Definition 2.1 (Rational plane affine curve). A plane affine curve $C=\{f(x,y)=0\}\subset {𝔸}^2$ is rational if it has a rational parametrisation, i.e. $\exists \varphi (t),\psi (t)\in K(t)$ such that:

• (i) ${𝔸}^1\to {𝔸}^2$, $t\mapsto (\varphi (t),\psi (t))$ is injective on ${𝔸}^1\setminus \{\text{finite set}\}$.
• (ii) $f(\varphi (t),\psi (t))=0$.