Atkin-Lehner |
2- 3- 11+ 13- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
58344i |
Isogeny class |
Conductor |
58344 |
Conductor |
∏ cp |
168 |
Product of Tamagawa factors cp |
deg |
451584 |
Modular degree for the optimal curve |
Δ |
-42038628762317616 = -1 · 24 · 37 · 114 · 136 · 17 |
Discriminant |
Eigenvalues |
2- 3- -2 -2 11+ 13- 17+ 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-76219,12738206] |
[a1,a2,a3,a4,a6] |
Generators |
[-169:4563:1] [-130:4524:1] |
Generators of the group modulo torsion |
j |
-3060547801156175872/2627414297644851 |
j-invariant |
L |
10.305076206561 |
L(r)(E,1)/r! |
Ω |
0.33098829857891 |
Real period |
R |
0.74129193796978 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000007 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
116688d1 |
Quadratic twists by: -4 |