| 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 |
Weierstrass coefficients |
Weierstrass equation |
mod-$m$ images |
| 5054.a1 |
5054a2 |
5054.a |
5054a |
$2$ |
$7$ |
\( 2 \cdot 7 \cdot 19^{2} \) |
\( - 2^{35} \cdot 7 \cdot 19^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$7$ |
7.8.0.1 |
7B |
$1064$ |
$96$ |
$2$ |
$4.981947658$ |
$1$ |
|
$2$ |
$17640$ |
$1.566700$ |
$-133179212896925841/240518168576$ |
$[1, -1, 0, -75754, 8056692]$ |
\(y^2+xy=x^3-x^2-75754x+8056692\) |
7.8.0.a.1, 56.16.0.d.1, 133.48.0.?, 1064.96.2.? |
| 5054.a2 |
5054a1 |
5054.a |
5054a |
$2$ |
$7$ |
\( 2 \cdot 7 \cdot 19^{2} \) |
\( - 2^{5} \cdot 7^{7} \cdot 19^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$7$ |
7.8.0.1 |
7B |
$1064$ |
$96$ |
$2$ |
$0.711706808$ |
$1$ |
|
$2$ |
$2520$ |
$0.593744$ |
$53261199/26353376$ |
$[1, -1, 0, 56, -4704]$ |
\(y^2+xy=x^3-x^2+56x-4704\) |
7.8.0.a.1, 56.16.0.d.1, 133.48.0.?, 1064.96.2.? |
| 5054.b1 |
5054b2 |
5054.b |
5054b |
$2$ |
$7$ |
\( 2 \cdot 7 \cdot 19^{2} \) |
\( - 2^{35} \cdot 7 \cdot 19^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$7$ |
7.16.0.2 |
7B.2.3 |
$1064$ |
$96$ |
$2$ |
$1.639997960$ |
$1$ |
|
$2$ |
$335160$ |
$3.038918$ |
$-133179212896925841/240518168576$ |
$[1, -1, 1, -27347262, -55124114227]$ |
\(y^2+xy+y=x^3-x^2-27347262x-55124114227\) |
7.16.0-7.a.1.1, 56.32.0-56.d.1.2, 133.48.0.?, 1064.96.2.? |
| 5054.b2 |
5054b1 |
5054.b |
5054b |
$2$ |
$7$ |
\( 2 \cdot 7 \cdot 19^{2} \) |
\( - 2^{5} \cdot 7^{7} \cdot 19^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$7$ |
7.16.0.1 |
7B.2.1 |
$1064$ |
$96$ |
$2$ |
$0.234285422$ |
$1$ |
|
$4$ |
$47880$ |
$2.065964$ |
$53261199/26353376$ |
$[1, -1, 1, 20148, 32163887]$ |
\(y^2+xy+y=x^3-x^2+20148x+32163887\) |
7.16.0-7.a.1.2, 56.32.0-56.d.1.1, 133.48.0.?, 1064.96.2.? |
| 5054.c1 |
5054c6 |
5054.c |
5054c |
$6$ |
$18$ |
\( 2 \cdot 7 \cdot 19^{2} \) |
\( 2^{9} \cdot 7^{2} \cdot 19^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.6, 9.12.0.1 |
2B, 3B |
$9576$ |
$864$ |
$21$ |
$1$ |
$1$ |
|
$0$ |
$42768$ |
$1.885321$ |
$2251439055699625/25088$ |
$[1, 1, 1, -985718, 376273267]$ |
\(y^2+xy+y=x^3+x^2-985718x+376273267\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.b.1, 9.12.0.a.1, $\ldots$ |
| 5054.c2 |
5054c5 |
5054.c |
5054c |
$6$ |
$18$ |
\( 2 \cdot 7 \cdot 19^{2} \) |
\( - 2^{18} \cdot 7 \cdot 19^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.1, 9.12.0.1 |
2B, 3B |
$9576$ |
$864$ |
$21$ |
$1$ |
$1$ |
|
$1$ |
$21384$ |
$1.538748$ |
$-548347731625/1835008$ |
$[1, 1, 1, -61558, 5869939]$ |
\(y^2+xy+y=x^3+x^2-61558x+5869939\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.c.1, 9.12.0.a.1, $\ldots$ |
| 5054.c3 |
5054c4 |
5054.c |
5054c |
$6$ |
$18$ |
\( 2 \cdot 7 \cdot 19^{2} \) |
\( 2^{3} \cdot 7^{6} \cdot 19^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.6, 3.12.0.1 |
2B, 3Cs |
$9576$ |
$864$ |
$21$ |
$1$ |
$1$ |
|
$0$ |
$14256$ |
$1.336014$ |
$4956477625/941192$ |
$[1, 1, 1, -12823, 452773]$ |
\(y^2+xy+y=x^3+x^2-12823x+452773\) |
2.3.0.a.1, 3.12.0.a.1, 6.36.0.a.1, 8.6.0.b.1, 24.72.1.h.1, $\ldots$ |
| 5054.c4 |
5054c2 |
5054.c |
5054c |
$6$ |
$18$ |
\( 2 \cdot 7 \cdot 19^{2} \) |
\( 2 \cdot 7^{2} \cdot 19^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.6, 9.12.0.1 |
2B, 3B |
$9576$ |
$864$ |
$21$ |
$1$ |
$9$ |
$3$ |
$0$ |
$4752$ |
$0.786708$ |
$128787625/98$ |
$[1, 1, 1, -3798, -91615]$ |
\(y^2+xy+y=x^3+x^2-3798x-91615\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.b.1, 9.12.0.a.1, $\ldots$ |
| 5054.c5 |
5054c1 |
5054.c |
5054c |
$6$ |
$18$ |
\( 2 \cdot 7 \cdot 19^{2} \) |
\( - 2^{2} \cdot 7 \cdot 19^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.1, 9.12.0.1 |
2B, 3B |
$9576$ |
$864$ |
$21$ |
$1$ |
$9$ |
$3$ |
$1$ |
$2376$ |
$0.440135$ |
$-15625/28$ |
$[1, 1, 1, -188, -2087]$ |
\(y^2+xy+y=x^3+x^2-188x-2087\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.c.1, 9.12.0.a.1, $\ldots$ |
| 5054.c6 |
5054c3 |
5054.c |
5054c |
$6$ |
$18$ |
\( 2 \cdot 7 \cdot 19^{2} \) |
\( - 2^{6} \cdot 7^{3} \cdot 19^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.1, 3.12.0.1 |
2B, 3Cs |
$9576$ |
$864$ |
$21$ |
$1$ |
$1$ |
|
$1$ |
$7128$ |
$0.989441$ |
$9938375/21952$ |
$[1, 1, 1, 1617, 42677]$ |
\(y^2+xy+y=x^3+x^2+1617x+42677\) |
2.3.0.a.1, 3.12.0.a.1, 6.36.0.a.1, 8.6.0.c.1, 14.6.0.b.1, $\ldots$ |
