\\ Pari/GP code for working with elliptic curve 6.6.1397493.1-64.1-a2
\\ (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([-3,5,9,-3,-3,1]),Polrev([2,-8,0,4,-1,0]),Polrev([1,5,-3,-2,1,0]),Polrev([3,-24,-12,10,2,-1]),Polrev([-4,-7,-10,-5,1,1])], K);

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

\\ Compute the norm of the conductor: 
idealnorm(K, 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]