\\ Pari/GP code for working with elliptic curve 3.3.81.1-27.1-a3

\\ (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^3 - 3*a - 1);

\\ Define the curve: 
E = ellinit([0, a^2 - 1, a + 1, 17*a^2 - 3*a - 53, -56*a^2 + 17*a + 164],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]