Atkin-Lehner |
3- 19+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
31407d |
Isogeny class |
Conductor |
31407 |
Conductor |
∏ cp |
18 |
Product of Tamagawa factors cp |
deg |
15984 |
Modular degree for the optimal curve |
Δ |
-2959198947 = -1 · 33 · 194 · 292 |
Discriminant |
Eigenvalues |
-1 3- 2 -1 6 1 -4 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,173,-2452] |
[a1,a2,a3,a4,a6] |
Generators |
[11:23:1] |
Generators of the group modulo torsion |
j |
4392287/22707 |
j-invariant |
L |
5.3173895224843 |
L(r)(E,1)/r! |
Ω |
0.71703065596105 |
Real period |
R |
0.4119914909788 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
94221g1 31407a1 |
Quadratic twists by: -3 -19 |