| 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 |
| 1859.a1 |
1859b1 |
1859.a |
1859b |
$1$ |
$1$ |
\( 11 \cdot 13^{2} \) |
\( - 11 \cdot 13^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$22$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$672$ |
$0.592977$ |
$-262144/1859$ |
$0.89320$ |
$4.04510$ |
$[0, -1, 1, -225, -4665]$ |
\(y^2+y=x^3-x^2-225x-4665\) |
22.2.0.a.1 |
$[]$ |
| 1859.b1 |
1859a3 |
1859.b |
1859a |
$3$ |
$25$ |
\( 11 \cdot 13^{2} \) |
\( - 11 \cdot 13^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
25.60.0.2 |
5B.4.2 |
$7150$ |
$1200$ |
$37$ |
$32.12215141$ |
$1$ |
|
$0$ |
$10800$ |
$1.779184$ |
$-52893159101157376/11$ |
$1.09296$ |
$7.15970$ |
$[0, -1, 1, -1321636, -584371175]$ |
\(y^2+y=x^3-x^2-1321636x-584371175\) |
5.12.0.a.2, 22.2.0.a.1, 25.60.0.a.2, 65.24.0-5.a.2.1, 110.24.1.?, $\ldots$ |
$[(1158131342675917/51474, 39412566954338806189979/51474)]$ |
| 1859.b2 |
1859a2 |
1859.b |
1859a |
$3$ |
$25$ |
\( 11 \cdot 13^{2} \) |
\( - 11^{5} \cdot 13^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.60.0.1 |
5Cs.4.1 |
$7150$ |
$1200$ |
$37$ |
$6.424430282$ |
$1$ |
|
$0$ |
$2160$ |
$0.974464$ |
$-122023936/161051$ |
$1.01300$ |
$4.67567$ |
$[0, -1, 1, -1746, -50295]$ |
\(y^2+y=x^3-x^2-1746x-50295\) |
5.60.0.a.1, 22.2.0.a.1, 65.120.0-5.a.1.1, 110.120.5.?, 275.300.12.?, $\ldots$ |
$[(7045/6, 573985/6)]$ |
| 1859.b3 |
1859a1 |
1859.b |
1859a |
$3$ |
$25$ |
\( 11 \cdot 13^{2} \) |
\( - 11 \cdot 13^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
25.60.0.1 |
5B.4.1 |
$7150$ |
$1200$ |
$37$ |
$1.284886056$ |
$1$ |
|
$0$ |
$432$ |
$0.169746$ |
$-4096/11$ |
$0.82546$ |
$3.37914$ |
$[0, -1, 1, -56, 405]$ |
\(y^2+y=x^3-x^2-56x+405\) |
5.12.0.a.1, 22.2.0.a.1, 25.60.0.a.1, 65.24.0-5.a.1.1, 110.24.1.?, $\ldots$ |
$[(-3/2, 165/2)]$ |
