Atkin-Lehner |
2- 3+ 5+ 53+ |
Signs for the Atkin-Lehner involutions |
Class |
127200bw |
Isogeny class |
Conductor |
127200 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
147456 |
Modular degree for the optimal curve |
Δ |
21465000000 = 26 · 34 · 57 · 53 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 2 -4 -2 2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-8758,-312488] |
[a1,a2,a3,a4,a6] |
Generators |
[-54:8:1] [116:468:1] |
Generators of the group modulo torsion |
j |
74299881664/21465 |
j-invariant |
L |
10.803368230112 |
L(r)(E,1)/r! |
Ω |
0.49351654464865 |
Real period |
R |
10.945294890153 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000001309 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
127200cz1 25440t1 |
Quadratic twists by: -4 5 |