\\ Pari/GP code for working with elliptic curve 2.0.3.1-75.1-a8 \\ (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(a^2 - a + 1); \\ Define the curve: E = ellinit([1, 1, 1, -2160, -39540],K) \\ Compute the discriminant: E.disc \\ Compute the norm of the discriminant: norm(E.disc) \\ Compute the j-invariant: E.j \\ Compute the order of the torsion subgroup: elltors(E)[1] \\ Compute the torsion subgroup: elltors(E)[2] \\ Compute the generators of the torsion subgroup: elltors(E)[3]