\\ Pari/GP code for working with elliptic curve 3.3.49.1-41.3-a1

\\ (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(Pol(Vecrev([1, -2, -1, 1])));

\\ Define the curve: 
E = ellinit([Pol(Vecrev([1,0,0])),Pol(Vecrev([-3,-1,1])),Pol(Vecrev([0,0,0])),Pol(Vecrev([-68,101,-91])),Pol(Vecrev([-304,852,-646]))], 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]