Atkin-Lehner |
2+ 3+ 11+ |
Signs for the Atkin-Lehner involutions |
Class |
3168d |
Isogeny class |
Conductor |
3168 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
768 |
Modular degree for the optimal curve |
Δ |
13856832 = 26 · 39 · 11 |
Discriminant |
Eigenvalues |
2+ 3+ -2 -4 11+ 4 6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-81,-216] |
[a1,a2,a3,a4,a6] |
Generators |
[-5:8:1] |
Generators of the group modulo torsion |
j |
46656/11 |
j-invariant |
L |
2.7801820033459 |
L(r)(E,1)/r! |
Ω |
1.6185368503633 |
Real period |
R |
1.7177131325258 |
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 |
3168f1 6336br1 3168r1 79200co1 |
Quadratic twists by: -4 8 -3 5 |