| 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 |
| 2233.a1 |
2233a4 |
2233.a |
2233a |
$4$ |
$4$ |
\( 7 \cdot 11 \cdot 29 \) |
\( 7^{3} \cdot 11^{8} \cdot 29 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.12.0.6 |
2B |
$1624$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$5376$ |
$1.387524$ |
$16798320881842096017/2132227789307$ |
$0.97557$ |
$5.74079$ |
$[1, -1, 1, -53356, 4756540]$ |
\(y^2+xy+y=x^3-x^2-53356x+4756540\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 28.12.0-4.c.1.1, 56.24.0-56.z.1.10, $\ldots$ |
$[]$ |
| 2233.a2 |
2233a3 |
2233.a |
2233a |
$4$ |
$4$ |
\( 7 \cdot 11 \cdot 29 \) |
\( 7^{12} \cdot 11^{2} \cdot 29 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
4.12.0.8 |
2B |
$1624$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$5376$ |
$1.387524$ |
$1048626554636928177/48569076788309$ |
$0.99097$ |
$5.38107$ |
$[1, -1, 1, -21166, -1131504]$ |
\(y^2+xy+y=x^3-x^2-21166x-1131504\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 56.24.0-56.z.1.12, 58.6.0.a.1, 116.24.0.?, $\ldots$ |
$[]$ |
| 2233.a3 |
2233a2 |
2233.a |
2233a |
$4$ |
$4$ |
\( 7 \cdot 11 \cdot 29 \) |
\( 7^{6} \cdot 11^{4} \cdot 29^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
4.12.0.1 |
2Cs |
$812$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$2688$ |
$1.040949$ |
$5249244962308257/1448621666569$ |
$0.97197$ |
$4.69412$ |
$[1, -1, 1, -3621, 61556]$ |
\(y^2+xy+y=x^3-x^2-3621x+61556\) |
2.6.0.a.1, 4.12.0-2.a.1.1, 28.24.0-28.b.1.1, 116.24.0.?, 812.48.0.? |
$[]$ |
| 2233.a4 |
2233a1 |
2233.a |
2233a |
$4$ |
$4$ |
\( 7 \cdot 11 \cdot 29 \) |
\( - 7^{3} \cdot 11^{2} \cdot 29^{4} \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
4.12.0.7 |
2B |
$1624$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$3$ |
$1344$ |
$0.694376$ |
$22062729659823/29354283343$ |
$0.91629$ |
$4.01844$ |
$[1, -1, 1, 584, 6050]$ |
\(y^2+xy+y=x^3-x^2+584x+6050\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 14.6.0.b.1, 28.24.0-28.g.1.2, 232.24.0.?, $\ldots$ |
$[]$ |
| 2233.b1 |
2233b1 |
2233.b |
2233b |
$2$ |
$3$ |
\( 7 \cdot 11 \cdot 29 \) |
\( - 7 \cdot 11^{2} \cdot 29^{3} \) |
$1$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
3.8.0.1 |
3B.1.1 |
$1218$ |
$16$ |
$0$ |
$2.325469379$ |
$1$ |
|
$4$ |
$336$ |
$0.103075$ |
$-28094464000/20657483$ |
$0.84860$ |
$3.22637$ |
$[0, 1, 1, -63, 271]$ |
\(y^2+y=x^3+x^2-63x+271\) |
3.8.0-3.a.1.2, 406.2.0.?, 1218.16.0.? |
$[(31, 170)]$ |
| 2233.b2 |
2233b2 |
2233.b |
2233b |
$2$ |
$3$ |
\( 7 \cdot 11 \cdot 29 \) |
\( - 7^{3} \cdot 11^{6} \cdot 29 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
3.8.0.2 |
3B.1.2 |
$1218$ |
$16$ |
$0$ |
$0.775156459$ |
$1$ |
|
$4$ |
$1008$ |
$0.652381$ |
$15252992000000/17621717267$ |
$0.97270$ |
$3.93664$ |
$[0, 1, 1, 517, -4340]$ |
\(y^2+y=x^3+x^2+517x-4340\) |
3.8.0-3.a.1.1, 406.2.0.?, 1218.16.0.? |
$[(278, 4658)]$ |
