\\ Pari/GP code for working with elliptic curve 6.6.371293.1-1.1-a4

\\ (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([-1, -3, 6, 4, -5, -1, 1]));

\\ Define the curve: 
E = ellinit([Polrev([2,6,-4,-5,1,1]),Polrev([-5,4,5,-1,-1,0]),Polrev([1,6,-3,-5,1,1]),Polrev([-4629,26993,-5670,-39313,849,9022]),Polrev([-462,1693284,-821368,-2641015,158368,611845])], 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]