Atkin-Lehner |
2+ 3- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
51264i |
Isogeny class |
Conductor |
51264 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
24576 |
Modular degree for the optimal curve |
Δ |
265752576 = 212 · 36 · 89 |
Discriminant |
Eigenvalues |
2+ 3- 2 2 -4 -4 2 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1044,12960] |
[a1,a2,a3,a4,a6] |
j |
42144192/89 |
j-invariant |
L |
3.4936993925648 |
L(r)(E,1)/r! |
Ω |
1.7468496974908 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
51264j1 25632c1 5696c1 |
Quadratic twists by: -4 8 -3 |