Atkin-Lehner |
2+ 5- 13+ 67- |
Signs for the Atkin-Lehner involutions |
Class |
69680i |
Isogeny class |
Conductor |
69680 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
18432 |
Modular degree for the optimal curve |
Δ |
111488000 = 210 · 53 · 13 · 67 |
Discriminant |
Eigenvalues |
2+ 2 5- 3 -2 13+ -4 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-120,32] |
[a1,a2,a3,a4,a6] |
Generators |
[14:30:1] |
Generators of the group modulo torsion |
j |
188183524/108875 |
j-invariant |
L |
10.822629756235 |
L(r)(E,1)/r! |
Ω |
1.5800540390315 |
Real period |
R |
1.1415885668125 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000747 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34840f1 |
Quadratic twists by: -4 |