Atkin-Lehner |
2+ 3- 5+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
69360x |
Isogeny class |
Conductor |
69360 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
73728 |
Modular degree for the optimal curve |
Δ |
17379049680 = 24 · 32 · 5 · 176 |
Discriminant |
Eigenvalues |
2+ 3- 5+ 0 -4 6 17+ 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-4431,-114840] |
[a1,a2,a3,a4,a6] |
j |
24918016/45 |
j-invariant |
L |
2.3408471212946 |
L(r)(E,1)/r! |
Ω |
0.58521178283437 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
34680bc1 240a1 |
Quadratic twists by: -4 17 |