| 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 |
| 53816.a1 |
53816a2 |
53816.a |
53816a |
$2$ |
$2$ |
\( 2^{3} \cdot 7 \cdot 31^{2} \) |
\( 2^{11} \cdot 7^{2} \cdot 31^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.6 |
2B |
$56$ |
$12$ |
$0$ |
$1.851949677$ |
$1$ |
|
$3$ |
$241920$ |
$1.482325$ |
$3543122/49$ |
$1.08036$ |
$3.97574$ |
$[0, 1, 0, -38760, 2888944]$ |
\(y^2=x^3+x^2-38760x+2888944\) |
2.3.0.a.1, 8.6.0.b.1, 28.6.0.c.1, 56.12.0.k.1 |
$[(-21, 1922)]$ |
| 53816.a2 |
53816a1 |
53816.a |
53816a |
$2$ |
$2$ |
\( 2^{3} \cdot 7 \cdot 31^{2} \) |
\( - 2^{10} \cdot 7 \cdot 31^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.1 |
2B |
$56$ |
$12$ |
$0$ |
$3.703899354$ |
$1$ |
|
$3$ |
$120960$ |
$1.135752$ |
$-4/7$ |
$1.03482$ |
$3.39073$ |
$[0, 1, 0, -320, 121264]$ |
\(y^2=x^3+x^2-320x+121264\) |
2.3.0.a.1, 8.6.0.c.1, 14.6.0.b.1, 56.12.0.n.1 |
$[(76, 736)]$ |
| 53816.b1 |
53816d1 |
53816.b |
53816d |
$1$ |
$1$ |
\( 2^{3} \cdot 7 \cdot 31^{2} \) |
\( - 2^{11} \cdot 7 \cdot 31^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$1736$ |
$2$ |
$0$ |
$3.141364770$ |
$1$ |
|
$0$ |
$122880$ |
$1.479591$ |
$-2/217$ |
$0.91686$ |
$3.76957$ |
$[0, -1, 0, -320, -955412]$ |
\(y^2=x^3-x^2-320x-955412\) |
1736.2.0.? |
$[(1057/3, 21142/3)]$ |
| 53816.c1 |
53816b2 |
53816.c |
53816b |
$2$ |
$2$ |
\( 2^{3} \cdot 7 \cdot 31^{2} \) |
\( 2^{10} \cdot 7^{5} \cdot 31^{12} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$868$ |
$12$ |
$0$ |
$44.91956532$ |
$1$ |
|
$1$ |
$11980800$ |
$3.688000$ |
$4575904097608151172/14916274366567$ |
$1.08678$ |
$6.47210$ |
$[0, 0, 0, -335022859, 2353602742038]$ |
\(y^2=x^3-335022859x+2353602742038\) |
2.3.0.a.1, 28.6.0.a.1, 124.6.0.?, 868.12.0.? |
$[(92965195265967387099/37136245, 866251388630856214834817786868/37136245)]$ |
| 53816.c2 |
53816b1 |
53816.c |
53816b |
$2$ |
$2$ |
\( 2^{3} \cdot 7 \cdot 31^{2} \) |
\( - 2^{8} \cdot 7^{10} \cdot 31^{9} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$868$ |
$12$ |
$0$ |
$22.45978266$ |
$1$ |
|
$1$ |
$5990400$ |
$3.341427$ |
$-839504640199248/8415220142959$ |
$1.02115$ |
$5.82201$ |
$[0, 0, 0, -11992319, 68420095970]$ |
\(y^2=x^3-11992319x+68420095970\) |
2.3.0.a.1, 28.6.0.b.1, 62.6.0.b.1, 868.12.0.? |
$[(-224874581963/7361, 86199562096579430/7361)]$ |
| 53816.d1 |
53816c4 |
53816.d |
53816c |
$4$ |
$4$ |
\( 2^{3} \cdot 7 \cdot 31^{2} \) |
\( 2^{11} \cdot 7 \cdot 31^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.9 |
2B |
$1736$ |
$48$ |
$0$ |
$35.70889811$ |
$1$ |
