Let $p(x,y)$ be a polynomial defining an affine algebraic plane curve. I'm interested in such $p$ with the property that $p(x,y)=-p(y,x)$. I've tried and failed to find references for plane curves with this type of symmetry, but this seems like a natural enough condition that it must be well-studied.
What are some references/key words/terms I should consult to learn more about such curves?