Atkin-Lehner |
2- 13+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
78416t |
Isogeny class |
Conductor |
78416 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
580608 |
Modular degree for the optimal curve |
Δ |
-110669862633734144 = -1 · 221 · 137 · 292 |
Discriminant |
Eigenvalues |
2- -1 3 -3 -4 13+ -1 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,116216,4823792] |
[a1,a2,a3,a4,a6] |
Generators |
[724:21632:1] |
Generators of the group modulo torsion |
j |
8780064047/5597696 |
j-invariant |
L |
4.5347843426007 |
L(r)(E,1)/r! |
Ω |
0.2076457434685 |
Real period |
R |
0.68247009686384 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000003385 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
9802b1 6032d1 |
Quadratic twists by: -4 13 |