The solvability of the inverse volcano problem over non-prime finite fields

Alexandru Ghitza, Dhruv Gupta, Maximilian Kortge

For a finite field ${\mathbf{F}}_{p^k}$ and a prime $\ell \ne p$, consider the graph $G$ of $\ell$-isogenies between ordinary elliptic curves over ${\mathbf{F}}_{p^k}$. Kohel proved t…