# How could you find the preimage of an isogeny function?

How do you know if an isogeny is surjective or not, and how do you tell how many points on E maps to E'? Does the answer lie in the degree of the isogeny function?

Isogenies are always surjective, but there's a nuance. They are surjective over the algebraic closure. The correct statement would be "for every $\mathbb{F}_{17}$-point on the green curve there are three $\bar{\mathbb{F}}_{17}$-points on the blue curve which map to it".