Atkin-Lehner |
2- 43+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
32336j |
Isogeny class |
Conductor |
32336 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
9504 |
Modular degree for the optimal curve |
Δ |
32336 = 24 · 43 · 47 |
Discriminant |
Eigenvalues |
2- 2 3 -2 0 -4 -3 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1349,-18628] |
[a1,a2,a3,a4,a6] |
Generators |
[-764051188:1026639:36594368] |
Generators of the group modulo torsion |
j |
16980930199552/2021 |
j-invariant |
L |
9.0088307428683 |
L(r)(E,1)/r! |
Ω |
0.78771614256557 |
Real period |
R |
11.436646091226 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999999 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8084b1 129344bh1 |
Quadratic twists by: -4 8 |