Atkin-Lehner |
3+ 7+ 17- 31- |
Signs for the Atkin-Lehner involutions |
Class |
77469a |
Isogeny class |
Conductor |
77469 |
Conductor |
∏ cp |
15 |
Product of Tamagawa factors cp |
deg |
272160 |
Modular degree for the optimal curve |
Δ |
-761222953971501 = -1 · 3 · 78 · 175 · 31 |
Discriminant |
Eigenvalues |
1 3+ -2 7+ 3 0 17- 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-41381,3484230] |
[a1,a2,a3,a4,a6] |
Generators |
[-78:2538:1] |
Generators of the group modulo torsion |
j |
-1359435900697/132046701 |
j-invariant |
L |
5.2129358101724 |
L(r)(E,1)/r! |
Ω |
0.49313656166817 |
Real period |
R |
0.70473187549814 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000874 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
77469t1 |
Quadratic twists by: -7 |