\\ Pari/GP code for working with elliptic curve 6.6.434581.1-49.1-a1 \\ (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, -2, 4, 5, -4, -2, 1])); \\ Define the curve: E = ellinit([Polrev([1,5,4,-8,-3,2]),Polrev([-2,-2,3,2,-1,0]),Polrev([-3,1,11,-5,-5,2]),Polrev([-1,-5,-2,13,4,-3]),Polrev([-1,-4,-1,12,4,-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]