Atkin-Lehner |
2+ 3- 7+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
68544bb |
Isogeny class |
Conductor |
68544 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
540672 |
Modular degree for the optimal curve |
Δ |
-509359151843426304 = -1 · 214 · 317 · 72 · 173 |
Discriminant |
Eigenvalues |
2+ 3- -1 7+ -3 -1 17+ 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,24432,-34306144] |
[a1,a2,a3,a4,a6] |
j |
135037162496/42645837339 |
j-invariant |
L |
0.55163129962343 |
L(r)(E,1)/r! |
Ω |
0.13790782680627 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68544ej1 8568i1 22848e1 |
Quadratic twists by: -4 8 -3 |