Atkin-Lehner |
2- 3+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
3312k |
Isogeny class |
Conductor |
3312 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
192 |
Modular degree for the optimal curve |
Δ |
9936 = 24 · 33 · 23 |
Discriminant |
Eigenvalues |
2- 3+ 2 -2 -4 -2 2 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-24,-45] |
[a1,a2,a3,a4,a6] |
Generators |
[45:300:1] |
Generators of the group modulo torsion |
j |
3538944/23 |
j-invariant |
L |
3.5801117531509 |
L(r)(E,1)/r! |
Ω |
2.157827865067 |
Real period |
R |
3.3182551871809 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
828a1 13248z1 3312j1 82800ch1 |
Quadratic twists by: -4 8 -3 5 |