| 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 |
| 6027.a1 |
6027c1 |
6027.a |
6027c |
$2$ |
$5$ |
\( 3 \cdot 7^{2} \cdot 41 \) |
\( - 3^{5} \cdot 7^{6} \cdot 41 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.12.0.1 |
5B.4.1 |
$8610$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$7200$ |
$0.486212$ |
$-122023936/9963$ |
$0.99771$ |
$3.49577$ |
$[0, -1, 1, -506, -4516]$ |
\(y^2+y=x^3-x^2-506x-4516\) |
5.12.0.a.1, 35.24.0-5.a.1.2, 246.2.0.?, 1230.24.1.?, 8610.48.1.? |
$[]$ |
| 6027.a2 |
6027c2 |
6027.a |
6027c |
$2$ |
$5$ |
\( 3 \cdot 7^{2} \cdot 41 \) |
\( - 3 \cdot 7^{6} \cdot 41^{5} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.12.0.2 |
5B.4.2 |
$8610$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$36000$ |
$1.290932$ |
$841232384/347568603$ |
$1.09016$ |
$4.45717$ |
$[0, -1, 1, 964, 307124]$ |
\(y^2+y=x^3-x^2+964x+307124\) |
5.12.0.a.2, 35.24.0-5.a.2.2, 246.2.0.?, 1230.24.1.?, 8610.48.1.? |
$[]$ |
| 6027.b1 |
6027b1 |
6027.b |
6027b |
$1$ |
$1$ |
\( 3 \cdot 7^{2} \cdot 41 \) |
\( - 3^{7} \cdot 7^{7} \cdot 41^{5} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$3444$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$107520$ |
$2.012321$ |
$2813193182704463/1773642581109$ |
$0.99360$ |
$5.42837$ |
$[1, 1, 1, 144108, -6237750]$ |
\(y^2+xy+y=x^3+x^2+144108x-6237750\) |
3444.2.0.? |
$[]$ |
| 6027.c1 |
6027d1 |
6027.c |
6027d |
$1$ |
$1$ |
\( 3 \cdot 7^{2} \cdot 41 \) |
\( - 3^{5} \cdot 7^{7} \cdot 41 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$3444$ |
$2$ |
$0$ |
$2.371073768$ |
$1$ |
|
$2$ |
$3840$ |
$0.592435$ |
$-38272753/69741$ |
$0.83138$ |
$3.51086$ |
$[1, 1, 1, -344, -5146]$ |
\(y^2+xy+y=x^3+x^2-344x-5146\) |
3444.2.0.? |
$[(62, 434)]$ |
| 6027.d1 |
6027h4 |
6027.d |
6027h |
$4$ |
$4$ |
\( 3 \cdot 7^{2} \cdot 41 \) |
\( 3 \cdot 7^{10} \cdot 41 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.6 |
2B |
$6888$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$10752$ |
$1.185375$ |
$31366144171153/295323$ |
$0.93188$ |
$4.91179$ |
$[1, 0, 0, -32194, 2220665]$ |
\(y^2+xy=x^3-32194x+2220665\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 84.12.0.?, 168.24.0.?, $\ldots$ |
$[]$ |
| 6027.d2 |
6027h3 |
6027.d |
6027h |
$4$ |
$4$ |
\( 3 \cdot 7^{2} \cdot 41 \) |
\( 3 \cdot 7^{7} \cdot 41^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.8 |
2B |
$6888$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$10752$ |
$1.185375$ |
$351447414193/59340981$ |
$0.90324$ |
$4.39577$ |
$[1, 0, 0, -7204, -198661]$ |
\(y^2+xy=x^3-7204x-198661\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 42.6.0.a.1, 84.24.0.?, 984.24.0.?, $\ldots$ |
$[]$ |
| 6027.d3 |
6027h2 |
6027.d |
6027h |
$4$ |
$4$ |
\( 3 \cdot 7^{2} \cdot 41 \) |
\( 3^{2} \cdot 7^{8} \cdot 41^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.1 |
2Cs |
$3444$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$5376$ |
$0.838802$ |
$8205738913/741321$ |
$0.86504$ |
$3.96410$ |
$[1, 0, 0, -2059, 32864]$ |
\(y^2+xy=x^3-2059x+32864\) |
2.6.0.a.1, 4.12.0-2.a.1.1, 84.24.0.?, 492.24.0.?, 1148.24.0.?, $\ldots$ |
$[]$ |
| 6027.d4 |
6027h1 |
6027.d |
6027h |
$4$ |
$4$ |
\( 3 \cdot 7^{2} \cdot 41 \) |
\( - 3^{4} \cdot 7^{7} \cdot 41 \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.7 |
2B |
$6888$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$3$ |
$2688$ |
$0.492229$ |
$2924207/23247$ |
$0.82859$ |
$3.34427$ |
$[1, 0, 0, 146, 2435]$ |
\(y^2+xy=x^3+146x+2435\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 168.24.0.?, 574.6.0.?, 984.24.0.?, $\ldots$ |
$[]$ |
| 6027.e1 |
6027g1 |
6027.e |
6027g |
$1$ |
$1$ |
\( 3 \cdot 7^{2} \cdot 41 \) |
\( - 3 \cdot 7^{6} \cdot 41 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$246$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$1152$ |
$0.056796$ |
$32768/123$ |
$0.85567$ |
$2.73149$ |
$[0, 1, 1, 33, 179]$ |
\(y^2+y=x^3+x^2+33x+179\) |
246.2.0.? |
$[]$ |
| 6027.f1 |
6027a1 |
6027.f |
6027a |
$1$ |
$1$ |
\( 3 \cdot 7^{2} \cdot 41 \) |
\( - 3^{17} \cdot 7^{9} \cdot 41 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$3444$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$78336$ |
$2.005028$ |
$38996155237031/1816098112269$ |
$0.99901$ |
$5.43949$ |
$[1, 1, 0, 34618, 22115157]$ |
\(y^2+xy=x^3+x^2+34618x+22115157\) |
3444.2.0.? |
$[]$ |
| 6027.g1 |
6027e1 |
6027.g |
6027e |
$1$ |
$1$ |
\( 3 \cdot 7^{2} \cdot 41 \) |
\( - 3 \cdot 7^{2} \cdot 41^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$8.048390441$ |
$1$ |
|
$0$ |
$2976$ |
$0.297985$ |
$-3072832000000/5043$ |
$1.01203$ |
$3.75062$ |
$[0, -1, 1, -1108, -13833]$ |
\(y^2+y=x^3-x^2-1108x-13833\) |
6.2.0.a.1 |
$[(18825/8, 2560891/8)]$ |
| 6027.h1 |
6027f1 |
6027.h |
6027f |
$1$ |
$1$ |
\( 3 \cdot 7^{2} \cdot 41 \) |
\( - 3 \cdot 7^{8} \cdot 41^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$20832$ |
$1.270939$ |
$-3072832000000/5043$ |
$1.01203$ |
$5.09201$ |
$[0, 1, 1, -54308, 4853237]$ |
\(y^2+y=x^3+x^2-54308x+4853237\) |
6.2.0.a.1 |
$[]$ |
