| 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 |
Intrinsic torsion order |
Weierstrass coefficients |
Weierstrass equation |
mod-$m$ images |
MW-generators |
Manin constant |
| 123969.a1 |
123969b1 |
123969.a |
123969b |
$1$ |
$1$ |
\( 3 \cdot 31^{2} \cdot 43 \) |
\( - 3^{3} \cdot 31^{8} \cdot 43 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$516$ |
$2$ |
$0$ |
$1.878469757$ |
$1$ |
|
$2$ |
$460800$ |
$1.556412$ |
$-912673/1115721$ |
$0.88159$ |
$3.57988$ |
$1$ |
$[1, 1, 1, -1942, 1513532]$ |
\(y^2+xy+y=x^3+x^2-1942x+1513532\) |
516.2.0.? |
$[(90, 1396)]$ |
$1$ |
| 123969.b1 |
123969c1 |
123969.b |
123969c |
$1$ |
$1$ |
\( 3 \cdot 31^{2} \cdot 43 \) |
\( - 3^{4} \cdot 31^{6} \cdot 43 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$86$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$239760$ |
$1.249880$ |
$-799178752/3483$ |
$0.95634$ |
$3.50539$ |
$1$ |
$[0, 1, 1, -18579, -984607]$ |
\(y^2+y=x^3+x^2-18579x-984607\) |
86.2.0.? |
$[ ]$ |
$1$ |
| 123969.c1 |
123969a4 |
123969.c |
123969a |
$4$ |
$4$ |
\( 3 \cdot 31^{2} \cdot 43 \) |
\( 3^{12} \cdot 31^{6} \cdot 43 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$31992$ |
$48$ |
$0$ |
$43.20188693$ |
$1$ |
|
$0$ |
$864000$ |
$1.933821$ |
$1616855892553/22851963$ |
$1.05806$ |
$4.15385$ |
$2$ |
$[1, 1, 0, -234984, -43402887]$ |
\(y^2+xy=x^3+x^2-234984x-43402887\) |
2.3.0.a.1, 4.6.0.c.1, 24.12.0.z.1, 124.12.0.?, 172.12.0.?, $\ldots$ |
$[(161080372755087674431/255599550, 1981411752119549603873264915021/255599550)]$ |
$1$ |
| 123969.c2 |
123969a2 |
123969.c |
123969a |
$4$ |
$4$ |
\( 3 \cdot 31^{2} \cdot 43 \) |
\( 3^{6} \cdot 31^{6} \cdot 43^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.6.0.1 |
2Cs |
$15996$ |
$48$ |
$0$ |
$21.60094346$ |
$1$ |
|
$2$ |
$432000$ |
$1.587248$ |
$2845178713/1347921$ |
$0.95310$ |
$3.61303$ |
$1$ |
$[1, 1, 0, -28369, 771400]$ |
\(y^2+xy=x^3+x^2-28369x+771400\) |
2.6.0.a.1, 12.12.0.b.1, 124.12.0.?, 172.12.0.?, 372.24.0.?, $\ldots$ |
$[(72699782231/5450, 19362926544520279/5450)]$ |
$1$ |
| 123969.c3 |
123969a1 |
123969.c |
123969a |
$4$ |
$4$ |
\( 3 \cdot 31^{2} \cdot 43 \) |
\( 3^{3} \cdot 31^{6} \cdot 43 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$31992$ |
$48$ |
$0$ |
$10.80047173$ |
$1$ |
|
$1$ |
$216000$ |
$1.240673$ |
$1630532233/1161$ |
$0.91317$ |
$3.56556$ |
$2$ |
$[1, 1, 0, -23564, 1381635]$ |
\(y^2+xy=x^3+x^2-23564x+1381635\) |
2.3.0.a.1, 4.6.0.c.1, 24.12.0.z.1, 248.12.0.?, 258.6.0.?, $\ldots$ |
$[(1529494/25, 1869296297/25)]$ |
$1$ |
| 123969.c4 |
123969a3 |
123969.c |
123969a |
$4$ |
$4$ |
\( 3 \cdot 31^{2} \cdot 43 \) |
\( - 3^{3} \cdot 31^{6} \cdot 43^{4} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$31992$ |
$48$ |
$0$ |
$10.80047173$ |
$1$ |
|
$0$ |
$864000$ |
$1.933821$ |
$129784785047/92307627$ |
$0.98681$ |
$3.93877$ |
$2$ |
$[1, 1, 0, 101366, 5986747]$ |
\(y^2+xy=x^3+x^2+101366x+5986747\) |
2.3.0.a.1, 4.6.0.c.1, 6.6.0.a.1, 12.12.0.g.1, 124.12.0.?, $\ldots$ |
$[(17545574/193, 88820833955/193)]$ |
$1$ |
