| 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 |
Manin constant |
| 5566.a1 |
5566b1 |
5566.a |
5566b |
$1$ |
$1$ |
\( 2 \cdot 11^{2} \cdot 23 \) |
\( 2^{13} \cdot 11^{7} \cdot 23 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$2024$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$12480$ |
$1.188238$ |
$70393838689/2072576$ |
$0.88845$ |
$4.56433$ |
$[1, 0, 1, -10409, -399060]$ |
\(y^2+xy+y=x^3-10409x-399060\) |
2024.2.0.? |
$[ ]$ |
$1$ |
| 5566.b1 |
5566c1 |
5566.b |
5566c |
$1$ |
$1$ |
\( 2 \cdot 11^{2} \cdot 23 \) |
\( 2^{3} \cdot 11^{7} \cdot 23 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$2024$ |
$2$ |
$0$ |
$0.480004153$ |
$1$ |
|
$4$ |
$2880$ |
$0.533726$ |
$5545233/2024$ |
$0.79572$ |
$3.46873$ |
$[1, -1, 0, -446, 2316]$ |
\(y^2+xy=x^3-x^2-446x+2316\) |
2024.2.0.? |
$[(-19, 70)]$ |
$1$ |
| 5566.c1 |
5566a1 |
5566.c |
5566a |
$1$ |
$1$ |
\( 2 \cdot 11^{2} \cdot 23 \) |
\( 2^{15} \cdot 11^{3} \cdot 23^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.6.0.1 |
3Ns |
$6072$ |
$24$ |
$1$ |
$2.819654792$ |
$1$ |
|
$2$ |
$10080$ |
$0.939333$ |
$691510653107/398688256$ |
$1.04659$ |
$3.99514$ |
$[1, 1, 0, -2026, -2988]$ |
\(y^2+xy=x^3+x^2-2026x-2988\) |
3.6.0.b.1, 33.12.0.a.1, 552.12.0.?, 2024.2.0.?, 6072.24.1.? |
$[(-27, 195)]$ |
$1$ |
| 5566.d1 |
5566e1 |
5566.d |
5566e |
$1$ |
$1$ |
\( 2 \cdot 11^{2} \cdot 23 \) |
\( 2^{7} \cdot 11^{7} \cdot 23 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$2024$ |
$2$ |
$0$ |
$0.142109635$ |
$1$ |
|
$6$ |
$6720$ |
$0.937838$ |
$11867954041/32384$ |
$0.87031$ |
$4.35791$ |
$[1, 0, 0, -5750, 166948]$ |
\(y^2+xy=x^3-5750x+166948\) |
2024.2.0.? |
$[(-12, 490)]$ |
$1$ |
| 5566.e1 |
5566f2 |
5566.e |
5566f |
$2$ |
$3$ |
\( 2 \cdot 11^{2} \cdot 23 \) |
\( 2^{3} \cdot 11^{7} \cdot 23^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$6072$ |
$16$ |
$0$ |
$0.894101761$ |
$1$ |
|
$4$ |
$31680$ |
$1.367357$ |
$6894801108937/1070696$ |
$0.92497$ |
$5.09589$ |
$[1, 0, 0, -47979, 4040521]$ |
\(y^2+xy=x^3-47979x+4040521\) |
3.4.0.a.1, 33.8.0-3.a.1.1, 552.8.0.?, 2024.2.0.?, 6072.16.0.? |
$[(120, 61)]$ |
$1$ |
| 5566.e2 |
5566f1 |
5566.e |
5566f |
$2$ |
$3$ |
\( 2 \cdot 11^{2} \cdot 23 \) |
\( 2 \cdot 11^{9} \cdot 23 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$6072$ |
$16$ |
$0$ |
$2.682305285$ |
$1$ |
|
$0$ |
$10560$ |
$0.818051$ |
$169112377/61226$ |
$0.83749$ |
$3.86500$ |
$[1, 0, 0, -1394, -12374]$ |
\(y^2+xy=x^3-1394x-12374\) |
3.4.0.a.1, 33.8.0-3.a.1.2, 552.8.0.?, 2024.2.0.?, 6072.16.0.? |
$[(-125/2, 367/2)]$ |
$1$ |
| 5566.f1 |
5566h1 |
5566.f |
5566h |
$1$ |
$1$ |
\( 2 \cdot 11^{2} \cdot 23 \) |
\( 2^{3} \cdot 11^{13} \cdot 23 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$2024$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$342720$ |
$2.738304$ |
$2712917065234165678953/3585639464$ |
$1.04537$ |
$7.39059$ |
$[1, -1, 1, -35157904, -80229668021]$ |
\(y^2+xy+y=x^3-x^2-35157904x-80229668021\) |
2024.2.0.? |
$[ ]$ |
$1$ |
| 5566.g1 |
5566g1 |
5566.g |
5566g |
$1$ |
$1$ |
\( 2 \cdot 11^{2} \cdot 23 \) |
\( 2^{5} \cdot 11^{11} \cdot 23 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$2024$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$24000$ |
$1.654940$ |
$90452336967369/118533536$ |
$0.97074$ |
$5.39435$ |
$[1, -1, 1, -113158, -14606347]$ |
\(y^2+xy+y=x^3-x^2-113158x-14606347\) |
2024.2.0.? |
$[ ]$ |
$1$ |
| 5566.h1 |
5566i2 |
5566.h |
5566i |
$2$ |
$2$ |
\( 2 \cdot 11^{2} \cdot 23 \) |
\( 2^{5} \cdot 11^{6} \cdot 23^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.6 |
2B |
$184$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$14000$ |
$1.107038$ |
$545138290809/16928$ |
$1.08081$ |
$4.80167$ |
$[1, -1, 1, -20593, 1142529]$ |
\(y^2+xy+y=x^3-x^2-20593x+1142529\) |
2.3.0.a.1, 8.6.0.b.1, 92.6.0.?, 184.12.0.? |
$[ ]$ |
$1$ |
| 5566.h2 |
5566i1 |
5566.h |
5566i |
$2$ |
$2$ |
\( 2 \cdot 11^{2} \cdot 23 \) |
\( - 2^{10} \cdot 11^{6} \cdot 23 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.1 |
2B |
$184$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$7000$ |
$0.760466$ |
$-116930169/23552$ |
$1.03422$ |
$3.85685$ |
$[1, -1, 1, -1233, 19649]$ |
\(y^2+xy+y=x^3-x^2-1233x+19649\) |
2.3.0.a.1, 8.6.0.c.1, 46.6.0.a.1, 184.12.0.? |
$[ ]$ |
$1$ |
| 5566.i1 |
5566d1 |
5566.i |
5566d |
$1$ |
$1$ |
\( 2 \cdot 11^{2} \cdot 23 \) |
\( 2^{15} \cdot 11^{9} \cdot 23^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.6.0.1 |
3Ns |
$6072$ |
$24$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$110880$ |
$2.138279$ |
$691510653107/398688256$ |
$1.04659$ |
$5.66335$ |
$[1, 1, 1, -245209, 2751079]$ |
\(y^2+xy+y=x^3+x^2-245209x+2751079\) |
3.6.0.b.1, 33.12.0.a.1, 552.12.0.?, 2024.2.0.?, 6072.24.1.? |
$[ ]$ |
$1$ |
