Atkin-Lehner |
2- 3+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
12696o |
Isogeny class |
Conductor |
12696 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
50688 |
Modular degree for the optimal curve |
Δ |
1470884593104 = 24 · 33 · 237 |
Discriminant |
Eigenvalues |
2- 3+ -2 4 4 -2 2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-109679,14017344] |
[a1,a2,a3,a4,a6] |
Generators |
[993443:24808315:1331] |
Generators of the group modulo torsion |
j |
61604313088/621 |
j-invariant |
L |
4.20572791454 |
L(r)(E,1)/r! |
Ω |
0.76878563883278 |
Real period |
R |
10.941223930576 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
25392q1 101568bd1 38088h1 552d1 |
Quadratic twists by: -4 8 -3 -23 |