\\ Pari/GP code for working with elliptic curve 6.6.371293.1-53.5-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([-1, -3, 6, 4, -5, -1, 1]));

\\ Define the curve: 
E = ellinit([Polrev([-1,1,1,0,0,0]),Polrev([-3,-1,4,4,-1,-1]),Polrev([-1,3,1,-4,0,1]),Polrev([-4,-14,12,21,-3,-5]),Polrev([-2,-7,9,15,-2,-4])], 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]