| 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 |
| 61009.a1 |
61009a2 |
61009.a |
61009a |
$2$ |
$19$ |
\( 13^{2} \cdot 19^{2} \) |
\( - 13^{6} \cdot 19^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-19})$ |
$-19$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$14.76988213$ |
$1$ |
|
$0$ |
$893760$ |
$2.404545$ |
$-884736$ |
$1.31757$ |
$5.04454$ |
$[0, 0, 1, -2318342, -1359997376]$ |
\(y^2+y=x^3-2318342x-1359997376\) |
|
$[(22534096/113, 9651213903/113)]$ |
| 61009.a2 |
61009a1 |
61009.a |
61009a |
$2$ |
$19$ |
\( 13^{2} \cdot 19^{2} \) |
\( - 13^{6} \cdot 19^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-19})$ |
$-19$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$0.777362217$ |
$1$ |
|
$4$ |
$47040$ |
$0.932326$ |
$-884736$ |
$1.31757$ |
$3.44122$ |
$[0, 0, 1, -6422, 198279]$ |
\(y^2+y=x^3-6422x+198279\) |
|
$[(39, 84)]$ |
| 61009.b1 |
61009b3 |
61009.b |
61009b |
$3$ |
$9$ |
\( 13^{2} \cdot 19^{2} \) |
\( - 13^{6} \cdot 19^{7} \) |
$2$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
27.36.0.1 |
3B |
$13338$ |
$1296$ |
$43$ |
$4.695009198$ |
$1$ |
|
$2$ |
$2332800$ |
$2.788132$ |
$-50357871050752/19$ |
$1.10495$ |
$5.86331$ |
$[0, -1, 1, -46936257, 123784336522]$ |
\(y^2+y=x^3-x^2-46936257x+123784336522\) |
3.4.0.a.1, 9.12.0.a.1, 27.36.0.a.1, 38.2.0.a.1, 78.8.0.?, $\ldots$ |
$[(320386/9, 30140/9), (98726/5, 91451/5)]$ |
| 61009.b2 |
61009b2 |
61009.b |
61009b |
$3$ |
$9$ |
\( 13^{2} \cdot 19^{2} \) |
\( - 13^{6} \cdot 19^{9} \) |
$2$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.36.0.2 |
3Cs |
$13338$ |
$1296$ |
$43$ |
$4.695009198$ |
$1$ |
|
$4$ |
$777600$ |
$2.238827$ |
$-89915392/6859$ |
$1.03310$ |
$4.67334$ |
$[0, -1, 1, -569417, 176136937]$ |
\(y^2+y=x^3-x^2-569417x+176136937\) |
3.12.0.a.1, 9.36.0.b.1, 38.2.0.a.1, 78.24.0.?, 114.24.1.?, $\ldots$ |
$[(127, 10288), (451, 3295)]$ |
| 61009.b3 |
61009b1 |
61009.b |
61009b |
$3$ |
$9$ |
\( 13^{2} \cdot 19^{2} \) |
\( - 13^{6} \cdot 19^{7} \) |
$2$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
27.36.0.1 |
3B |
$13338$ |
$1296$ |
$43$ |
$4.695009198$ |
$1$ |
|
$2$ |
$259200$ |
$1.689522$ |
$32768/19$ |
$1.31757$ |
$3.94359$ |
$[0, -1, 1, 40673, 125972]$ |
\(y^2+y=x^3-x^2+40673x+125972\) |
3.4.0.a.1, 9.12.0.a.1, 27.36.0.a.1, 38.2.0.a.1, 78.8.0.?, $\ldots$ |
$[(250/3, 30491/3), (-66/7, 91342/7)]$ |
