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 if and only if its group order is divisible by if , and if . Furthermore, we give formulae for the proportion of \ {0,1} for which the Edwards curve is complete or original, relative to the total number of in each isogeny class.