Computation of Sets of Rational Points of Genus-3 Curves via the Dem'Janenko–Manin Method

DOI10.1112/S1461157000000991zbMath1108.14017MaRDI QIDQ3430814

Martine Girard, Leopoldo Kulesz

Publication date: 4 April 2007

Published in: LMS Journal of Computation and Mathematics (Search for Journal in Brave)

Full work available at URL: http://www.lms.ac.uk/jcm/8/lms2005-025/

Mathematics Subject Classification ID

Rational points (14G05) Computational aspects of algebraic curves (14Q05) [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)

Rational points on curves ⋮ THE EXPLICIT MORDELL CONJECTURE FOR FAMILIES OF CURVES

Uses Software

• Magma

Cites Work

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• Diophantine approximation on abelian varieties
• Effective Chabauty
• Finiteness theorems for abelian varieties over number fields.
• Siegel's theorem in the compact case
• Application of the method of Dem'yanenko-Manin to certain families of curves of genus 2 or 3
• Cycles of quadratic polynomials and rational points on a genus-2 curve
• Rational points on families of curves with genus at least 2
• Infinite descent on elliptic curves
• Remarques sur un mémoire d'Hermite
• Covering collections and a challenge problem of Serre
• Group generated by the Weierstrass points of a plane quartic
• The Difference Between the Weil Height and the Canonical Height on Elliptic Curves
• Rational Points on Certain Families of Curves of Genus at Least 2
• N-Covers of hyperelliptic curves
• Courbes elliptiques de rang ≥ 5 sur Q(t) avec un groupe de torsion isomorphe à Z/2Z × Z/2Z
• Large torsion subgroups of split Jacobians of curves of genus two or three
• On a Theorem of Dem'Janenko

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