Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Trace of Frobenius endomorphism of an elliptic curve with complex
  multiplication   Let E be an elliptic curve with complex multiplication by R, where R is an
order of discriminant D<-4 of an imaginary quadratic field K . If a prime
number p is decomposed completely in the ring class field associated with R,
then E has good reduction at a prime ideal P of K dividing p and there exist
positive integers u and v such that 4p=u^2-Dv^2. It is well known that square
of the trace a_P of Frobenius endomorphism of the reduction of E modulo P is
equal to u^2. We determine whether a_P=u or a_P=-u in the case the class number
of R is 2 or 3 and D is divided by 3,4 or 5. This article is a revised version
of the authors' preprint DMIS-RR-02-5,2002.

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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: cs
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The categories of this paper are: physics
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas