Supersingular isogeny graphs are very complicated and intricate, and are used extensively by cryptographers. On the other side of things, the structure of ordinary isogeny graphs is well understood connected components look like volcanoes. Throughout this talk we will explore the ordinary
-isogeny graph over
for various prime numbers
and
, and answer the following question, given a volcano-shaped graph, can we always find an isogeny graph in which our volcano lives as a connected component?