Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetric diophantine systems and families of elliptic curves of high
  rank   While there has been considerable interest in the problem of finding elliptic
curves of high rank over $\mathbb{Q}$, very few parametrized families of
elliptic curves of generic rank $\geq 8$ have been published. In this paper we
use solutions of certain symmetric diophantine systems to construct several
parametrized families of elliptic curves with their generic ranks ranging from
at least 8 to at least 12. Specific numerical values of the parameters yield
elliptic curves with quite large coefficients and we could therefore determine
the precise rank only in a few cases where the rank of the elliptic curve $\leq
13$. It is, however, expected that the parametrized families of elliptic curves
obtained in this paper would yield examples of elliptic curves with much higher
rank.

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The categories of this paper are: atom-ph
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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: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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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: astro-ph
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The categories of this paper are: q-bio