\\ Pari/GP code for working with elliptic curve 6.6.434581.1-71.1-a3

\\ (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, -2, 4, 5, -4, -2, 1]));

\\ Define the curve: 
E = ellinit([Polrev([-2,3,5,-4,-2,1]),Polrev([-2,-3,6,-1,-3,1]),Polrev([-1,2,7,-6,-4,2]),Polrev([-14,-1,51,-10,-30,10]),Polrev([6,17,-39,-31,55,-15])], 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]