Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Higher descents on an elliptic curve with a rational 2-torsion point   Let $E$ be an elliptic curve over a number field $K$. Descent calculations on
$E$ can be used to find upper bounds for the rank of the Mordell-Weil group,
and to compute covering curves that assist in the search for generators of this
group. The general method of 4-descent, developed in the PhD theses of Siksek,
Womack and Stamminger, has been implemented in Magma (when $K={\mathbb Q}$) and
works well for elliptic curves with sufficiently small discriminant. By
extending work of Bremner and Cassels, we describe the improvements that can be
made when $E$ has a rational 2-torsion point. In particular, when $E$ has full
rational 2-torsion, we describe a method for 8-descent that is practical for
elliptic curves $E/{\mathbb Q}$ with large discriminant.

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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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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: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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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: econ
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The categories of this paper are: funct-an
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The categories of this paper are: physics