Atkin-Lehner |
2- 13- 83- |
Signs for the Atkin-Lehner involutions |
Class |
69056p |
Isogeny class |
Conductor |
69056 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
20736 |
Modular degree for the optimal curve |
Δ |
-14363648 = -1 · 210 · 132 · 83 |
Discriminant |
Eigenvalues |
2- -3 -2 -1 3 13- 1 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-16,184] |
[a1,a2,a3,a4,a6] |
Generators |
[-6:8:1] [1:13:1] |
Generators of the group modulo torsion |
j |
-442368/14027 |
j-invariant |
L |
5.9798368221297 |
L(r)(E,1)/r! |
Ω |
1.8560380065832 |
Real period |
R |
0.8054572159793 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999876 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69056h1 17264b1 |
Quadratic twists by: -4 8 |