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 |
30446.e1 |
30446c1 |
30446.e |
30446c |
$1$ |
$1$ |
\( 2 \cdot 13 \cdot 1171 \) |
\( 2^{2} \cdot 13^{2} \cdot 1171 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$4684$ |
$2$ |
$0$ |
$0.471323148$ |
$1$ |
|
$4$ |
$4480$ |
$-0.138643$ |
$6321363049/791596$ |
$0.85660$ |
$2.18596$ |
$[1, 0, 1, -39, 78]$ |
\(y^2+xy+y=x^3-39x+78\) |
4684.2.0.? |
$[(-3, 14)]$ |
243568.d1 |
243568d1 |
243568.d |
243568d |
$1$ |
$1$ |
\( 2^{4} \cdot 13 \cdot 1171 \) |
\( 2^{14} \cdot 13^{2} \cdot 1171 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$4684$ |
$2$ |
$0$ |
$0.938122954$ |
$1$ |
|
$4$ |
$107520$ |
$0.554504$ |
$6321363049/791596$ |
$0.85660$ |
$2.49009$ |
$[0, -1, 0, -616, -5008]$ |
\(y^2=x^3-x^2-616x-5008\) |
4684.2.0.? |
$[(-14, 26)]$ |
274014.r1 |
274014r1 |
274014.r |
274014r |
$1$ |
$1$ |
\( 2 \cdot 3^{2} \cdot 13 \cdot 1171 \) |
\( 2^{2} \cdot 3^{6} \cdot 13^{2} \cdot 1171 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$4684$ |
$2$ |
$0$ |
$3.205464079$ |
$1$ |
|
$0$ |
$134400$ |
$0.410663$ |
$6321363049/791596$ |
$0.85660$ |
$2.32881$ |
$[1, -1, 1, -347, -2113]$ |
\(y^2+xy+y=x^3-x^2-347x-2113\) |
4684.2.0.? |
$[(-101/3, 580/3)]$ |
395798.u1 |
395798u1 |
395798.u |
395798u |
$1$ |
$1$ |
\( 2 \cdot 13^{2} \cdot 1171 \) |
\( 2^{2} \cdot 13^{8} \cdot 1171 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$4684$ |
$2$ |
$0$ |
$2.106803080$ |
$1$ |
|
$0$ |
$752640$ |
$1.143831$ |
$6321363049/791596$ |
$0.85660$ |
$2.94498$ |
$[1, 0, 0, -6510, 178424]$ |
\(y^2+xy=x^3-6510x+178424\) |
4684.2.0.? |
$[(355/2, 4039/2)]$ |