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 |
MW-generators |
4008.a1 |
4008d1 |
4008.a |
4008d |
$1$ |
$1$ |
\( 2^{3} \cdot 3 \cdot 167 \) |
\( - 2^{11} \cdot 3^{8} \cdot 167 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$1336$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$1792$ |
$0.476532$ |
$219804478/1095687$ |
$[0, -1, 0, 160, -2196]$ |
\(y^2=x^3-x^2+160x-2196\) |
1336.2.0.? |
$[]$ |
4008.b1 |
4008c1 |
4008.b |
4008c |
$1$ |
$1$ |
\( 2^{3} \cdot 3 \cdot 167 \) |
\( - 2^{11} \cdot 3^{2} \cdot 167 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$1336$ |
$2$ |
$0$ |
$3.426139440$ |
$1$ |
|
$2$ |
$576$ |
$0.161314$ |
$-1405190738/1503$ |
$[0, 1, 0, -296, -2064]$ |
\(y^2=x^3+x^2-296x-2064\) |
1336.2.0.? |
$[(43, 258)]$ |
4008.c1 |
4008b2 |
4008.c |
4008b |
$2$ |
$2$ |
\( 2^{3} \cdot 3 \cdot 167 \) |
\( 2^{11} \cdot 3^{2} \cdot 167^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.6 |
2B |
$1336$ |
$12$ |
$0$ |
$2.684207969$ |
$1$ |
|
$3$ |
$1280$ |
$0.399617$ |
$1911343250/251001$ |
$[0, 1, 0, -328, 1904]$ |
\(y^2=x^3+x^2-328x+1904\) |
2.3.0.a.1, 8.6.0.b.1, 668.6.0.?, 1336.12.0.? |
$[(23, 84)]$ |
4008.c2 |
4008b1 |
4008.c |
4008b |
$2$ |
$2$ |
\( 2^{3} \cdot 3 \cdot 167 \) |
\( - 2^{10} \cdot 3^{4} \cdot 167 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.1 |
2B |
$1336$ |
$12$ |
$0$ |
$1.342103984$ |
$1$ |
|
$5$ |
$640$ |
$0.053043$ |
$3429500/13527$ |
$[0, 1, 0, 32, 176]$ |
\(y^2=x^3+x^2+32x+176\) |
2.3.0.a.1, 8.6.0.c.1, 334.6.0.?, 1336.12.0.? |
$[(-1, 12)]$ |
4008.d1 |
4008a2 |
4008.d |
4008a |
$2$ |
$2$ |
\( 2^{3} \cdot 3 \cdot 167 \) |
\( 2^{10} \cdot 3^{5} \cdot 167^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$2004$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$3520$ |
$0.844630$ |
$14566408766500/6777027$ |
$[0, 1, 0, -5128, -143008]$ |
\(y^2=x^3+x^2-5128x-143008\) |
2.3.0.a.1, 12.6.0.a.1, 668.6.0.?, 2004.12.0.? |
$[]$ |
4008.d2 |
4008a1 |
4008.d |
4008a |
$2$ |
$2$ |
\( 2^{3} \cdot 3 \cdot 167 \) |
\( - 2^{8} \cdot 3^{10} \cdot 167 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$2004$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$1760$ |
$0.498057$ |
$-8346562000/9861183$ |
$[0, 1, 0, -268, -3040]$ |
\(y^2=x^3+x^2-268x-3040\) |
2.3.0.a.1, 12.6.0.b.1, 334.6.0.?, 2004.12.0.? |
$[]$ |