\\ Pari/GP code for working with elliptic curve 5.5.65657.1-5.1-b1

\\ (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, 5, 2, -5, -1, 1]));

\\ Define the curve: 
E = ellinit([Polrev([-1,-1,1,0,0]),Polrev([-9,-10,13,4,-3]),Polrev([0,0,0,0,0]),Polrev([1145,4382,-3297,-1524,846]),Polrev([27278,102303,-77364,-36469,20454])], 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]