New curves of genus 2 over the field of rational numbers whose Jacobians contain torsion points of high order

DOI10.1134/S1064562415020325zbMath1356.11038OpenAlexW2297990914MaRDI QIDQ492740

M. M. Petrunin, Vladimir Platonov

Publication date: 21 August 2015

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

Full work available at URL: https://doi.org/10.1134/s1064562415020325

zbMATH Keywords

elliptic curvesJacobianstorsion pointsabsolutely simple abelian variety

Mathematics Subject Classification ID

Special algebraic curves and curves of low genus (14H45) [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 (2)

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

Cites Work

• On the simplicity of Jacobians for hyperelliptic curves of genus 2 over the field of rational numbers with torsion points of high order
• A new local-global principle for quadratic function fields
• Arithmetic of quadratic fields and torsion in Jacobians
• New orders of torsion points in Jacobians of curves of genus 2 over the rational number field
• On the torsion problem in Jacobians of curves of genus 2 over the rational number field
• Large torsion subgroups of split Jacobians of curves of genus two or three
• Number-theoretic properties of hyperelliptic fields and the torsion problem in Jacobians of hyperelliptic curves over the rational number field

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