\\ Pari/GP code for working with elliptic curve 2.2.29.1-7.2-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^2 - a - 7);

\\ Define the curve: 
E = ellinit([a, -1, 0, -a + 3, 0],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]