\\ Pari/GP code for working with elliptic curve 6.6.453789.1-41.6-c1

\\ (Note that not all these functions may be available, and some may take a long time to execute.)

\\ Define the base number field: 
K = nfinit(Polrev([1, -8, 8, 6, -6, -1, 1]));

\\ Define the curve: 
E = ellinit([Polrev([-4,3,2,-4,0,1]),Polrev([-7,7,6,-6,-1,1]),Polrev([0,-3,0,1,0,0]),Polrev([5,-22,-9,11,3,-1]),Polrev([-6,37,-2,-31,2,6])], K);

\\ Compute the conductor: 
ellglobalred(E)[1]

\\ Compute the norm of the conductor: 
idealnorm(ellglobalred(E)[1])

\\ Compute the discriminant: 
E.disc

\\ Compute the norm of the discriminant: 
norm(E.disc)

\\ Compute the j-invariant: 
E.j

\\ Compute the torsion subgroup: 
T = elltors(E); T[2]

\\ Compute the order of the torsion subgroup: 
T[1]

\\ Compute the generators of the torsion subgroup: 
T[3]