Atkin-Lehner |
3- 7- 19+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
86583u |
Isogeny class |
Conductor |
86583 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
559104 |
Modular degree for the optimal curve |
Δ |
-77223123925227 = -1 · 32 · 79 · 193 · 31 |
Discriminant |
Eigenvalues |
-2 3- 2 7- -4 4 3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-105072,-13151176] |
[a1,a2,a3,a4,a6] |
Generators |
[19659:465202:27] |
Generators of the group modulo torsion |
j |
-3179116785664/1913661 |
j-invariant |
L |
4.7818396313817 |
L(r)(E,1)/r! |
Ω |
0.13258115113738 |
Real period |
R |
9.0168164779061 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999967388 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
86583q1 |
Quadratic twists by: -7 |