Supersingular Isogeny Graphs from Algebraic Modular Curves

Abstract

We describe and compare algorithms for computing supersingular isogeny graphs. Along the way, we obtain a formula for the trace of the adjacency matrix of a general supersingular isogeny graph, and we prove a conjecture recently posed by Nakaya.

arXiv comment30 pages; Changes in V3: Added proof of general trace formula, rearranged sections, streamlined previous arguments/algorithms