Consider $X\subseteq \mathbb P^1_{\mathbb C}\times \mathbb P^1_{\mathbb C}$ defined by the equation $(x_0^3+x_1^3)y_0^2+y_1^2(x_0^3-x_1^3)$ and $f:X\to \mathbb P^1_{\mathbb C}$ defined by $([a_0:a_1],[b_0:b_1])\mapsto [a_0:a_1]$.
My question si how do we find the degree of this morphism ? Since it's $[K(\mathbb P^1_{\mathbb C}),K(X)]$ and $X$ is projective, we can replace $X$ by an affine chart, which could be $X\cap (U_0\times U_0)$ where $U_0$ is the cart of $\mathbb P^1_{\mathbb C}$ defined by $\{x_0\neq 0\}$ so the first coordinate is non zero. in this case we would've that $U$ is defined by the equation $1+x_1^3+y_1^2-x_1^3y_1^2$.
So $K(U)=\operatorname{Frac}(A(U))\cong \operatorname{Frac}\mathbb C[x,y]/(1+x^3+y^2-x^3y^2)$ but i can't compute the required dimension.
Is there maybe an other way or I should continue with this ?