Atkin-Lehner |
5+ 29+ 53- |
Signs for the Atkin-Lehner involutions |
Class |
7685b |
Isogeny class |
Conductor |
7685 |
Conductor |
∏ cp |
3 |
Product of Tamagawa factors cp |
deg |
2544 |
Modular degree for the optimal curve |
Δ |
-21587165 = -1 · 5 · 29 · 533 |
Discriminant |
Eigenvalues |
-1 -3 5+ 1 -3 -4 -2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,42,186] |
[a1,a2,a3,a4,a6] |
Generators |
[-2:10:1] [13:46:1] |
Generators of the group modulo torsion |
j |
8377795791/21587165 |
j-invariant |
L |
2.3073732656385 |
L(r)(E,1)/r! |
Ω |
1.5042775845946 |
Real period |
R |
0.51129155267339 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000004 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
122960j1 69165p1 38425a1 |
Quadratic twists by: -4 -3 5 |