Parallel LLL-reduction for bounding the integral solutions of elliptic Diophantine equations

DOI10.1090/S0025-5718-08-02160-1zbMath1215.11057OpenAlexW2024652203MaRDI QIDQ3055141

Lajos Hajdu, Tünde Kovács

Publication date: 7 November 2010

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

Full work available at URL: https://doi.org/10.1090/s0025-5718-08-02160-1

zbMATH Keywords

elliptic curvesintegral pointsLLL-reduction

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Computer solution of Diophantine equations (11Y50) Cubic and quartic Diophantine equations (11D25)

Related Items (3)

Diophantine equations coming from binomial near-collisions ⋮ Solving 𝑆-unit, Mordell, Thue, Thue–Mahler and Generalized Ramanujan–Nagell Equations via the Shimura–Taniyama Conjecture ⋮ Parallel LLL-reduction for bounding the integral solutions of elliptic Diophantine equations

Cites Work

• Optimal systems of fundamental \(S\)-units for LLL-reduction
• Explicit bounds for the solutions of elliptic equations with rational coefficients
• An upper bound for the size of integral solutions to \(Y^ m= f(X)\)
• Parallel LLL-reduction for bounding the integral solutions of elliptic Diophantine equations
• Elliptic binomial diophantine equations
• Solving elliptic diophantine equations by estimating linear forms in elliptic logarithms
• Computing integral points on elliptic curves
• On the size of integer solutions of elliptic equations
• Computing all integer solutions of a genus 1 equation
• On the Elliptic Logarithm Method for Elliptic Diophantine Equations: Reflections and an Improvement
• On the magnitude of integer points on elliptic curves
• Minorations de formes linéaires de logarithmes elliptiques
• Solving elliptic diophantine equations by estimating linear forms in elliptic logarithms. The case of quartic equations
• The Diophantine Equation y ² = ax ³ +bx ² +cx +d
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