Atkin-Lehner |
2+ 5+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
71200f |
Isogeny class |
Conductor |
71200 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
24576 |
Modular degree for the optimal curve |
Δ |
89000000 = 26 · 56 · 89 |
Discriminant |
Eigenvalues |
2+ 0 5+ -2 -4 -4 2 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-725,-7500] |
[a1,a2,a3,a4,a6] |
Generators |
[-16:2:1] [75:600:1] |
Generators of the group modulo torsion |
j |
42144192/89 |
j-invariant |
L |
9.0543702004643 |
L(r)(E,1)/r! |
Ω |
0.92017441820718 |
Real period |
R |
4.9199206266184 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000018 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
71200m1 2848d1 |
Quadratic twists by: -4 5 |