Nonexistence of elliptic curves with good reduction everywhere over real quadratic fields
type: Item
instance of: scholarly article
title: Nonexistence of elliptic curves with good reduction everywhere over real quadratic fields
zbMATH Open document ID: 0895.11023
author: Masanari Kida
author: Takaaki Kagawa
published in: Journal of Number Theory
publication date: 1997-11-18T00:00:00Z
review text: The authors prove two theorems about the existence of elliptic curves with everywhere good reduction. In both they show that over certain classes of real quadratic fields all such curves must have a point of order two. Numerous examples are given.
Mathematics Subject Classification ID: 11G05
Mathematics Subject Classification ID: 14H52
zbMATH DE Number: 1088549
zbMATH Keywords: elliptic curves
zbMATH Keywords: good reduction
zbMATH Keywords: real quadratic fields
MaRDI profile type: Publication
full work available at URL: jnth.1997.2177
OpenAlex ID: W1982044767
cites work: Elliptic curves with trivial conductor over quadratic fields
cites work: Modular symbols for 1(N) and elliptic curves with everywhere good reduction
cites work: There are no abelian varieties over \(\mathbb Z\).
cites work: Q3754097
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DOI: 10.1006/JNTH.1997.2177
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description: scientific article; zbMATH DE number 1088549