Atkin-Lehner |
2- 3+ 13+ 53- |
Signs for the Atkin-Lehner involutions |
Class |
8268b |
Isogeny class |
Conductor |
8268 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
2688 |
Modular degree for the optimal curve |
Δ |
47326032 = 24 · 34 · 13 · 532 |
Discriminant |
Eigenvalues |
2- 3+ 0 -2 6 13+ 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-333,2430] |
[a1,a2,a3,a4,a6] |
Generators |
[9:9:1] |
Generators of the group modulo torsion |
j |
256000000000/2957877 |
j-invariant |
L |
3.5682789988071 |
L(r)(E,1)/r! |
Ω |
2.0215012456299 |
Real period |
R |
0.58838763295695 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
33072u1 24804d1 107484a1 |
Quadratic twists by: -4 -3 13 |