Rational points and the elliptic Chabauty method.

DOI10.5802/jtnb.389zbMath1097.11014OpenAlexW2014002675MaRDI QIDQ1424572

Sylvain Duquesne

Publication date: 16 March 2004

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=JTNB_2003__15_1_99_0

zbMATH Keywords

rational pointsWeierstrass preparation theorembielliptic curveelliptic Chabauty methodgenus 4 curve

Mathematics Subject Classification ID

Rational points (14G05) Counting solutions of Diophantine equations (11D45) [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)] Higher degree equations; Fermat's equation (11D41) Power series rings (13J05)

Related Items (1)

Rational points on a certain genus 2 curve

Uses Software

• mwrank

Cites Work

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• Rational points on hyperelliptic curves and an explicit Weierstrass preparation theorem
• Effective Chabauty
• Finiteness theorems for abelian varieties over number fields.
• Infinite descent on elliptic curves
• Finding rational points on bielliptic genus 2 curves
• ON ℚ-DERIVED POLYNOMIALS
• Covering collections and a challenge problem of Serre
• Implementing 2-descent for Jacobians of hyperelliptic curves
• Computing Heights on Elliptic Curves
• Rings of convergent power series and Weierstrass Preparation Theorem
• Computing the rank of elliptic curves over real quadratic number fields of class number 1
• Computing the $p$-Selmer group of an elliptic curve
• Computing the Rank of Elliptic Curves over Number Fields

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