Atkin-Lehner |
3+ 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
61347g |
Isogeny class |
Conductor |
61347 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
5225472 |
Modular degree for the optimal curve |
Δ |
-235076302748106963 = -1 · 39 · 114 · 138 |
Discriminant |
Eigenvalues |
0 3+ -2 5 11- 13+ 2 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-66609209,-209220120484] |
[a1,a2,a3,a4,a6] |
j |
-462482914449031168/3326427 |
j-invariant |
L |
1.6910870393404 |
L(r)(E,1)/r! |
Ω |
0.026423235117845 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
16 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
61347h1 4719b1 |
Quadratic twists by: -11 13 |