Atkin-Lehner |
2- 3- 7+ 11- |
Signs for the Atkin-Lehner involutions |
Class |
81312bo |
Isogeny class |
Conductor |
81312 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
184320 |
Modular degree for the optimal curve |
Δ |
6050065057344 = 26 · 32 · 72 · 118 |
Discriminant |
Eigenvalues |
2- 3- -2 7+ 11- 2 -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-18674,968856] |
[a1,a2,a3,a4,a6] |
Generators |
[-116:1260:1] [66:168:1] |
Generators of the group modulo torsion |
j |
6352182208/53361 |
j-invariant |
L |
11.609576579149 |
L(r)(E,1)/r! |
Ω |
0.75963762192206 |
Real period |
R |
7.6415229079573 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999998466 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
81312n1 7392f1 |
Quadratic twists by: -4 -11 |