|
$1$ |
$230400$ |
$1.714960$ |
$1443468546/7$ |
$1.04654$ |
$4.52744$ |
$[0, 0, 0, -287339, -59284090]$ |
\(y^2=x^3-287339x-59284090\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 56.24.0.bp.1, 248.24.0.?, $\ldots$ |
$[(3220590534067210/76143, 182769223151045764132480/76143)]$ |
| 53816.d2 |
53816c3 |
53816.d |
53816c |
$4$ |
$4$ |
\( 2^{3} \cdot 7 \cdot 31^{2} \) |
\( 2^{11} \cdot 7^{4} \cdot 31^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.15 |
2B |
$1736$ |
$48$ |
$0$ |
$8.927224528$ |
$1$ |
|
$1$ |
$230400$ |
$1.714960$ |
$11090466/2401$ |
$1.11706$ |
$4.08049$ |
$[0, 0, 0, -56699, 4111158]$ |
\(y^2=x^3-56699x+4111158\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.k.1, 56.24.0.v.1, 124.12.0.?, $\ldots$ |
$[(100874/35, 1045568/35)]$ |
| 53816.d3 |
53816c2 |
53816.d |
53816c |
$4$ |
$4$ |
\( 2^{3} \cdot 7 \cdot 31^{2} \) |
\( 2^{10} \cdot 7^{2} \cdot 31^{6} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.3 |
2Cs |
$1736$ |
$48$ |
$0$ |
$17.85444905$ |
$1$ |
|
$3$ |
$115200$ |
$1.368387$ |
$740772/49$ |
$1.06534$ |
$3.76844$ |
$[0, 0, 0, -18259, -893730]$ |
\(y^2=x^3-18259x-893730\) |
2.6.0.a.1, 8.12.0.a.1, 28.12.0.b.1, 56.24.0.d.1, 124.12.0.?, $\ldots$ |
$[(160536323/17, 2034042178560/17)]$ |
| 53816.d4 |
53816c1 |
53816.d |
53816c |
$4$ |
$4$ |
\( 2^{3} \cdot 7 \cdot 31^{2} \) |
\( - 2^{8} \cdot 7 \cdot 31^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.9 |
2B |
$1736$ |
$48$ |
$0$ |
$8.927224528$ |
$1$ |
|
$3$ |
$57600$ |
$1.021814$ |
$432/7$ |
$0.89152$ |
$3.26010$ |
$[0, 0, 0, 961, -59582]$ |
\(y^2=x^3+961x-59582\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 14.6.0.b.1, 28.12.0.g.1, $\ldots$ |
$[(555489, 414012254)]$ |
| 53816.e1 |
53816e2 |
53816.e |
53816e |
$2$ |
$2$ |
\( 2^{3} \cdot 7 \cdot 31^{2} \) |
\( 2^{10} \cdot 7 \cdot 31^{8} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$868$ |
$12$ |
$0$ |
$1$ |
$4$ |
$2$ |
$1$ |
$307200$ |
$1.815086$ |
$290046852/6727$ |
$0.88427$ |
$4.31649$ |
$[0, 0, 0, -133579, 18410838]$ |
\(y^2=x^3-133579x+18410838\) |
2.3.0.a.1, 28.6.0.a.1, 124.6.0.?, 868.12.0.? |
$[ ]$ |
| 53816.e2 |
53816e1 |
53816.e |
53816e |
$2$ |
$2$ |
\( 2^{3} \cdot 7 \cdot 31^{2} \) |
\( - 2^{8} \cdot 7^{2} \cdot 31^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$868$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$153600$ |
$1.468513$ |
$432/1519$ |
$0.99214$ |
$3.75730$ |
$[0, 0, 0, 961, 893730]$ |
\(y^2=x^3+961x+893730\) |
2.3.0.a.1, 28.6.0.b.1, 62.6.0.b.1, 868.12.0.? |
$[ ]$ |
