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An Infinite Family of Curves of Genus 2 over the Field of Rational Numbers Whose Jacobian Varieties Contain Rational Points of Order 28

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Abstract

We have found an infinite family of nonisomorphic hyperelliptic curves of genus two over the field of rational numbers whose Jacobian varieties contain rational points of order 28. Previously, only 10 such curves were known.

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Authors and Affiliations

  1. Scientific Research Institute for System Analysis, Russian Academy of Sciences, Moscow, 117218, Russia

    V. P. Platonov & G. V. Fedorov

Authors
  1. V. P. Platonov
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  2. G. V. Fedorov
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Correspondence to V. P. Platonov.

Additional information

Original Russian Text © V.P. Platonov, G.V. Fedorov, 2018, published in Doklady Akademii Nauk, 2018, Vol. 482, No. 4.

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Platonov, V.P., Fedorov, G.V. An Infinite Family of Curves of Genus 2 over the Field of Rational Numbers Whose Jacobian Varieties Contain Rational Points of Order 28. Dokl. Math. 98, 468–471 (2018). https://doi.org/10.1134/S1064562418060182

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  • DOI: https://doi.org/10.1134/S1064562418060182

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