Atkin-Lehner |
3+ 13+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
8619d |
Isogeny class |
Conductor |
8619 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
48384 |
Modular degree for the optimal curve |
Δ |
10109350825353 = 36 · 138 · 17 |
Discriminant |
Eigenvalues |
-1 3+ 4 -2 -6 13+ 17- -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-44366,-3612094] |
[a1,a2,a3,a4,a6] |
j |
2000852317801/2094417 |
j-invariant |
L |
0.65795202048098 |
L(r)(E,1)/r! |
Ω |
0.32897601024049 |
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 |
25857e1 663a1 |
Quadratic twists by: -3 13 |