Q:

System of parameters for a local ring

I need some help to solve this problem. This is the kind of problem that makes me stuck at the very beginning. 

Let $K$ be an algebraically closed field, $X = \{(x,y)\in\mathbb{A}^2_K: \ y^2-x^3=0\}$ an affine variety and $\mathfrak{m}$ the maximal ideal in $X$ corresponding to the point $(0,0)\in X$. I want to localize the coordinate ring $\mathcal{O}(X)$ in $\mathfrak{m}$, so I will have a system of parameters for the local ring $\mathcal{O}_\mathfrak{m}$.

All I know about system of parameters is the following:
Proposition: let $R$ be a Noetherian local ring with maximal ideal $\mathfrak{m}$. Then the dimension of $R$ is the minimum $n\in\mathbb{N}$ such that there is $r_1,\ldots,r_n\in R$ with $\sqrt{(r_1,\ldots,r_n)} = \mathfrak{m}$. In this case, the $r_i$'s a system of parameters for $R$.
But this is not helping much. Thank you very much for the help.

A:

Thought isn't clear, the question seems to ask for finding a sop of the local ring $$K[X,Y]_{(X,Y)}/(X^3-Y^2).$$
This ring is $1$-dimensional, so a sop has only one element. There are two clear contenders. Prove that each one of them does the job. 

