\\ Pari/GP code for working with elliptic curve 3.3.81.1-51.1-a5 \\ (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, -3, 0, 1])); \\ Define the curve: E = ellinit([Polrev([-1,1,1]),Polrev([-1,1,1]),Polrev([0,0,0]),Polrev([7,17,-3]),Polrev([-7,-13,17])], 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]