Atkin-Lehner |
2- 19+ 71- |
Signs for the Atkin-Lehner involutions |
Class |
86336k |
Isogeny class |
Conductor |
86336 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
8640 |
Modular degree for the optimal curve |
Δ |
-6129856 = -1 · 26 · 19 · 712 |
Discriminant |
Eigenvalues |
2- 0 1 -1 1 -6 -1 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-32,-138] |
[a1,a2,a3,a4,a6] |
Generators |
[11:29:1] |
Generators of the group modulo torsion |
j |
-56623104/95779 |
j-invariant |
L |
5.1183845162487 |
L(r)(E,1)/r! |
Ω |
0.94883116110972 |
Real period |
R |
2.6972051085766 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000012514 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
86336e1 21584d1 |
Quadratic twists by: -4 8 |