Atkin-Lehner |
2+ 3- 11- 43+ |
Signs for the Atkin-Lehner involutions |
Class |
34056j |
Isogeny class |
Conductor |
34056 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
4021945488 = 24 · 312 · 11 · 43 |
Discriminant |
Eigenvalues |
2+ 3- 2 1 11- 4 -4 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-399,-317] |
[a1,a2,a3,a4,a6] |
Generators |
[-1:9:1] |
Generators of the group modulo torsion |
j |
602275072/344817 |
j-invariant |
L |
7.1868783983778 |
L(r)(E,1)/r! |
Ω |
1.1581734845517 |
Real period |
R |
1.5513389173211 |
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 |
68112h1 11352l1 |
Quadratic twists by: -4 -3 |