How to show ideals factor modulo an elliptic curve? That is $\langle f\rangle= \prod \langle x-x_p,y-y_p\rangle $ where $x_p$, $y_p$ is the intersection of $f$ with the elliptic curve points counted with multiplicity.
What's the easiest way to show this using mostly basic ring theory
Also is this true for other curves besides elliptic