Atkin-Lehner |
2- 3+ 5- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
12240bg |
Isogeny class |
Conductor |
12240 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
768 |
Modular degree for the optimal curve |
Δ |
-36720 = -1 · 24 · 33 · 5 · 17 |
Discriminant |
Eigenvalues |
2- 3+ 5- 1 -1 0 17+ 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,3,-9] |
[a1,a2,a3,a4,a6] |
Generators |
[6:15:1] |
Generators of the group modulo torsion |
j |
6912/85 |
j-invariant |
L |
5.221778212037 |
L(r)(E,1)/r! |
Ω |
1.796052066876 |
Real period |
R |
1.4536823036316 |
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 |
3060d1 48960dj1 12240bc1 61200dk1 |
Quadratic twists by: -4 8 -3 5 |