Atkin-Lehner |
2+ 13+ 83- |
Signs for the Atkin-Lehner involutions |
Class |
69056f |
Isogeny class |
Conductor |
69056 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
110592 |
Modular degree for the optimal curve |
Δ |
-12020137066496 = -1 · 227 · 13 · 832 |
Discriminant |
Eigenvalues |
2+ -1 1 3 -2 13+ 5 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-2465,-172511] |
[a1,a2,a3,a4,a6] |
j |
-6321363049/45853184 |
j-invariant |
L |
2.4003935999963 |
L(r)(E,1)/r! |
Ω |
0.30004919828086 |
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 |
69056k1 2158a1 |
Quadratic twists by: -4 8 |