Degree two map from a complex curve to $\mathbb{P}^1$

Question

Good morning! I am trying to find a degree two map $\eta$ from the algebraic curve $\mathcal{C}:y^3+x^3=1$ over $\mathbb{C}$ to $\mathbb{P}^1$ with $\eta(1,0)=\eta(0,1)$. I think that the map $$\eta:(x,y)\mapsto x+y$$ is the correct one. I am using the degree formula from Miranda's Algebraic Curves and Riemann Surfaces which state that $$\deg(\eta)=\sum_{p\in\eta^{-1}(y)}mult_p(\eta)$$ where $y\in\mathbb{P}^1$. I have chosen $y=1$ (using $\mathbb{P}^1=\mathbb{C}\cup\{\infty\}$) so that $\eta^{-1}(1)=\{(1,0);(0,1)\}$ so that $$\deg(\eta)=mult_{(1,0)}(\eta)+mult_{(0,1)}(\eta)$$ Is all this correct? Now I am stucked, how do I calculate multiplicities? I have found something about the relationship with orders but I have no clue now.