\\ Pari/GP code for working with elliptic curve 4.4.13888.1-28.2-b2

\\ (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([9, 6, -7, -2, 1]));

\\ Define the curve: 
E = ellinit([Polrev([1,-1/3,-2/3,1/3]),Polrev([0,1/3,2/3,-1/3]),Polrev([-2,-4/3,1/3,1/3]),Polrev([42,-61/3,-32/3,10/3]),Polrev([1802,-2383/3,-1574/3,541/3])], 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]