Atkin-Lehner |
2- 3- 7+ 11- |
Signs for the Atkin-Lehner involutions |
Class |
81312bq |
Isogeny class |
Conductor |
81312 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
73728 |
Modular degree for the optimal curve |
Δ |
-17703899136 = -1 · 212 · 36 · 72 · 112 |
Discriminant |
Eigenvalues |
2- 3- -3 7+ 11- -3 -3 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-337,6719] |
[a1,a2,a3,a4,a6] |
Generators |
[-1:-84:1] [-22:63:1] |
Generators of the group modulo torsion |
j |
-8565568/35721 |
j-invariant |
L |
10.372922335561 |
L(r)(E,1)/r! |
Ω |
1.0710991747245 |
Real period |
R |
0.20175773986065 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999305 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
81312bj1 81312z1 |
Quadratic twists by: -4 -11 |