I evaluated Divison polynomials using
R.<A,B>=PolynomialRing(ZZ)
E = EllipticCurve([A,B])
g = E.division_polynomial(k)
The results i noticed were just function of $x$ , In theory i saw that division polynomials for k even depends on y. In there something I am unable to notice.
For example : E.division_polynomial(k) returned 4*x^3 + 4*A*x + 4*B but theory says it is 2y.
From this one can get a intuition that may be we are squaring them.
But E.division_polynomial(8) returned a degree $33$ polynomial which means that clearly we are not squaring things.
