Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Isogenies of elliptic curves over function fields   We prove two theorems concerning isogenies of elliptic curves over function
fields. The first one describes the variation of the height of the
$j$-invariant in an isogeny class. The second one is an "isogeny estimate",
providing an explicit bound on the degree of a minimal isogeny between two
isogenous elliptic curves. We also give several corollaries of these two
results.

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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: cs
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th