Some remarks concerning points of finite order on elliptic curves over global fields

DOI10.1007/BF02386030zbMath0348.14018OpenAlexW1965756903MaRDI QIDQ1234332

Gerhard Frey

Publication date: 1977

Published in: Arkiv för Matematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02386030

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Rational points (14G05) Arithmetic ground fields for curves (14H25) Special algebraic curves and curves of low genus (14H45) Local ground fields in algebraic geometry (14G20) Global ground fields in algebraic geometry (14G25) Diophantine equations (11D99)

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Cites Work

• Unnamed Item
• Points of finite order on elliptic curves with complex multiplication
• Torsion points on elliptic curves with given j-invariant
• Points of finite order on elliptic curves over number fields
• Modèles minimaux des variétés abéliennes sur les corps locaux et globaux
• Complements à un article de Hans Grauert sur la conjecture de Mordell
• Galois properties of points of finite order of elliptic curves
• Elliptische Funktionenkörper mit schlechter Reduktion und nichttrivialer Hasse-Invariante
• Kroneckerian Model of Fields of Elliptic Modular Functions
• О точках конечного порядка эллиптических кривых
• Points d'ordre $2p^h$ sur les courbes elliptiques
• Sur l'équation y² = x³ - Ax - B dans les corps p-adiques.