Atkin-Lehner |
2- 3- 7+ 89+ |
Signs for the Atkin-Lehner involutions |
Class |
89712p |
Isogeny class |
Conductor |
89712 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
276480 |
Modular degree for the optimal curve |
Δ |
-3333600313344 = -1 · 220 · 36 · 72 · 89 |
Discriminant |
Eigenvalues |
2- 3- -1 7+ 0 2 3 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-237963,44679994] |
[a1,a2,a3,a4,a6] |
Generators |
[282:14:1] |
Generators of the group modulo torsion |
j |
-499073536793161/1116416 |
j-invariant |
L |
6.0856549737233 |
L(r)(E,1)/r! |
Ω |
0.68523745908954 |
Real period |
R |
2.2202722942166 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999872154 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
11214p1 9968e1 |
Quadratic twists by: -4 -3 |