\\ Pari/GP code for working with elliptic curve 4.4.1125.1-25.1-a8

\\ (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, 4, -4, -1, 1]));

\\ Define the curve: 
E = ellinit([Polrev([1,-2,0,1]),Polrev([-3,-4,1,1]),Polrev([-1,1,1,0]),Polrev([109138,496253,-165053,-199462]),Polrev([27900618,126872829,-42163431,-50977357])], 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]