Atkin-Lehner |
2- 3- 11+ 43- |
Signs for the Atkin-Lehner involutions |
Class |
68112bu |
Isogeny class |
Conductor |
68112 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
Δ |
9.0887630181872E+19 |
Discriminant |
Eigenvalues |
2- 3- 2 0 11+ -2 6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1231059,256921490] |
[a1,a2,a3,a4,a6] |
j |
69099171213056977/30438083453184 |
j-invariant |
L |
2.7454780428274 |
L(r)(E,1)/r! |
Ω |
0.1715923775795 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
8514d2 22704bd2 |
Quadratic twists by: -4 -3 |