| 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 |
| 175.a1 |
175a2 |
175.a |
175a |
$2$ |
$5$ |
\( 5^{2} \cdot 7 \) |
\( - 5^{3} \cdot 7^{5} \) |
$1$ |
$\Z/5\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.24.0.1 |
5B.1.1 |
$70$ |
$48$ |
$1$ |
$0.664629997$ |
$1$ |
|
$14$ |
$40$ |
$0.054193$ |
$-2887553024/16807$ |
$0.98803$ |
$5.15452$ |
$[0, -1, 1, -148, 748]$ |
\(y^2+y=x^3-x^2-148x+748\) |
5.24.0-5.a.1.2, 70.48.1-70.d.1.4 |
$[(7, 2)]$ |
| 175.a2 |
175a1 |
175.a |
175a |
$2$ |
$5$ |
\( 5^{2} \cdot 7 \) |
\( - 5^{3} \cdot 7 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.24.0.3 |
5B.1.2 |
$70$ |
$48$ |
$1$ |
$0.132925999$ |
$1$ |
|
$10$ |
$8$ |
$-0.750526$ |
$4096/7$ |
$0.98030$ |
$2.67494$ |
$[0, -1, 1, 2, -2]$ |
\(y^2+y=x^3-x^2+2x-2\) |
5.24.0-5.a.2.2, 70.48.1-70.d.2.4 |
$[(2, 2)]$ |
| 175.b1 |
175b3 |
175.b |
175b |
$3$ |
$9$ |
\( 5^{2} \cdot 7 \) |
\( - 5^{15} \cdot 7 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.12.0.1 |
3B |
$630$ |
$144$ |
$3$ |
$0.833160004$ |
$1$ |
|
$4$ |
$144$ |
$0.932181$ |
$-250523582464/13671875$ |
$1.02112$ |
$6.96903$ |
$[0, -1, 1, -3283, -74657]$ |
\(y^2+y=x^3-x^2-3283x-74657\) |
3.4.0.a.1, 9.12.0.a.1, 15.8.0-3.a.1.1, 42.8.0-3.a.1.1, 45.24.0-9.a.1.2, $\ldots$ |
$[(397, 7812)]$ |
| 175.b2 |
175b1 |
175.b |
175b |
$3$ |
$9$ |
\( 5^{2} \cdot 7 \) |
\( - 5^{7} \cdot 7 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.12.0.1 |
3B |
$630$ |
$144$ |
$3$ |
$0.092573333$ |
$1$ |
|
$8$ |
$16$ |
$-0.166431$ |
$-262144/35$ |
$0.88715$ |
$4.32561$ |
$[0, -1, 1, -33, 93]$ |
\(y^2+y=x^3-x^2-33x+93\) |
3.4.0.a.1, 9.12.0.a.1, 15.8.0-3.a.1.2, 42.8.0-3.a.1.2, 45.24.0-9.a.1.1, $\ldots$ |
$[(-3, 12)]$ |
| 175.b3 |
175b2 |
175.b |
175b |
$3$ |
$9$ |
\( 5^{2} \cdot 7 \) |
\( - 5^{9} \cdot 7^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.12.0.1 |
3Cs |
$630$ |
$144$ |
$3$ |
$0.277720001$ |
$1$ |
|
$6$ |
$48$ |
$0.382875$ |
$71991296/42875$ |
$1.06493$ |
$5.37267$ |
$[0, -1, 1, 217, -282]$ |
\(y^2+y=x^3-x^2+217x-282\) |
3.12.0.a.1, 15.24.0-3.a.1.1, 42.24.0-3.a.1.1, 63.36.0.b.1, 70.2.0.a.1, $\ldots$ |
$[(12, 62)]$ |
| 175.c1 |
175c2 |
175.c |
175c |
$2$ |
$5$ |
\( 5^{2} \cdot 7 \) |
\( - 5^{9} \cdot 7^{5} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.24.0.2 |
5B.1.4 |
$70$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$200$ |
$0.858912$ |
$-2887553024/16807$ |
$0.98803$ |
$7.02423$ |
$[0, 1, 1, -3708, 86119]$ |
\(y^2+y=x^3+x^2-3708x+86119\) |
5.24.0-5.a.1.1, 70.48.1-70.d.1.2 |
$[]$ |
| 175.c2 |
175c1 |
175.c |
175c |
$2$ |
$5$ |
\( 5^{2} \cdot 7 \) |
\( - 5^{9} \cdot 7 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.24.0.4 |
5B.1.3 |
$70$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$40$ |
$0.054193$ |
$4096/7$ |
$0.98030$ |
$4.54465$ |
$[0, 1, 1, 42, -131]$ |
\(y^2+y=x^3+x^2+42x-131\) |
5.24.0-5.a.2.1, 70.48.1-70.d.2.3 |
$[]$ |
