Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computing endomorphism rings of Jacobians of genus 2 curves over finite
  fields   We present algorithms which, given a genus 2 curve $C$ defined over a finite
field and a quartic CM field $K$, determine whether the endomorphism ring of
the Jacobian $J$ of $C$ is the full ring of integers in $K$. In particular, we
present probabilistic algorithms for computing the field of definition of, and
the action of Frobenius on, the subgroups $J[\ell^d]$ for prime powers
$\ell^d$. We use these algorithms to create the first implementation of
Eisentr\"ager and Lauter's algorithm for computing Igusa class polynomials via
the Chinese Remainder Theorem \cite{el}, and we demonstrate the algorithm for a
few small examples. We observe that in practice the running time of the CRT
algorithm is dominated not by the endomorphism ring computation but rather by
the need to compute $p^3$ curves for many small primes $p$.

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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph