Atkin-Lehner |
3- 11- 17- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
31977v |
Isogeny class |
Conductor |
31977 |
Conductor |
∏ cp |
72 |
Product of Tamagawa factors cp |
deg |
101376 |
Modular degree for the optimal curve |
Δ |
-361663981506729 = -1 · 37 · 116 · 173 · 19 |
Discriminant |
Eigenvalues |
-1 3- -1 -3 11- -6 17- 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-8978,-969550] |
[a1,a2,a3,a4,a6] |
Generators |
[144:769:1] [210:2419:1] |
Generators of the group modulo torsion |
j |
-109771509498841/496109714001 |
j-invariant |
L |
4.761383479867 |
L(r)(E,1)/r! |
Ω |
0.22248707315117 |
Real period |
R |
0.29723221746163 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999991 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
10659e1 |
Quadratic twists by: -3 |