\\ Pari/GP code for working with elliptic curve 6.6.703493.1-41.4-e2 \\ (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, -9, 2, 11, -5, -2, 1])); \\ Define the curve: E = ellinit([Polrev([-1,14,5,-12,-1,2]),Polrev([4,-7,-6,6,1,-1]),Polrev([-5,9,11,-11,-2,2]),Polrev([28,-156,-71,169,3,-30]),Polrev([63,-561,-157,635,-28,-115])], 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]