Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Counting Models of Genus One Curves   Let C be a soluble smooth genus one curve over a Henselian discrete valuation
field. There is a unique minimal Weierstrass equation defining C up to
isomorphism. In this paper we consider genus one equations of degree n defining
C, namely a (generalised) binary quartic when n = 2, a ternary cubic when n =
3, and a pair of quaternary quadrics when n = 4. In general, minimal genus one
equations of degree n are not unique up to isomorphism. We explain how the
number of minimal genus one equations of degree n varies according to the
Kodaira symbol of the Jacobian of C. Then we count these equations up to
isomorphism over a number field of class number 1.

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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat