| 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 |
| 6776.a1 |
6776d1 |
6776.a |
6776d |
$1$ |
$1$ |
\( 2^{3} \cdot 7 \cdot 11^{2} \) |
\( - 2^{8} \cdot 7^{4} \cdot 11^{9} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.4.0.1 |
|
$44$ |
$8$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$109824$ |
$1.817831$ |
$-1905527808/2401$ |
$0.99681$ |
$5.49775$ |
$[0, 0, 0, -218284, -39296444]$ |
\(y^2=x^3-218284x-39296444\) |
4.4.0.a.1, 22.2.0.a.1, 44.8.0.a.1 |
$[]$ |
| 6776.b1 |
6776b1 |
6776.b |
6776b |
$1$ |
$1$ |
\( 2^{3} \cdot 7 \cdot 11^{2} \) |
\( - 2^{8} \cdot 7^{4} \cdot 11^{3} \) |
$2$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.4.0.1 |
|
$44$ |
$8$ |
$0$ |
$0.062267026$ |
$1$ |
|
$34$ |
$9984$ |
$0.618883$ |
$-1905527808/2401$ |
$0.99681$ |
$3.86674$ |
$[0, 0, 0, -1804, 29524]$ |
\(y^2=x^3-1804x+29524\) |
4.4.0.a.1, 22.2.0.a.1, 44.8.0.a.1 |
$[(26, 14), (33, 77)]$ |
| 6776.c1 |
6776h2 |
6776.c |
6776h |
$2$ |
$2$ |
\( 2^{3} \cdot 7 \cdot 11^{2} \) |
\( 2^{10} \cdot 7^{2} \cdot 11^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$308$ |
$12$ |
$0$ |
$1.754529804$ |
$1$ |
|
$5$ |
$15360$ |
$1.264660$ |
$1354435492/539$ |
$0.87282$ |
$4.80045$ |
$[0, 1, 0, -28112, 1804240]$ |
\(y^2=x^3+x^2-28112x+1804240\) |
2.3.0.a.1, 28.6.0.c.1, 44.6.0.a.1, 308.12.0.? |
$[(88, 140)]$ |
| 6776.c2 |
6776h1 |
6776.c |
6776h |
$2$ |
$2$ |
\( 2^{3} \cdot 7 \cdot 11^{2} \) |
\( - 2^{8} \cdot 7 \cdot 11^{8} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$308$ |
$12$ |
$0$ |
$0.877264902$ |
$1$ |
|
$7$ |
$7680$ |
$0.918087$ |
$-810448/847$ |
$0.75673$ |
$3.91895$ |
$[0, 1, 0, -1492, 36672]$ |
\(y^2=x^3+x^2-1492x+36672\) |
2.3.0.a.1, 14.6.0.b.1, 44.6.0.b.1, 308.12.0.? |
$[(-26, 242)]$ |
| 6776.d1 |
6776e1 |
6776.d |
6776e |
$1$ |
$1$ |
\( 2^{3} \cdot 7 \cdot 11^{2} \) |
\( - 2^{8} \cdot 7^{2} \cdot 11^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$22$ |
$2$ |
$0$ |
$1.184493825$ |
$1$ |
|
$4$ |
$11520$ |
$1.263729$ |
$-1024/65219$ |
$1.07918$ |
$4.36143$ |
$[0, -1, 0, -161, -261611]$ |
\(y^2=x^3-x^2-161x-261611\) |
22.2.0.a.1 |
$[(147, 1694)]$ |
| 6776.e1 |
6776a3 |
6776.e |
6776a |
$4$ |
$4$ |
\( 2^{3} \cdot 7 \cdot 11^{2} \) |
\( 2^{10} \cdot 7^{4} \cdot 11^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.8 |
2B |
$616$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$15360$ |
$1.426327$ |
$1707831108/26411$ |
$0.90642$ |
$4.82674$ |
$[0, 0, 0, -30371, -2009810]$ |
\(y^2=x^3-30371x-2009810\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 44.24.0-44.h.1.1, 56.24.0-56.z.1.5, 616.48.0.? |
$[]$ |
| 6776.e2 |
6776a2 |
6776.e |
6776a |
$4$ |
$4$ |
\( 2^{3} \cdot 7 \cdot 11^{2} \) |
\( 2^{8} \cdot 7^{2} \cdot 11^{8} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.1 |
2Cs |
