Loops of isogeny graphs of supersingular elliptic curves at j = 0

摘要

We improve Adj et al.'s bound in [1, Theorem 12] from p 4l to p 3l for the loops of E-0 : y(2) = x(3) 1 in the l-isogeny graph G(l)(F-p2, -2p) of supersingular elliptic curves over F-p2 with trace -2p. (C) 2019 Elsevier Inc. All rights reserved.