\\ Pari/GP code for working with elliptic curve 4.4.13968.1-4.2-c1

\\ (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([4, 8, -7, -2, 1]));

\\ Define the curve: 
E = ellinit([Polrev([-2,-1/2,1/2,0]),Polrev([0,-2,-1/2,1/2]),Polrev([-1,1/2,1/2,0]),Polrev([-125876,146797/2,57713/2,-12062]),Polrev([-18756361,11009111,4323424,-1811281])], 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]