000215074 001__ 215074
000215074 005__ 20190317000354.0
000215074 022__ $$a0022-314X
000215074 0247_ $$a10.1016/j.jnt.2011.12.013$$2doi
000215074 037__ $$aARTICLE
000215074 245__ $$aOn isogeny classes of Edwards curves over finite fields
000215074 260__ $$bElsevier$$c2012
000215074 269__ $$a2012
000215074 336__ $$aJournal Articles
000215074 520__ $$aWe 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.
000215074 6531_ $$aEdwards curves
000215074 6531_ $$aLegendre curves
000215074 6531_ $$aIsogeny classes
000215074 700__ $$aAhmadi, Omran
000215074 700__ $$0247766$$g242282$$aGranger, Robert
000215074 773__ $$j132$$tJournal of Number Theory$$k6$$q1337-1358
000215074 8564_ $$uhttp://www.sciencedirect.com/science/article/pii/S0022314X1200025X$$zURL
000215074 909C0 $$xU10403$$0252433$$pIIF
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000215074 937__ $$aEPFL-ARTICLE-215074
000215074 973__ $$rREVIEWED$$sPUBLISHED$$aOTHER
000215074 980__ $$aARTICLE