\\ Pari/GP code for working with elliptic curve 4.4.18625.1-11.1-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([41, 9, -14, -1, 1]));

\\ Define the curve: 
E = ellinit([Polrev([-6,0,1,0]),Polrev([-37/6,1/3,1,-1/6]),Polrev([-35/6,-4/3,1,1/6]),Polrev([-3918,-2374,349,228]),Polrev([-143503/3,-88993/3,4234,8573/3])], 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]