Atkin-Lehner |
2- 3- 7+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
85176bu |
Isogeny class |
Conductor |
85176 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
5419008 |
Modular degree for the optimal curve |
Δ |
108449822110226688 = 28 · 39 · 73 · 137 |
Discriminant |
Eigenvalues |
2- 3- 2 7+ 4 13+ -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-61041279,183562324738] |
[a1,a2,a3,a4,a6] |
Generators |
[9685403:-26048088:2197] |
Generators of the group modulo torsion |
j |
27923315228972368/120393 |
j-invariant |
L |
7.777566220106 |
L(r)(E,1)/r! |
Ω |
0.22496392722965 |
Real period |
R |
8.6431259334703 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000007676 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
28392k1 6552j1 |
Quadratic twists by: -3 13 |