\\ Pari/GP code for working with elliptic curve 4.4.10816.1-1.1-b1
\\ (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, 10, -9, -2, 1]));

\\ Define the curve: 
E = ellinit([Polrev([-8/5,-11/5,1/5,1/5]),Polrev([-1,1,0,0]),Polrev([1,0,0,0]),Polrev([-177/5,256/5,-536/5,-241/5]),Polrev([-1997/5,16341/5,-13036/5,-7111/5])], 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]