| 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 |
| 862.a1 |
862b1 |
862.a |
862b |
$1$ |
$1$ |
\( 2 \cdot 431 \) |
\( - 2^{6} \cdot 431 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$862$ |
$2$ |
$0$ |
$0.142026780$ |
$1$ |
|
$8$ |
$192$ |
$-0.212900$ |
$-38238692409/27584$ |
$0.88652$ |
$3.60518$ |
$[1, -1, 0, -70, 244]$ |
\(y^2+xy=x^3-x^2-70x+244\) |
862.2.0.? |
$[(4, 2)]$ |
| 862.b1 |
862a1 |
862.b |
862a |
$1$ |
$1$ |
\( 2 \cdot 431 \) |
\( - 2^{2} \cdot 431 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$862$ |
$2$ |
$0$ |
$0.398868295$ |
$1$ |
|
$4$ |
$32$ |
$-0.696661$ |
$357911/1724$ |
$0.76407$ |
$2.18650$ |
$[1, 0, 1, 1, -2]$ |
\(y^2+xy+y=x^3+x-2\) |
862.2.0.? |
$[(1, 0)]$ |
| 862.c1 |
862f1 |
862.c |
862f |
$1$ |
$1$ |
\( 2 \cdot 431 \) |
\( - 2^{8} \cdot 431 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$862$ |
$2$ |
$0$ |
$0.119218691$ |
$1$ |
|
$8$ |
$128$ |
$-0.352928$ |
$-912673/110336$ |
$0.86812$ |
$2.82143$ |
$[1, 1, 1, -2, 15]$ |
\(y^2+xy+y=x^3+x^2-2x+15\) |
862.2.0.? |
$[(1, 3)]$ |
| 862.d1 |
862e1 |
862.d |
862e |
$2$ |
$5$ |
\( 2 \cdot 431 \) |
\( - 2^{20} \cdot 431 \) |
$1$ |
$\Z/5\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$5$ |
5.24.0.1 |
5B.1.1 |
$4310$ |
$48$ |
$1$ |
$2.137778577$ |
$1$ |
|
$10$ |
$640$ |
$0.643229$ |
$-1646417855125441/451936256$ |
$0.94554$ |
$5.18369$ |
$[1, 1, 1, -2460, 45949]$ |
\(y^2+xy+y=x^3+x^2-2460x+45949\) |
5.24.0-5.a.1.2, 862.2.0.?, 4310.48.1.? |
$[(23, 35)]$ |
| 862.d2 |
862e2 |
862.d |
862e |
$2$ |
$5$ |
\( 2 \cdot 431 \) |
\( - 2^{4} \cdot 431^{5} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$5$ |
5.24.0.3 |
5B.1.2 |
$4310$ |
$48$ |
$1$ |
$0.427555715$ |
$1$ |
|
$0$ |
$3200$ |
$1.447948$ |
$402337908227545919/237961300338416$ |
$1.02084$ |
$5.99712$ |
$[1, 1, 1, 15380, -102531]$ |
\(y^2+xy+y=x^3+x^2+15380x-102531\) |
5.24.0-5.a.2.2, 862.2.0.?, 4310.48.1.? |
$[(3127/3, 181057/3)]$ |
| 862.e1 |
862c2 |
862.e |
862c |
$2$ |
$2$ |
\( 2 \cdot 431 \) |
\( 2^{3} \cdot 431^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.6.0.6 |
2B |
$3448$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$108$ |
$-0.114383$ |
$4227952113/1486088$ |
$1.02426$ |
$3.27920$ |
$[1, -1, 1, -34, -39]$ |
\(y^2+xy+y=x^3-x^2-34x-39\) |
2.3.0.a.1, 8.6.0.b.1, 1724.6.0.?, 3448.12.0.? |
$[]$ |
| 862.e2 |
862c1 |
862.e |
862c |
$2$ |
$2$ |
\( 2 \cdot 431 \) |
\( - 2^{6} \cdot 431 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.6.0.1 |
2B |
$3448$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$54$ |
$-0.460957$ |
$27818127/27584$ |
$0.87279$ |
$2.53596$ |
$[1, -1, 1, 6, -7]$ |
\(y^2+xy+y=x^3-x^2+6x-7\) |
2.3.0.a.1, 8.6.0.c.1, 862.6.0.?, 3448.12.0.? |
$[]$ |
| 862.f1 |
862d2 |
862.f |
862d |
$2$ |
$3$ |
\( 2 \cdot 431 \) |
\( - 2^{4} \cdot 431^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
3.8.0.2 |
3B.1.2 |
$2586$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$432$ |
$0.427968$ |
$-41314084993/1281007856$ |
$0.94098$ |
$4.20817$ |
$[1, 0, 0, -72, -1744]$ |
\(y^2+xy=x^3-72x-1744\) |
3.8.0-3.a.1.1, 862.2.0.?, 2586.16.0.? |
$[]$ |
| 862.f2 |
862d1 |
862.f |
862d |
$2$ |
$3$ |
\( 2 \cdot 431 \) |
\( - 2^{12} \cdot 431 \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
3.8.0.1 |
3B.1.1 |
$2586$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$144$ |
$-0.121338$ |
$56181887/1765376$ |
$0.88358$ |
$3.22817$ |
$[1, 0, 0, 8, 64]$ |
\(y^2+xy=x^3+8x+64\) |
3.8.0-3.a.1.2, 862.2.0.?, 2586.16.0.? |
$[]$ |
