Integral points on the congruent number curve

DOI10.1090/tran/8732OpenAlexW3015301017WikidataQ114093744 ScholiaQ114093744MaRDI QIDQ5098847

Stephanie Chan

Publication date: 31 August 2022

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.03331

zbMATH Keywords

Lang's conjecturecongruent numbers\(abc\) conjectureintegral points on elliptic curves

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Counting solutions of Diophantine equations (11D45) Cubic and quartic Diophantine equations (11D25)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Sphere packing bounds via spherical codes
• Lower bounds for height functions
• The canonical height and integral points on elliptic curves
• Lower bound for the canonical height on elliptic curves
• The size of Selmer groups for the congruent number problem. II. With an appendix by P. Monsky.
• \(S\)-integer points on elliptic curves
• Integral points in arithmetic progression on \(y^2= x(x^2-n^2)\)
• An inequality for the discriminant of a polynomial
• The parity of the rank of the Mordell-Weil group
• Integral Points on Elliptic Curves and Explicit Valuations of Division Polynomials
• Equations de Fermat--Pell--Mahler simultanees
• The Diophantine equation x⁴ - Dy² = 1, II
• Arithmetic on Curves of Genus 1 : III. The Tate-Šafarevič and Selmer Groups
• Arithmetic on Curves of Genus 1. IV. Proof of the Hauptvermutung.
• The Difference Between the Weil Height and the Canonical Height on Elliptic Curves
• Linear Growth for Certain Elliptic Fibrations
• A quantitative version of Siegel's theorem: integral points on elliptic curves and Catalan curves.
• Computing Heights on Elliptic Curves
• On consecutive integers of the form ax², by² and cz²
• The Diophantine equation $b^2X^4-dY^2=1$
• On the number of integral points on algebraic curves
• On the number of rational points on certain elliptic curves
• Integral points on elliptic curves and 3-torsion in class groups
• The Closest Packing of Spherical Caps in n Dimensions
• On the number of solutions of simultaneous Pell equations
• Integer points on elliptic curves

This page was built for publication: Integral points on the congruent number curve