Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On families of 9-congruent elliptic curves   We compute equations for the families of elliptic curves 9-congruent to a
given elliptic curve. We use these to find infinitely many non-trivial pairs of
9-congruent elliptic curves over Q, i.e. pairs of non-isogenous elliptic curves
over Q whose 9-torsion subgroups are isomorphic as Galois modules.

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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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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: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph