Atkin-Lehner |
2- 3- 59- |
Signs for the Atkin-Lehner involutions |
Class |
33984bq |
Isogeny class |
Conductor |
33984 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
24576 |
Modular degree for the optimal curve |
Δ |
135300907008 = 220 · 37 · 59 |
Discriminant |
Eigenvalues |
2- 3- 0 0 -4 -4 -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1740,-21616] |
[a1,a2,a3,a4,a6] |
Generators |
[-32:36:1] [-20:72:1] |
Generators of the group modulo torsion |
j |
3048625/708 |
j-invariant |
L |
8.3481101791556 |
L(r)(E,1)/r! |
Ω |
0.7515762572773 |
Real period |
R |
2.7768673166307 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999997 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
33984g1 8496l1 11328j1 |
Quadratic twists by: -4 8 -3 |