\\ Pari/GP code for working with elliptic curve 5.5.65657.1-27.1-b1 \\ (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, 5, 2, -5, -1, 1])); \\ Define the curve: E = ellinit([Polrev([1,1,0,0,0]),Polrev([0,6,-3,-2,1]),Polrev([3,2,-4,-1,1]),Polrev([-4,-16,1,3,0]),Polrev([-4,-16,-22,1,5])], 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]