Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Heron Quadrilaterals via elliptic curves   A Heron quadrilateral is a cyclic quadrilateral whose area and side lengths
are rational. In this work, we establish a correspondence between Heron
quadrilaterals and a family of elliptic curves of the form $y^2 = x3+/alpha
x^2-n^2x.$
  This correspondence generalizes the notions of Goins and Maddox who
established a similar connection between Heron triangles and elliptic curves.
We further study this family of elliptic curves, looking at their torsion
groups and ranks. We also explore their connection with congruent numbers,
which are the /alpha = 0 case. Congruent numbers are positive integers which
are the area of a right triangle with rational side lengths. This is a new
characterization of congruent numbers in terms of Heron Quadrilaterals.

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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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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: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: cs
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The categories of this paper are: patt-sol