\\ Pari/GP code for working with elliptic curve 4.4.5744.1-16.1-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, -5, 0, 1]));

\\ Define the curve: 
E = ellinit([Polrev([0,5,1,-1]),Polrev([1,1,-1,0]),Polrev([-1,-1,1,0]),Polrev([-12,43,7,-10]),Polrev([-34,112,18,-25])], 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]