Atkin-Lehner |
2- 5+ 11- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
78320bd |
Isogeny class |
Conductor |
78320 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
81920 |
Modular degree for the optimal curve |
Δ |
133432217600 = 212 · 52 · 114 · 89 |
Discriminant |
Eigenvalues |
2- -2 5+ -2 11- 4 -6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-3256,68244] |
[a1,a2,a3,a4,a6] |
Generators |
[44:110:1] |
Generators of the group modulo torsion |
j |
932288503609/32576225 |
j-invariant |
L |
3.2449648628742 |
L(r)(E,1)/r! |
Ω |
1.0317298168328 |
Real period |
R |
0.39314615249405 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999989664 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
4895a1 |
Quadratic twists by: -4 |