An infinite family of curves of genus 2 over the field of rational numbers whose Jacobian varieties contain rational points of order 28

DOI10.1134/S1064562418060182zbMath1427.14062OpenAlexW2900233263MaRDI QIDQ1709857

G. V. Fedorov, Vladimir Platonov

Publication date: 15 January 2019

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562418060182

zbMATH Keywords

Jacobianrational pointshyperelliptic curves

Mathematics Subject Classification ID

Rational points (14G05) Jacobians, Prym varieties (14H40) Coverings of curves, fundamental group (14H30) [https://portal.mardi4nfdi.de/w/index.php?title=+Special%3ASearch&search=%22Curves+of+arbitrary+genus+or+genus+%28%0D%0Ae+1%29+over+global+fields%22&go=Go Curves of arbitrary genus or genus ( e 1) over global fields (11G30)]

Related Items (3)

Аналитические и теоретико-числовые свойства двумерных сигма-функций ⋮ Vladimir Petrovich Platonov ⋮ Unnamed Item

Cites Work

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• On the simplicity of Jacobians for hyperelliptic curves of genus 2 over the field of rational numbers with torsion points of high order
• New curves of genus 2 over the field of rational numbers whose Jacobians contain torsion points of high order
• New orders of torsion points in Jacobians of curves of genus 2 over the rational number field
• Curves of genus 2 with a rational torsion divisor of order 23
• Large rational torsion on abelian varieties
• Arithmetic variety of moduli for genus two
• On the problem of periodicity of continued fractions in hyperelliptic fields
• Number-theoretic properties of hyperelliptic fields and the torsion problem in Jacobians of hyperelliptic curves over the rational number field
• Genus-2 Jacobians with torsion points of large order

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