| 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 |
| 6664.a1 |
6664a1 |
6664.a |
6664a |
$1$ |
$1$ |
\( 2^{3} \cdot 7^{2} \cdot 17 \) |
\( - 2^{10} \cdot 7^{8} \cdot 17^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$68$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$32256$ |
$1.270084$ |
$-1660932/4913$ |
$0.86662$ |
$4.38775$ |
$[0, 0, 0, -4459, 283318]$ |
\(y^2=x^3-4459x+283318\) |
68.2.0.a.1 |
$[]$ |
| 6664.b1 |
6664e2 |
6664.b |
6664e |
$2$ |
$2$ |
\( 2^{3} \cdot 7^{2} \cdot 17 \) |
\( 2^{11} \cdot 7^{6} \cdot 17^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.6 |
2B |
$136$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$6144$ |
$0.841110$ |
$6097250/289$ |
$0.87700$ |
$3.96655$ |
$[0, 1, 0, -2368, -43296]$ |
\(y^2=x^3+x^2-2368x-43296\) |
2.3.0.a.1, 8.6.0.b.1, 68.6.0.c.1, 136.12.0.? |
$[]$ |
| 6664.b2 |
6664e1 |
6664.b |
6664e |
$2$ |
$2$ |
\( 2^{3} \cdot 7^{2} \cdot 17 \) |
\( 2^{10} \cdot 7^{6} \cdot 17 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.1 |
2B |
$136$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$3072$ |
$0.494536$ |
$62500/17$ |
$0.89869$ |
$3.36759$ |
$[0, 1, 0, -408, 2176]$ |
\(y^2=x^3+x^2-408x+2176\) |
2.3.0.a.1, 8.6.0.c.1, 34.6.0.a.1, 136.12.0.? |
$[]$ |
| 6664.c1 |
6664b1 |
6664.c |
6664b |
$1$ |
$1$ |
\( 2^{3} \cdot 7^{2} \cdot 17 \) |
\( - 2^{11} \cdot 7^{4} \cdot 17^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$136$ |
$2$ |
$0$ |
$4.334300904$ |
$1$ |
|
$0$ |
$5472$ |
$0.892459$ |
$-3241463778/4913$ |
$0.96554$ |
$4.23764$ |
$[0, 0, 0, -5243, -146314]$ |
\(y^2=x^3-5243x-146314\) |
136.2.0.? |
$[(337/2, 799/2)]$ |
| 6664.d1 |
6664c1 |
6664.d |
6664c |
$1$ |
$1$ |
\( 2^{3} \cdot 7^{2} \cdot 17 \) |
\( - 2^{11} \cdot 7^{10} \cdot 17^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$136$ |
$2$ |
$0$ |
$9.572317657$ |
$1$ |
|
$0$ |
$38304$ |
$1.865414$ |
$-3241463778/4913$ |
$0.96554$ |
$5.56372$ |
$[0, 0, 0, -256907, 50185702]$ |
\(y^2=x^3-256907x+50185702\) |
136.2.0.? |
$[(14529/2, 1735063/2)]$ |
| 6664.e1 |
6664d1 |
6664.e |
6664d |
$2$ |
$2$ |
\( 2^{3} \cdot 7^{2} \cdot 17 \) |
\( 2^{8} \cdot 7^{6} \cdot 17 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.3 |
2B |
$952$ |
$48$ |
$0$ |
$2.261163448$ |
$1$ |
|
$3$ |
$2880$ |
$0.364751$ |
$35152/17$ |
$0.75928$ |
$3.14477$ |
$[0, -1, 0, -212, -412]$ |
\(y^2=x^3-x^2-212x-412\) |
2.3.0.a.1, 4.6.0.b.1, 34.6.0.a.1, 56.12.0-4.b.1.3, 68.24.0.f.1, $\ldots$ |
$[(16, 6)]$ |
| 6664.e2 |
6664d2 |
6664.e |
6664d |
$2$ |
$2$ |
\( 2^{3} \cdot 7^{2} \cdot 17 \) |
\( - 2^{10} \cdot 7^{6} \cdot 17^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.5 |
2B |
$952$ |
$48$ |
$0$ |
$4.522326897$ |
$1$ |
|
$3$ |
$5760$ |
$0.711325$ |
$415292/289$ |
$0.87236$ |
$3.58269$ |
$[0, -1, 0, 768, -3940]$ |
\(y^2=x^3-x^2+768x-3940\) |
2.3.0.a.1, 4.6.0.a.1, 28.12.0-4.a.1.1, 68.12.0.d.1, 136.24.0.?, $\ldots$ |
$[(7502, 649740)]$ |
| 6664.f1 |
6664f1 |
6664.f |
6664f |
$1$ |
$1$ |
\( 2^{3} \cdot 7^{2} \cdot 17 \) |
\( - 2^{10} \cdot 7^{2} \cdot 17^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$68$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$4608$ |
$0.297129$ |
$-1660932/4913$ |
$0.86662$ |
$3.06166$ |
$[0, 0, 0, -91, -826]$ |
\(y^2=x^3-91x-826\) |
68.2.0.a.1 |
$[]$ |
