Atkin-Lehner |
2+ 3- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
27456bd |
Isogeny class |
Conductor |
27456 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
18432 |
Modular degree for the optimal curve |
Δ |
1174238208 = 210 · 36 · 112 · 13 |
Discriminant |
Eigenvalues |
2+ 3- 0 -2 11- 13+ -2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-2133,37179] |
[a1,a2,a3,a4,a6] |
Generators |
[30:33:1] |
Generators of the group modulo torsion |
j |
1048576000000/1146717 |
j-invariant |
L |
6.0044885419042 |
L(r)(E,1)/r! |
Ω |
1.5346277164249 |
Real period |
R |
0.65211130986785 |
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 |
27456bj1 1716a1 82368r1 |
Quadratic twists by: -4 8 -3 |