Two-descent on some genus two curves

DOI10.1016/j.indag.2021.06.004zbMath1480.11082arXiv2102.12977OpenAlexW3175312424MaRDI QIDQ2040156

Gert-Jan van der Heiden, Tim Evink, Jaap Top

Publication date: 12 July 2021

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2102.12977

zbMATH Keywords

hyperelliptic curverational points2-Selmer group2-torsion Tate-Shafarevich groupRédei symbols

Mathematics Subject Classification ID

Rational points (14G05) [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)

Infinitely many hyperelliptic curves with exactly two rational points ⋮ A remark on prime (non)congruent numbers

Uses Software

• Magma
• LMFDB

Cites Work

• Albime triangles over quadratic fields
• Idempotent relations and factors of Jacobians
• Three constructions of rational points on \(Y^ 2=X^ 3\pm NX\)
• On the equation \(Y^ 2=(X+p)(X^ 2+p^ 2)\)
• Chebotarëv and his density theorem
• The Magma algebra system. I: The user language
• Cycles of quadratic polynomials and rational points on a genus-2 curve
• 2-descent on the Jacobians of hyperelliptic curves
• The Cassels-Tate pairing on polarized Abelian varieties
• Two-cover descent on hyperelliptic curves
• On the Equation Y 2 = X(X 2 + p)
• Decomposing Jacobians of curves with extra automorphisms

This page was built for publication: Two-descent on some genus two curves