Atkin-Lehner |
3+ 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
61347d |
Isogeny class |
Conductor |
61347 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
64512 |
Modular degree for the optimal curve |
Δ |
-296110251723 = -1 · 3 · 112 · 138 |
Discriminant |
Eigenvalues |
0 3+ -2 3 11- 13+ -2 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-1239,-30691] |
[a1,a2,a3,a4,a6] |
j |
-360448/507 |
j-invariant |
L |
1.5309612482868 |
L(r)(E,1)/r! |
Ω |
0.3827403114165 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
61347e1 4719f1 |
Quadratic twists by: -11 13 |