\\ Pari/GP code for working with elliptic curve 3.3.733.1-8.1-c2 \\ (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([8, -7, -1, 1])); \\ Define the curve: E = ellinit([Polrev([-5,0,1]),Polrev([6,1,-1]),Polrev([0,0,0]),Polrev([29606060477,-14148462393,-9319242867]),Polrev([2907886170331433,-1389651899205825,-915329396489703])], 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]