Atkin-Lehner |
2- 3+ 11+ 43+ |
Signs for the Atkin-Lehner involutions |
Class |
68112bb |
Isogeny class |
Conductor |
68112 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
24192 |
Modular degree for the optimal curve |
Δ |
-24724656 = -1 · 24 · 33 · 113 · 43 |
Discriminant |
Eigenvalues |
2- 3+ -3 1 11+ -4 -3 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-564,-5161] |
[a1,a2,a3,a4,a6] |
j |
-45927972864/57233 |
j-invariant |
L |
0.97959675419032 |
L(r)(E,1)/r! |
Ω |
0.48979837159789 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
17028d1 68112bg2 |
Quadratic twists by: -4 -3 |