| 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 |
| 53371.a1 |
53371b1 |
53371.a |
53371b |
$1$ |
$1$ |
\( 19 \cdot 53^{2} \) |
\( - 19^{3} \cdot 53^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$38$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$775008$ |
$2.071053$ |
$25102282752/19266931$ |
$0.88962$ |
$4.38841$ |
$[0, 0, 1, 171349, -15594866]$ |
\(y^2+y=x^3+171349x-15594866\) |
38.2.0.a.1 |
$[]$ |
| 53371.b1 |
53371a3 |
53371.b |
53371a |
$3$ |
$9$ |
\( 19 \cdot 53^{2} \) |
\( - 19 \cdot 53^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
27.36.0.1 |
3B |
$54378$ |
$1296$ |
$43$ |
$36.37381481$ |
$1$ |
|
$0$ |
$432432$ |
$2.018585$ |
$-50357871050752/19$ |
$1.10495$ |
$5.08698$ |
$[0, -1, 1, -2161057, -1222057453]$ |
\(y^2+y=x^3-x^2-2161057x-1222057453\) |
3.4.0.a.1, 9.12.0.a.1, 27.36.0.a.1, 38.2.0.a.1, 114.8.0.?, $\ldots$ |
$[(230411945527579281/10946089, 54549308864490039357867145/10946089)]$ |
| 53371.b2 |
53371a2 |
53371.b |
53371a |
$3$ |
$9$ |
\( 19 \cdot 53^{2} \) |
\( - 19^{3} \cdot 53^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.36.0.2 |
3Cs |
$54378$ |
$1296$ |
$43$ |
$12.12460493$ |
$1$ |
|
$0$ |
$144144$ |
$1.469278$ |
$-89915392/6859$ |
$1.03310$ |
$3.88239$ |
$[0, -1, 1, -26217, -1729538]$ |
\(y^2+y=x^3-x^2-26217x-1729538\) |
3.12.0.a.1, 9.36.0.b.1, 38.2.0.a.1, 114.24.1.?, 159.24.0.?, $\ldots$ |
$[(9212228/77, 27792637118/77)]$ |
| 53371.b3 |
53371a1 |
53371.b |
53371a |
$3$ |
$9$ |
\( 19 \cdot 53^{2} \) |
\( - 19 \cdot 53^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
27.36.0.1 |
3B |
$54378$ |
$1296$ |
$43$ |
$4.041534979$ |
$1$ |
|
$0$ |
$48048$ |
$0.919972$ |
$32768/19$ |
$1.31757$ |
$3.14367$ |
$[0, -1, 1, 1873, -2003]$ |
\(y^2+y=x^3-x^2+1873x-2003\) |
3.4.0.a.1, 9.12.0.a.1, 27.36.0.a.1, 38.2.0.a.1, 114.8.0.?, $\ldots$ |
$[(1465/7, 96739/7)]$ |
