The Arithmetic of Elliptic Curves
《The Arithmetic of Elliptic Curves》 · 第 59 页 · Chapter III，Section 3「Elliptic Curves」，Proposition 3.1(a)
There exist functions $x,y\in K(E)$ such that $\phi=[x,y,1]:E\to\mathbb P^2$ gives an isomorphism of $E/K$ onto a curve given by a Weierstrass equation, with $\phi(O)=[0,1,0]$. The functions $x$ and $y$ are called Weierstrass coordinates for the elliptic curve $E$.