| 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 |
| 231.a1 |
231a5 |
231.a |
231a |
$6$ |
$8$ |
\( 3 \cdot 7 \cdot 11 \) |
\( 3^{8} \cdot 7 \cdot 11^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.24.0.55 |
2B |
$3696$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$160$ |
$0.622790$ |
$10206027697760497/5557167$ |
$1.00022$ |
$6.77305$ |
$[1, 1, 1, -4519, -118810]$ |
\(y^2+xy+y=x^3+x^2-4519x-118810\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 28.24.0-28.h.1.1, 48.48.0-48.e.2.7, $\ldots$ |
$[]$ |
| 231.a2 |
231a3 |
231.a |
231a |
$6$ |
$8$ |
\( 3 \cdot 7 \cdot 11 \) |
\( 3^{4} \cdot 7^{2} \cdot 11^{4} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
4.24.0.6 |
2Cs |
$1848$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$2$ |
$80$ |
$0.276217$ |
$2533811507137/58110129$ |
$0.95470$ |
$5.24780$ |
$[1, 1, 1, -284, -1924]$ |
\(y^2+xy+y=x^3+x^2-284x-1924\) |
2.6.0.a.1, 4.24.0-4.b.1.1, 24.48.0-24.i.1.3, 28.48.0-28.c.1.3, 88.48.0.?, $\ldots$ |
$[]$ |
| 231.a3 |
231a2 |
231.a |
231a |
$6$ |
$8$ |
\( 3 \cdot 7 \cdot 11 \) |
\( 3^{2} \cdot 7^{4} \cdot 11^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
4.24.0.5 |
2Cs |
$1848$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$6$ |
$40$ |
$-0.070357$ |
$6570725617/2614689$ |
$0.92677$ |
$4.15365$ |
$[1, 1, 1, -39, 36]$ |
\(y^2+xy+y=x^3+x^2-39x+36\) |
2.6.0.a.1, 4.24.0-4.b.1.3, 24.48.0-24.i.2.9, 56.48.0-56.m.1.10, 88.48.0.?, $\ldots$ |
$[]$ |
| 231.a4 |
231a1 |
231.a |
231a |
$6$ |
$8$ |
\( 3 \cdot 7 \cdot 11 \) |
\( 3 \cdot 7^{2} \cdot 11 \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.24.0.45 |
2B |
$3696$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$3$ |
$20$ |
$-0.416931$ |
$4354703137/1617$ |
$0.90109$ |
$4.07806$ |
$[1, 1, 1, -34, 62]$ |
\(y^2+xy+y=x^3+x^2-34x+62\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 48.48.0-48.e.1.7, 66.6.0.a.1, $\ldots$ |
$[]$ |
| 231.a5 |
231a6 |
231.a |
231a |
$6$ |
$8$ |
\( 3 \cdot 7 \cdot 11 \) |
\( - 3^{2} \cdot 7 \cdot 11^{8} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.24.0.55 |
2B |
$3696$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$160$ |
$0.622790$ |
$3288008303/13504609503$ |
$1.06765$ |
$5.65574$ |
$[1, 1, 1, 31, -5578]$ |
\(y^2+xy+y=x^3+x^2+31x-5578\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 14.6.0.b.1, 24.48.0-24.bz.2.11, $\ldots$ |
$[]$ |
| 231.a6 |
231a4 |
231.a |
231a |
$6$ |
$8$ |
\( 3 \cdot 7 \cdot 11 \) |
\( - 3 \cdot 7^{8} \cdot 11 \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.24.0.45 |
2B |
$3696$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$2$ |
$80$ |
$0.276217$ |
$221115865823/190238433$ |
$0.96278$ |
$4.79970$ |
$[1, 1, 1, 126, 432]$ |
\(y^2+xy+y=x^3+x^2+126x+432\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 24.48.0-24.bz.1.3, 88.48.0.?, $\ldots$ |
$[]$ |
