\\ Pari/GP code for working with elliptic curve 4.4.19821.1-27.2-d2 \\ (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([3, 6, -8, -1, 1])); \\ Define the curve: E = ellinit([Polrev([0,-2,1/3,1/3]),Polrev([5,0,-1,0]),Polrev([0,1,0,0]),Polrev([9,-1,-1,0]),Polrev([5,-2,-2/3,1/3])], 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]