Atkin-Lehner |
3+ 5- 31- 37+ |
Signs for the Atkin-Lehner involutions |
Class |
51615b |
Isogeny class |
Conductor |
51615 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
7616 |
Modular degree for the optimal curve |
Δ |
5729265 = 33 · 5 · 31 · 372 |
Discriminant |
Eigenvalues |
-1 3+ 5- 2 4 2 -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-47,54] |
[a1,a2,a3,a4,a6] |
Generators |
[-6:12:1] |
Generators of the group modulo torsion |
j |
416832723/212195 |
j-invariant |
L |
4.9027702141126 |
L(r)(E,1)/r! |
Ω |
2.1201320230101 |
Real period |
R |
2.3124834495658 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000015 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
51615a1 |
Quadratic twists by: -3 |