Atkin-Lehner |
2- 3+ 11+ 83+ |
Signs for the Atkin-Lehner involutions |
Class |
32868a |
Isogeny class |
Conductor |
32868 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
7680 |
Modular degree for the optimal curve |
Δ |
-6310656 = -1 · 28 · 33 · 11 · 83 |
Discriminant |
Eigenvalues |
2- 3+ -3 -2 11+ 6 -1 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-144,676] |
[a1,a2,a3,a4,a6] |
Generators |
[-12:26:1] [8:6:1] |
Generators of the group modulo torsion |
j |
-47775744/913 |
j-invariant |
L |
7.1596834988431 |
L(r)(E,1)/r! |
Ω |
2.3836341299865 |
Real period |
R |
0.50061398606814 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999991 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
32868b1 |
Quadratic twists by: -3 |