Atkin-Lehner |
2+ 3+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
27072d |
Isogeny class |
Conductor |
27072 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
18432 |
Modular degree for the optimal curve |
Δ |
15156854784 = 214 · 39 · 47 |
Discriminant |
Eigenvalues |
2+ 3+ -3 3 1 4 4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-864,-7776] |
[a1,a2,a3,a4,a6] |
Generators |
[-126:351:8] |
Generators of the group modulo torsion |
j |
221184/47 |
j-invariant |
L |
5.2758679037123 |
L(r)(E,1)/r! |
Ω |
0.89382599047748 |
Real period |
R |
2.9512835607375 |
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 |
27072bu1 1692a1 27072g1 |
Quadratic twists by: -4 8 -3 |