$308$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$3$ |
$7680$ |
$1.079754$ |
$12869712/5929$ |
$0.92155$ |
$4.11545$ |
$[0, 0, 0, -3751, 39930]$ |
\(y^2=x^3-3751x+39930\) |
2.6.0.a.1, 4.12.0-2.a.1.1, 28.24.0-28.b.1.3, 44.24.0-44.a.1.2, 308.48.0.? |
$[]$ |
| 6776.e3 |
6776a1 |
6776.e |
6776a |
$4$ |
$4$ |
\( 2^{3} \cdot 7 \cdot 11^{2} \) |
\( 2^{4} \cdot 7 \cdot 11^{7} \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.7 |
2B |
$616$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$3$ |
$3840$ |
$0.733180$ |
$121485312/77$ |
$0.96765$ |
$4.05563$ |
$[0, 0, 0, -3146, 67881]$ |
\(y^2=x^3-3146x+67881\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 56.24.0-56.z.1.13, 88.24.0.?, 154.6.0.?, $\ldots$ |
$[]$ |
| 6776.e4 |
6776a4 |
6776.e |
6776a |
$4$ |
$4$ |
\( 2^{3} \cdot 7 \cdot 11^{2} \) |
\( - 2^{10} \cdot 7 \cdot 11^{10} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.6 |
2B |
$616$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$15360$ |
$1.426327$ |
$139863132/102487$ |
$0.92001$ |
$4.54306$ |
$[0, 0, 0, 13189, 300806]$ |
\(y^2=x^3+13189x+300806\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 14.6.0.b.1, 28.12.0.g.1, $\ldots$ |
$[]$ |
| 6776.f1 |
6776i2 |
6776.f |
6776i |
$2$ |
$2$ |
\( 2^{3} \cdot 7 \cdot 11^{2} \) |
\( 2^{11} \cdot 7^{6} \cdot 11^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$616$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$23040$ |
$1.698338$ |
$2415899250/1294139$ |
$1.20887$ |
$4.94463$ |
$[0, 0, 0, -42955, -934362]$ |
\(y^2=x^3-42955x-934362\) |
2.3.0.a.1, 28.6.0.c.1, 88.6.0.?, 616.12.0.? |
$[]$ |
| 6776.f2 |
6776i1 |
6776.f |
6776i |
$2$ |
$2$ |
\( 2^{3} \cdot 7 \cdot 11^{2} \) |
\( - 2^{10} \cdot 7^{3} \cdot 11^{8} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$616$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$11520$ |
$1.351765$ |
$66325500/41503$ |
$0.93491$ |
$4.45848$ |
$[0, 0, 0, 10285, -114466]$ |
\(y^2=x^3+10285x-114466\) |
2.3.0.a.1, 14.6.0.b.1, 88.6.0.?, 616.12.0.? |
$[]$ |
| 6776.g1 |
6776c3 |
6776.g |
6776c |
$4$ |
$4$ |
\( 2^{3} \cdot 7 \cdot 11^{2} \) |
\( 2^{11} \cdot 7 \cdot 11^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.9 |
2B |
$616$ |
$48$ |
$0$ |
$13.14802192$ |
$1$ |
|
$1$ |
$10240$ |
$1.196915$ |
$1443468546/7$ |
$1.04654$ |
$4.88625$ |
$[0, 0, 0, -36179, -2648690]$ |
\(y^2=x^3-36179x-2648690\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 56.24.0.bp.1, 88.24.0.?, $\ldots$ |
$[(4190626/115, 6399164376/115)]$ |
| 6776.g2 |
6776c4 |
6776.g |
6776c |
$4$ |
$4$ |
\( 2^{3} \cdot 7 \cdot 11^{2} \) |
\( 2^{11} \cdot 7^{4} \cdot 11^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.15 |
2B |
$616$ |
$48$ |
$0$ |
$3.287005482$ |
$1$ |
|
$3$ |
$10240$ |
$1.196915$ |
$11090466/2401$ |
$1.11706$ |
$4.33431$ |
$[0, 0, 0, -7139, 183678]$ |
