Atkin-Lehner |
2- 3- 7+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
54684i |
Isogeny class |
Conductor |
54684 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
169344 |
Modular degree for the optimal curve |
Δ |
900486635666688 = 28 · 39 · 78 · 31 |
Discriminant |
Eigenvalues |
2- 3- 0 7+ -3 -4 -3 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-41160,-2871596] |
[a1,a2,a3,a4,a6] |
Generators |
[245:1323:1] [-139:405:1] |
Generators of the group modulo torsion |
j |
7168000/837 |
j-invariant |
L |
9.5172559842985 |
L(r)(E,1)/r! |
Ω |
0.33773587126184 |
Real period |
R |
2.3482985754381 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999963 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
18228j1 54684k1 |
Quadratic twists by: -3 -7 |