Atkin-Lehner |
3- 5- 11+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
8415n |
Isogeny class |
Conductor |
8415 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
69888 |
Modular degree for the optimal curve |
Δ |
72787695556640625 = 313 · 512 · 11 · 17 |
Discriminant |
Eigenvalues |
-1 3- 5- 0 11+ 2 17- -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-123557,10564364] |
[a1,a2,a3,a4,a6] |
j |
286150792766867209/99845947265625 |
j-invariant |
L |
0.95175809687382 |
L(r)(E,1)/r! |
Ω |
0.31725269895794 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
2805d1 42075w1 92565bq1 |
Quadratic twists by: -3 5 -11 |