THEOREM OF THE DAY The Lutz-Nagell Theorem For the elliptic curve y2 = x3 + ax2 + bx + c, with a, b, and c integers and having (non-zero) discriminant function D = −4a3c + a2b2 + 18abc − 4b3 − 27c2, let P = (X, Y)

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Strong Diophantine triples Andrej Dujella and Vinko Petriˇcevi´c Abstract We prove that there exist infinitely many triples a, b, c of non-zero rationals with the property that a2 + 1, b2 + 1, c2 + 1, ab + 1, ac + 1

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• Nagell–Lutz theorem
• Elliptic curve
• Diophantus
• Nagell
• Mathematics
• Number theory
• Diophantine equations

Elliptic curves with large torsion and positive rank over number fields of small degree and ECM factorization Andrej Dujella and Filip Najman Abstract In this paper, we present several methods for construction of ellipti

Source URL: bib.irb.hr

• Elliptic curves
• Curvature
• Differential geometry
• Finite fields
• Group theory
• Lenstra elliptic curve factorization
• Torsion of a curve
• Torsion subgroup
• Nagell–Lutz theorem
• Abstract algebra
• Geometry
• Mathematics

Contents 1 Introduction

Source URL: www.math.umd.edu

• Elliptic curves
• Abelian varieties
• Cryptography
• Class field theory
• Number theory
• Mordell–Weil theorem
• Tate–Shafarevich group
• Nagell–Lutz theorem
• Weil pairing
• Abstract algebra
• Algebra
• Mathematics

PDF Document

Source URL: forumgeom.fau.edu

• Analytic number theory
• Elliptic curve
• Group theory
• Integer triangle
• Nagell–Lutz theorem
• Pi
• Trigonometric functions
• Rational point
• Birch and Swinnerton-Dyer conjecture
• Mathematics
• Mathematical analysis
• Number theory