Atkin-Lehner |
3- 13+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
8619l |
Isogeny class |
Conductor |
8619 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
912 |
Modular degree for the optimal curve |
Δ |
-8619 = -1 · 3 · 132 · 17 |
Discriminant |
Eigenvalues |
-2 3- 3 2 -4 13+ 17- -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-4,4] |
[a1,a2,a3,a4,a6] |
Generators |
[1:1:1] |
Generators of the group modulo torsion |
j |
-53248/51 |
j-invariant |
L |
3.3502367245615 |
L(r)(E,1)/r! |
Ω |
3.7633958886616 |
Real period |
R |
0.89021639595642 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
25857l1 8619k1 |
Quadratic twists by: -3 13 |