\\ Pari/GP code for working with elliptic curve 5.5.36497.1-39.1-b8

\\ (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, 1, 5, -3, -2, 1]));

\\ Define the curve: 
E = ellinit([Polrev([2,5,-3,-2,1]),Polrev([0,-5,2,2,-1]),Polrev([2,5,-3,-2,1]),Polrev([16767,-4349,-89524,-15206,22858]),Polrev([2228472,-559230,-11583514,-1981540,2975973])], 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]