Atkin-Lehner |
2- 7+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
32368u |
Isogeny class |
Conductor |
32368 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
4112640 |
Modular degree for the optimal curve |
Δ |
1470678069819766528 = 28 · 77 · 178 |
Discriminant |
Eigenvalues |
2- -3 2 7+ 0 4 17- -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-82061839,286127745178] |
[a1,a2,a3,a4,a6] |
Generators |
[98347370554006:-2362992439154:18799877179] |
Generators of the group modulo torsion |
j |
34222845097047888/823543 |
j-invariant |
L |
4.0544649717295 |
L(r)(E,1)/r! |
Ω |
0.19519493555107 |
Real period |
R |
20.771363561678 |
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 |
8092j1 129472cs1 32368bg1 |
Quadratic twists by: -4 8 17 |