\\ Pari/GP code for working with elliptic curve 4.4.18496.1-4.3-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([2, 12, -11, -2, 1]));

\\ Define the curve: 
E = ellinit([Polrev([-32/9,5/9,2/3,-1/9]),Polrev([-22/9,-14/9,1/3,1/9]),Polrev([-11/3,11/3,1,-1/3]),Polrev([-179/9,170/9,11/3,-16/9]),Polrev([-196/9,142/9,10/3,-14/9])], 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]