Atkin-Lehner |
2- 3+ 59+ |
Signs for the Atkin-Lehner involutions |
Class |
33984ba |
Isogeny class |
Conductor |
33984 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
73728 |
Modular degree for the optimal curve |
Δ |
77933322436608 = 226 · 39 · 59 |
Discriminant |
Eigenvalues |
2- 3+ 0 4 4 2 4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-11340,-188784] |
[a1,a2,a3,a4,a6] |
j |
31255875/15104 |
j-invariant |
L |
3.8843772100756 |
L(r)(E,1)/r! |
Ω |
0.48554715126004 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
33984d1 8496k1 33984bd1 |
Quadratic twists by: -4 8 -3 |