Atkin-Lehner |
2+ 3- 47- |
Signs for the Atkin-Lehner involutions |
Class |
27072y |
Isogeny class |
Conductor |
27072 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
61440 |
Modular degree for the optimal curve |
Δ |
301333429960704 = 214 · 311 · 473 |
Discriminant |
Eigenvalues |
2+ 3- 1 3 1 2 -2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-35472,2432032] |
[a1,a2,a3,a4,a6] |
Generators |
[-199:1269:1] |
Generators of the group modulo torsion |
j |
413269421056/25228989 |
j-invariant |
L |
6.7053100943696 |
L(r)(E,1)/r! |
Ω |
0.53669439649804 |
Real period |
R |
2.0822868464568 |
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 |
27072bz1 3384e1 9024n1 |
Quadratic twists by: -4 8 -3 |