\\ Pari/GP code for working with elliptic curve 6.6.1397493.1-37.1-a1

\\ (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, -6, 3, 10, -3, -3, 1]));

\\ Define the curve: 
E = ellinit([Polrev([-1,3,-2,-2,1,0]),Polrev([2,-3,2,2,-1,0]),Polrev([1,-2,-1,1,0,0]),Polrev([2,-12,9,8,-4,0]),Polrev([0,-4,6,3,-2,0])], 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]