\\ Pari/GP code for working with elliptic curve 6.6.434581.1-27.2-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, -2, 4, 5, -4, -2, 1]));

\\ Define the curve: 
E = ellinit([Polrev([1,2,3,-3,-2,1]),Polrev([6,1,-18,6,8,-3]),Polrev([-2,5,12,-10,-6,3]),Polrev([21,61,16,-58,-13,11]),Polrev([-825,-2871,-952,2735,744,-560])], 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]