Atkin-Lehner |
2+ 43- 47- |
Signs for the Atkin-Lehner involutions |
Class |
129344r |
Isogeny class |
Conductor |
129344 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
16128 |
Modular degree for the optimal curve |
Δ |
2069504 = 210 · 43 · 47 |
Discriminant |
Eigenvalues |
2+ 2 1 2 4 0 5 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-85,-267] |
[a1,a2,a3,a4,a6] |
Generators |
[-348:141:64] |
Generators of the group modulo torsion |
j |
67108864/2021 |
j-invariant |
L |
13.676165464777 |
L(r)(E,1)/r! |
Ω |
1.5736930009927 |
Real period |
R |
4.3452456998391 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999809275 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
129344u1 8084a1 |
Quadratic twists by: -4 8 |