Atkin-Lehner |
3- 5+ 7+ 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
75075bf |
Isogeny class |
Conductor |
75075 |
Conductor |
∏ cp |
120 |
Product of Tamagawa factors cp |
deg |
829440 |
Modular degree for the optimal curve |
Δ |
-53536191818484375 = -1 · 310 · 56 · 74 · 11 · 133 |
Discriminant |
Eigenvalues |
-1 3- 5+ 7+ 11+ 13- 0 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-86638,14834267] |
[a1,a2,a3,a4,a6] |
Generators |
[317:-4546:1] |
Generators of the group modulo torsion |
j |
-4602875775513625/3426316276383 |
j-invariant |
L |
3.9509624853216 |
L(r)(E,1)/r! |
Ω |
0.32593209089723 |
Real period |
R |
0.40406806557205 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002583 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
3003d1 |
Quadratic twists by: 5 |