Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Group Structure of Bachet Elliptic Curves over Finite Fields F_{p}   Bachet elliptic curves are the curves y^2=x^3+a^3 and in this work the group
structure E(F_{p}) of these curves over finite fields F_{p} is considered. It
is shown that there are two possible structures E(F_{p}){\cong}C_{p+1} or
E(F_{p}){\cong}C_{n}{\times}C_{nm}, for m,n{\in}{\mathbb{N}}, according to
p{\equiv}5 (mod6) and p{\equiv}1 (mod6), respectively. A result of Washington
is restated in a more specific way saying that if
E(F_{p}){\cong}Z_{n}{\times}Z_{n}, then p{\equiv}7 (mod12) and p=n^2{\mp}n+1.

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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
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The categories of this paper are: cs