\\ Pari/GP code for working with elliptic curve 4.4.19821.1-25.1-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(Polrev([3, 6, -8, -1, 1]));

\\ Define the curve: 
E = ellinit([Polrev([-4,-1,1,0]),Polrev([1,-6,-1/3,2/3]),Polrev([1,1,0,0]),Polrev([3,-30,1,3]),Polrev([26,53,-1/3,-22/3])], 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]