Show that $(x,y) \rightarrow (x,-y)$ is a group homomorphism from $E$ to itself where $E$ is an elliptic curve in Weierstrass form.
So $E$ is of the form $y^2=x^3+ax+b$. Would I just show that any point $P \in E$ maps to $-P$ and this operation is always perserved? How does this being an elliptic curve alter this basic problem? What's a good way to show that this mapping is a group homomorphism?