Atkin-Lehner |
2- 3+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
32448ch |
Isogeny class |
Conductor |
32448 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
86016 |
Modular degree for the optimal curve |
Δ |
-49347441721344 = -1 · 218 · 3 · 137 |
Discriminant |
Eigenvalues |
2- 3+ 2 -4 -4 13+ 2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,5183,304225] |
[a1,a2,a3,a4,a6] |
j |
12167/39 |
j-invariant |
L |
0.89687385096781 |
L(r)(E,1)/r! |
Ω |
0.44843692548247 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
32448be1 8112bh1 97344fo1 2496t1 |
Quadratic twists by: -4 8 -3 13 |