Atkin-Lehner |
2- 11+ 71- |
Signs for the Atkin-Lehner involutions |
Class |
24992b |
Isogeny class |
Conductor |
24992 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
10368 |
Modular degree for the optimal curve |
Δ |
4398592 = 29 · 112 · 71 |
Discriminant |
Eigenvalues |
2- -1 -2 1 11+ -1 2 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-6864,221188] |
[a1,a2,a3,a4,a6] |
Generators |
[48:2:1] |
Generators of the group modulo torsion |
j |
69863259742856/8591 |
j-invariant |
L |
3.2199405331662 |
L(r)(E,1)/r! |
Ω |
1.9048835400496 |
Real period |
R |
0.4225902089902 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
24992a1 49984k1 |
Quadratic twists by: -4 8 |