Atkin-Lehner |
3- 11+ 17- 19- |
Signs for the Atkin-Lehner involutions |
Class |
31977q |
Isogeny class |
Conductor |
31977 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
395136 |
Modular degree for the optimal curve |
Δ |
-3622720525399958499 = -1 · 313 · 117 · 17 · 193 |
Discriminant |
Eigenvalues |
0 3- 2 -3 11+ -1 17- 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,306006,64349401] |
[a1,a2,a3,a4,a6] |
j |
4346963661717536768/4969438306447131 |
j-invariant |
L |
1.9943779398903 |
L(r)(E,1)/r! |
Ω |
0.16619816165715 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
10659a1 |
Quadratic twists by: -3 |