@article{Ahmadi:215074,
title = {On isogeny classes of Edwards curves over finite fields},
author = {Ahmadi, Omran and Granger, Robert},
publisher = {Elsevier},
journal = {Journal of Number Theory},
number = {6},
volume = {132},
pages = {1337-1358},
year = {2012},
abstract = {We count the number of isogeny classes of Edwards curves over finite fields, answering a question recently posed by Rezaeian and Shparlinski. We also show that each isogeny class contains a {\em complete} Edwards curve, and that an Edwards curve is isogenous to an {\em original} Edwards curve over $\mathbb{F}_q$ if and only if its group order is divisible by $8$ if $q \equiv -1 \pmod{4}$, and $16$ if $q \equiv 1 \pmod{4}$. Furthermore, we give formulae for the proportion of $d \in \mathbb{F}_q$ \ {0,1} for which the Edwards curve $E_d$ is complete or original, relative to the total number of $d$ in each isogeny class.},
url = {http://infoscience.epfl.ch/record/215074},
doi = {10.1016/j.jnt.2011.12.013},
}