Atkin-Lehner |
13+ 17+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
8177a |
Isogeny class |
Conductor |
8177 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
9792 |
Modular degree for the optimal curve |
Δ |
522256813 = 132 · 174 · 37 |
Discriminant |
Eigenvalues |
2 1 0 1 5 13+ 17+ 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-6638,205963] |
[a1,a2,a3,a4,a6] |
j |
32351981100544000/522256813 |
j-invariant |
L |
6.0413028943536 |
L(r)(E,1)/r! |
Ω |
1.5103257235884 |
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 |
73593b1 106301a1 |
Quadratic twists by: -3 13 |