Atkin-Lehner |
2- 5+ 29- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
68150r |
Isogeny class |
Conductor |
68150 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
110592 |
Modular degree for the optimal curve |
Δ |
10388189687500 = 22 · 57 · 294 · 47 |
Discriminant |
Eigenvalues |
2- 1 5+ 1 3 3 0 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-5463,9917] |
[a1,a2,a3,a4,a6] |
Generators |
[142:-1521:1] |
Generators of the group modulo torsion |
j |
1153990560169/664844140 |
j-invariant |
L |
13.2316628271 |
L(r)(E,1)/r! |
Ω |
0.61554528997861 |
Real period |
R |
0.67174498781015 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000812 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
13630d1 |
Quadratic twists by: 5 |