Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 2-Selmer groups of hyperelliptic curves with two marked points   We consider the family of hyperelliptic curves over $\Q$ of fixed genus along
with a marked rational Weierstrass point and a marked rational non-Weierstrass
point. When these curves are ordered by height, we prove that the average
Mordell-Weil rank of their Jacobians is bounded above by 5/2. We prove this by
showing that the average rank of the 2-Selmer groups is bounded above by 6. We
also prove that the average size of the $\phi$-Selmer groups of a family of
isogenies associated to this family is exactly 2.

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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: cs