Atkin-Lehner |
5+ 29- 53+ |
Signs for the Atkin-Lehner involutions |
Class |
7685c |
Isogeny class |
Conductor |
7685 |
Conductor |
∏ cp |
3 |
Product of Tamagawa factors cp |
deg |
2352 |
Modular degree for the optimal curve |
Δ |
-6463085 = -1 · 5 · 293 · 53 |
Discriminant |
Eigenvalues |
1 1 5+ -3 -5 -6 -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-204,1107] |
[a1,a2,a3,a4,a6] |
Generators |
[-15:36:1] [9:0:1] |
Generators of the group modulo torsion |
j |
-932288503609/6463085 |
j-invariant |
L |
6.5208566926856 |
L(r)(E,1)/r! |
Ω |
2.3898234705899 |
Real period |
R |
0.90953115337237 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999992 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
122960k1 69165o1 38425g1 |
Quadratic twists by: -4 -3 5 |