Atkin-Lehner |
2- 3- 83+ |
Signs for the Atkin-Lehner involutions |
Class |
7968f |
Isogeny class |
Conductor |
7968 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
768 |
Modular degree for the optimal curve |
Δ |
-1019904 = -1 · 212 · 3 · 83 |
Discriminant |
Eigenvalues |
2- 3- -1 2 5 -4 -4 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-1,-49] |
[a1,a2,a3,a4,a6] |
Generators |
[13:48:1] |
Generators of the group modulo torsion |
j |
-64/249 |
j-invariant |
L |
5.1943786742414 |
L(r)(E,1)/r! |
Ω |
1.2583289200881 |
Real period |
R |
2.0639987650756 |
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 |
7968a1 15936c1 23904h1 |
Quadratic twists by: -4 8 -3 |