Atkin-Lehner |
2+ 3- 11+ 43- |
Signs for the Atkin-Lehner involutions |
Class |
22704j |
Isogeny class |
Conductor |
22704 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
7168 |
Modular degree for the optimal curve |
Δ |
49653648 = 24 · 38 · 11 · 43 |
Discriminant |
Eigenvalues |
2+ 3- 0 -1 11+ 6 6 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-648,-6561] |
[a1,a2,a3,a4,a6] |
Generators |
[-15:3:1] |
Generators of the group modulo torsion |
j |
1883643808000/3103353 |
j-invariant |
L |
6.6782356342079 |
L(r)(E,1)/r! |
Ω |
0.94622178463334 |
Real period |
R |
0.88222388010172 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
11352j1 90816bw1 68112p1 |
Quadratic twists by: -4 8 -3 |