Embedding of a Rieman surface of genus one in $\mathbb{P}^2$

Question

In Jost's Compact Riemann Surfaces, he proves that every compact Riemann surface of genus one can be embedded into $\mathbb{P}^2$. Moreover, he proves the image of the embedding is the zero set of a polynomial of the form $y^2=x^3+ax+b$. I'm fine with his proof up to this point, but then, he claims that the left-hand side has three distinct zeros without any proof. How can one show that these are indeed distinct?