Atkin-Lehner |
2- 3- 11+ 43+ |
Signs for the Atkin-Lehner involutions |
Class |
68112bl |
Isogeny class |
Conductor |
68112 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
9216 |
Modular degree for the optimal curve |
Δ |
5517072 = 24 · 36 · 11 · 43 |
Discriminant |
Eigenvalues |
2- 3- 0 -3 11+ -2 -2 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-45,27] |
[a1,a2,a3,a4,a6] |
Generators |
[-6:9:1] |
Generators of the group modulo torsion |
j |
864000/473 |
j-invariant |
L |
4.9032820027429 |
L(r)(E,1)/r! |
Ω |
2.095849253056 |
Real period |
R |
1.1697601809308 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999996452 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
17028q1 7568k1 |
Quadratic twists by: -4 -3 |