\\ Pari/GP code for working with elliptic curve 6.6.1241125.1-25.2-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, 7, 11, -2, -7, 0, 1]));

\\ Define the curve: 
E = ellinit([Polrev([-3,-8,-3,6,1,-1]),Polrev([-23,-65,-1,41,2,-6]),Polrev([-12,-29,0,20,1,-3]),Polrev([-84,-463,-59,303,22,-45]),Polrev([-12189,-58796,-6320,38079,2584,-5610])], 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]