Atkin-Lehner |
3+ 13+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
8619f |
Isogeny class |
Conductor |
8619 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
5232 |
Modular degree for the optimal curve |
Δ |
-24762387 = -1 · 3 · 134 · 172 |
Discriminant |
Eigenvalues |
2 3+ 4 -3 4 13+ 17- -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-56,-271] |
[a1,a2,a3,a4,a6] |
j |
-692224/867 |
j-invariant |
L |
4.991931575885 |
L(r)(E,1)/r! |
Ω |
0.83198859598083 |
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 |
25857p1 8619h1 |
Quadratic twists by: -3 13 |