Atkin-Lehner |
3- 11- 71- |
Signs for the Atkin-Lehner involutions |
Class |
77319u |
Isogeny class |
Conductor |
77319 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
69120 |
Modular degree for the optimal curve |
Δ |
-825248032191 = -1 · 38 · 116 · 71 |
Discriminant |
Eigenvalues |
1 3- -2 -2 11- 2 0 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,522,43335] |
[a1,a2,a3,a4,a6] |
Generators |
[-186:1173:8] [6:213:1] |
Generators of the group modulo torsion |
j |
12167/639 |
j-invariant |
L |
10.825079195318 |
L(r)(E,1)/r! |
Ω |
0.67824700963061 |
Real period |
R |
7.9801894011273 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000108 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
25773t1 639a1 |
Quadratic twists by: -3 -11 |