |
$0.596122623$ |
$1$ |
|
$8$ |
$96$ |
$0.519053$ |
$22930509321/6875$ |
$1.07717$ |
$5.96648$ |
$[1, -1, 1, -1480, 22272]$ |
\(y^2+xy+y=x^3-x^2-1480x+22272\) |
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, $\ldots$ |
$[(24, 0)]$ |
| 275.a2 |
275a3 |
275.a |
275a |
$4$ |
$4$ |
\( 5^{2} \cdot 11 \) |
\( 5^{7} \cdot 11^{4} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.8 |
2B |
$440$ |
$48$ |
$0$ |
$0.596122623$ |
$1$ |
|
$6$ |
$96$ |
$0.519053$ |
$2749884201/73205$ |
$0.94591$ |
$5.58888$ |
$[1, -1, 1, -730, -7228]$ |
\(y^2+xy+y=x^3-x^2-730x-7228\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 10.6.0.a.1, 20.24.0-20.g.1.1, 88.24.0.?, $\ldots$ |
$[(-16, 20)]$ |
| 275.a3 |
275a2 |
275.a |
275a |
$4$ |
$4$ |
\( 5^{2} \cdot 11 \) |
\( 5^{8} \cdot 11^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.1 |
2Cs |
$220$ |
$48$ |
$0$ |
$1.192245246$ |
$1$ |
|
$8$ |
$48$ |
$0.172480$ |
$8120601/3025$ |
$1.05560$ |
$4.55182$ |
$[1, -1, 1, -105, 272]$ |
\(y^2+xy+y=x^3-x^2-105x+272\) |
2.6.0.a.1, 4.12.0-2.a.1.1, 20.24.0-20.b.1.2, 44.24.0-44.a.1.3, 220.48.0.? |
$[(0, 16)]$ |
| 275.a4 |
275a1 |
275.a |
275a |
$4$ |
$4$ |
\( 5^{2} \cdot 11 \) |
\( - 5^{7} \cdot 11 \) |
$1$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.7 |
2B |
$440$ |
$48$ |
$0$ |
$2.384490492$ |
$1$ |
|
$7$ |
$24$ |
$-0.174094$ |
$59319/55$ |
$0.79207$ |
$3.67601$ |
$[1, -1, 1, 20, 22]$ |
\(y^2+xy+y=x^3-x^2+20x+22\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 40.24.0-40.z.1.4, 88.24.0.?, 110.6.0.?, $\ldots$ |
$[(8, 21)]$ |
| 275.b1 |
275b3 |
275.b |
275b |
$3$ |
$25$ |
\( 5^{2} \cdot 11 \) |
\( - 5^{6} \cdot 11 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
25.120.0.4 |
5B.1.3 |
$550$ |
$1200$ |
$37$ |
$1$ |
$25$ |
$5$ |
$0$ |
$700$ |
$1.301428$ |
$-52893159101157376/11$ |
$1.09296$ |
$8.57498$ |
$[0, 1, 1, -195508, -33338481]$ |
\(y^2+y=x^3+x^2-195508x-33338481\) |
5.24.0-5.a.2.1, 22.2.0.a.1, 25.120.0-25.a.2.1, 110.48.1.?, 275.600.12.?, $\ldots$ |
$[]$ |
| 275.b2 |
275b2 |
275.b |
275b |
$3$ |
$25$ |
\( 5^{2} \cdot 11 \) |
\( - 5^{6} \cdot 11^{5} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.120.0.2 |
5Cs.1.3 |
$550$ |
$1200$ |
$37$ |
$1$ |
$1$ |
|
$0$ |
$140$ |
$0.496709$ |
$-122023936/161051$ |
$1.01300$ |
$5.24579$ |
$[0, 1, 1, -258, -2981]$ |
\(y^2+y=x^3+x^2-258x-2981\) |
5.120.0-5.a.1.1, 22.2.0.a.1, 110.240.5.?, 275.600.12.?, 550.1200.37.? |
$[]$ |
| 275.b3 |
275b1 |
275.b |
275b |
$3$ |
$25$ |
\( 5^{2} \cdot 11 \) |
\( - 5^{6} \cdot 11 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
25.120.0.2 |
5B.1.4 |
$550$ |
$1200$ |
$37$ |
$1$ |
$1$ |
|
$0$ |
$28$ |
$-0.308010$ |
$-4096/11$ |
$0.82546$ |
$3.50813$ |
$[0, 1, 1, -8, 19]$ |
\(y^2+y=x^3+x^2-8x+19\) |
5.24.0-5.a.1.1, 22.2.0.a.1, 25.120.0-25.a.1.1, 110.48.1.?, 275.600.12.?, $\ldots$ |
$[]$ |
