\\ Pari/GP code for working with elliptic curve 4.4.2000.1-1.1-a4
\\ (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([5, 0, -5, 0, 1]));

\\ Define the curve: 
E = ellinit([Polrev([-2,-3,1,1]),Polrev([-1,1,0,0]),Polrev([-2,1,1,0]),Polrev([-619,-541,150,140]),Polrev([-7491,-6449,1963,1727])], 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]