Can we describe $\operatorname{Spec}A_{(f)}$, where $A:= \mathbb{Z}[x,y,z]/(y^2z+yz^2-x^3+xz^2)$, more explicitly?

Question

Literally, let $A:= \mathbb{Z}[x,y,z]/(y^2z+yz^2-x^3+xz^2)$ and $f \in A_{+}$ be a homogeneous element. Let $A_{(f)}$ be the subring of elements of degree zero of the localization $A_f$.

Q. Then can we describe $\operatorname{Spec}A_{(f)}$ more explicitly? How?

This problem is connected with my other question : Why $\operatorname{Proj}\mathbb{Z}[x,y,z]/(y^2z+yz^2-x^3+xz^2)$ is fibered surface over $\operatorname{Spec}\mathbb{Z}$?. Refer to the "second attempt for the question 2" at the bottom of the linked question.

Can anyone helps?