\\ Pari/GP code for working with elliptic curve 4.4.1125.1-31.2-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([1, 4, -4, -1, 1])); \\ Define the curve: E = ellinit([Polrev([1,-2,0,1]),Polrev([2,-2,-1,1]),Polrev([-1,0,1,0]),Polrev([-63,90,-4,-24]),Polrev([169,-250,26,49])], 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]