Let $P$ be a point on an elliptic curve $E$ and let $Q = \phi(P)$, where $\phi: E \to E'$ is an isogeny of degree $d$.
Given $E, E', P, Q$ and $d$, is it possible to find an isogeny $\phi': E \to E'$, not necessarily equal to $\phi$, such that $\phi'(P) = Q$?
If so, how? And what is the complexity of such an algorithm?
Follow up question: if it is possible, it is also possible for two pairs of points?