Atkin-Lehner |
2- 3+ 7+ 61- |
Signs for the Atkin-Lehner involutions |
Class |
81984bm |
Isogeny class |
Conductor |
81984 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
15360 |
Modular degree for the optimal curve |
Δ |
-62963712 = -1 · 214 · 32 · 7 · 61 |
Discriminant |
Eigenvalues |
2- 3+ 0 7+ 0 -4 3 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,27,-387] |
[a1,a2,a3,a4,a6] |
Generators |
[12:39:1] |
Generators of the group modulo torsion |
j |
128000/3843 |
j-invariant |
L |
4.3157490853275 |
L(r)(E,1)/r! |
Ω |
0.94884069179101 |
Real period |
R |
2.2742221752611 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002792 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
81984be1 20496d1 |
Quadratic twists by: -4 8 |