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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 917Z8 $$x242282 000215074 937__$$aEPFL-ARTICLE-215074
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