Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rank frequencies for quadratic twists of elliptic curves   We give explicit examples of infinite families of elliptic curves E over Q
with (nonconstant) quadratic twists over Q(t) of rank at least 2 and 3. We
recover some results announced by Mestre, as well as some additional families.
Suppose D is a squarefree integer and let r_E(D) denote the rank of the
quadratic twist of E by D. We apply results of Stewart and Top to our examples
to obtain results of the form #{D : |D| < x, r_E(D) >= 2} >> x^{1/3}, #{D : |D|
< x, r_E(D) >= 3} >> x^{1/6} for all sufficiently large x.

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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat