Diophantine analysis and torsion on elliptic curves

DOI10.1112/plms/pdl008zbMath1117.11033OpenAlexW2036107608MaRDI QIDQ3425564

Patrick Ingram

Publication date: 26 February 2007

Published in: Proceedings of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1112/plms/pdl008

zbMATH Keywords

\(\mathbb Q\)-rational isogenies of elliptic curves\textit{abc}-conjecture of Masser and Oesterléelliptic curves over field of rational numbersgroup \(E( \mathbb Q)\) of rational points on an elliptic curve \(E=E/{ \mathbb Q}\)group \(E(K)\) of \(K\)-rational points on elliptic curve \(E=E/K\) over finite extension \(K\) of \( \mathbb Q\)Roth theorem on Diophantine approximationthe Mazur theorem on possible torsion subgroups of \(E( \mathbb Q)\) for various \(E\)the torsion subgroup of \(E( \mathbb Q)\)

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Approximation to algebraic numbers (11J68)

Related Items (4)

Torsion of rational elliptic curves over cubic fields ⋮ Galois theory, discriminants and torsion subgroup of elliptic curves ⋮ On the ubiquity of trivial torsion on elliptic curves ⋮ Thue equations and torsion groups of elliptic curves

Cites Work

• Finiteness theorems for abelian varieties over number fields.
• Modular curves and the Eisenstein ideal
• Torsion points on elliptic curves
• Universal Bounds on the Torsion of Elliptic Curves
• Torsion Points on Certain Families of Elliptic Curves
• Torsion subgroups of elliptic curves in short Weierstrass form
• Rational approximations to algebraic numbers
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