\\ Pari/GP code for working with elliptic curve 4.4.8000.1-44.3-c2
\\ (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([20, 0, -10, 0, 1]));

\\ Define the curve: 
E = ellinit([Polrev([1,1,0,0]),Polrev([3,4,-1/2,-1/2]),Polrev([-3,0,1/2,0]),Polrev([-106,-67,29/2,19/2]),Polrev([1265,761,-175,-105])], 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]