Atkin-Lehner |
2+ 3- 5- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
89280cl |
Isogeny class |
Conductor |
89280 |
Conductor |
∏ cp |
56 |
Product of Tamagawa factors cp |
deg |
4730880 |
Modular degree for the optimal curve |
Δ |
-56233543680000000 = -1 · 217 · 311 · 57 · 31 |
Discriminant |
Eigenvalues |
2+ 3- 5- -3 3 2 0 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-59019852,174520033904] |
[a1,a2,a3,a4,a6] |
Generators |
[4453:2025:1] |
Generators of the group modulo torsion |
j |
-237947203935023980322/588515625 |
j-invariant |
L |
6.4775683079363 |
L(r)(E,1)/r! |
Ω |
0.23168368449413 |
Real period |
R |
0.49926201248064 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000005382 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
89280fz1 11160e1 29760e1 |
Quadratic twists by: -4 8 -3 |