Atkin-Lehner |
2+ 3- 13+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
83304d |
Isogeny class |
Conductor |
83304 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
31744 |
Modular degree for the optimal curve |
Δ |
1943315712 = 28 · 38 · 13 · 89 |
Discriminant |
Eigenvalues |
2+ 3- 0 -1 0 13+ 3 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-660,-6172] |
[a1,a2,a3,a4,a6] |
Generators |
[-14:18:1] |
Generators of the group modulo torsion |
j |
170368000/10413 |
j-invariant |
L |
5.956058585574 |
L(r)(E,1)/r! |
Ω |
0.94552213949012 |
Real period |
R |
0.78740337346556 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000011764 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
27768f1 |
Quadratic twists by: -3 |