Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On isogeny classes of Edwards curves over finite fields   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 $\F_q$ 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
$d \in \F_q \setminus \{0,1\}$ for which the Edwards curve $E_d$ is complete or
original, relative to the total number of $d$ in each isogeny class.

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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org