Atkin-Lehner |
2+ 3- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
51264q |
Isogeny class |
Conductor |
51264 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
74240 |
Modular degree for the optimal curve |
Δ |
-1009029312 = -1 · 26 · 311 · 89 |
Discriminant |
Eigenvalues |
2+ 3- 4 4 0 0 -6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-5898,-174350] |
[a1,a2,a3,a4,a6] |
j |
-486329388544/21627 |
j-invariant |
L |
4.3582505196222 |
L(r)(E,1)/r! |
Ω |
0.27239065763802 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
51264r1 25632l1 17088g1 |
Quadratic twists by: -4 8 -3 |