\\ Pari/GP code for working with elliptic curve 6.6.434581.1-1.1-a3 \\ (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([-4,1,15,-8,-7,3]),Polrev([-3,0,8,-2,-3,1]),Polrev([-2,0,8,-2,-3,1]),Polrev([-4,-3,12,4,-3,0]),Polrev([-15,-8,67,-19,-28,10])], 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]