### Division polynomials just a function of x !

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.