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

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

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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Veröffentlicht in:Doklady. Mathematics 2018-09, Vol.98 (2), p.468-471
Hauptverfasser: Platonov, V. P., Fedorov, G. V.
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Mathematics and Statistics
Numbers
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Zusammenfassung: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.
ISSN:1064-5624
1531-8362
DOI:10.1134/S1064562418060182