\(y^2=x^3-7139x+183678\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.k.1, 44.12.0-4.c.1.1, 56.24.0.v.1, $\ldots$ |
$[(-46, 644)]$ |
| 6776.g3 |
6776c2 |
6776.g |
6776c |
$4$ |
$4$ |
\( 2^{3} \cdot 7 \cdot 11^{2} \) |
\( 2^{10} \cdot 7^{2} \cdot 11^{6} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.3 |
2Cs |
$616$ |
$48$ |
$0$ |
$6.574010964$ |
$1$ |
|
$3$ |
$5120$ |
$0.850341$ |
$740772/49$ |
$1.06534$ |
$3.94895$ |
$[0, 0, 0, -2299, -39930]$ |
\(y^2=x^3-2299x-39930\) |
2.6.0.a.1, 8.12.0.a.1, 28.12.0.b.1, 44.12.0-2.a.1.1, 56.24.0.d.1, $\ldots$ |
$[(7194/5, 601128/5)]$ |
| 6776.g4 |
6776c1 |
6776.g |
6776c |
$4$ |
$4$ |
\( 2^{3} \cdot 7 \cdot 11^{2} \) |
\( - 2^{8} \cdot 7 \cdot 11^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.9 |
2B |
$616$ |
$48$ |
$0$ |
$3.287005482$ |
$1$ |
|
$3$ |
$2560$ |
$0.503768$ |
$432/7$ |
$0.89152$ |
$3.32120$ |
$[0, 0, 0, 121, -2662]$ |
\(y^2=x^3+121x-2662\) |
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, $\ldots$ |
$[(286, 4840)]$ |
| 6776.h1 |
6776g2 |
6776.h |
6776g |
$2$ |
$2$ |
\( 2^{3} \cdot 7 \cdot 11^{2} \) |
\( 2^{11} \cdot 7^{2} \cdot 11^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.6 |
2B |
$56$ |
$12$ |
$0$ |
$4.249617639$ |
$1$ |
|
$1$ |
$11520$ |
$0.964279$ |
$3543122/49$ |
$1.08036$ |
$4.20496$ |
$[0, -1, 0, -4880, 131276]$ |
\(y^2=x^3-x^2-4880x+131276\) |
2.3.0.a.1, 8.6.0.b.1, 28.6.0.c.1, 56.12.0.k.1 |
$[(85/2, 1533/2)]$ |
| 6776.h2 |
6776g1 |
6776.h |
6776g |
$2$ |
$2$ |
\( 2^{3} \cdot 7 \cdot 11^{2} \) |
\( - 2^{10} \cdot 7 \cdot 11^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.1 |
2B |
$56$ |
$12$ |
$0$ |
$2.124808819$ |
$1$ |
|
$3$ |
$5760$ |
$0.617705$ |
$-4/7$ |
$1.03482$ |
$3.48252$ |
$[0, -1, 0, -40, 5436]$ |
\(y^2=x^3-x^2-40x+5436\) |
2.3.0.a.1, 8.6.0.c.1, 14.6.0.b.1, 56.12.0.n.1 |
$[(81, 726)]$ |
| 6776.i1 |
6776f2 |
6776.i |
6776f |
$2$ |
$2$ |
\( 2^{3} \cdot 7 \cdot 11^{2} \) |
\( 2^{10} \cdot 7^{10} \cdot 11^{9} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$308$ |
$12$ |
$0$ |
$25.27234443$ |
$1$ |
|
$1$ |
$230400$ |
$2.703472$ |
$1278763167594532/375974556419$ |
$1.04359$ |
$6.36012$ |
$[0, -1, 0, -2757872, -1235503300]$ |
\(y^2=x^3-x^2-2757872x-1235503300\) |
2.3.0.a.1, 28.6.0.c.1, 44.6.0.a.1, 308.12.0.? |
$[(2172775497550/29319, 2245211518991421860/29319)]$ |
| 6776.i2 |
6776f1 |
6776.i |
6776f |
$2$ |
$2$ |
\( 2^{3} \cdot 7 \cdot 11^{2} \) |
\( - 2^{8} \cdot 7^{5} \cdot 11^{12} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$308$ |
$12$ |
$0$ |
$12.63617221$ |
$1$ |
|
$1$ |
$115200$ |
$2.356899$ |
$24226243449392/29774625727$ |
$0.97408$ |
$5.76656$ |
$[0, -1, 0, 463148, -128760828]$ |
\(y^2=x^3-x^2+463148x-128760828\) |
2.3.0.a.1, 14.6.0.b.1, 44.6.0.b.1, 308.12.0.? |
$[(4360492/87, 11942849314/87)]$ |
