In the book of Jurgen Jost, Compact Riemann Surface, is written (page 261):
" As Theorem 5.7.1, it can be shown that $z \rightarrow (1,\wp(z),\wp'(z))$ defines an embedding of $\mathbb{C}/\Lambda$ in $\mathbb{P}^{2}$. The image of $\mathbb{C}/\Lambda$ is then (by (5.10.2)) the plane algebraic curve defined by equation $y^{2}=4x^{3}-g_{2}x -g_{3}$."
Where (5.10.2) is: $\wp'(z)^{2}=4\wp(z)^{3}-g_{2}\wp(z) -g_{3}$.
My question is: why the image of $\mathbb{C}/\Lambda$ by the embedding is the algebric curve $y^{2}=4x^{3}-g_{2}x -g_{3}?$