Computing elliptic curves having good reduction everywhere over quadratic fields
type: Item
instance of: scholarly article
title: Computing elliptic curves having good reduction everywhere over quadratic fields
zbMATH Open document ID: 1023.14011
author: Masanari Kida
published in: Tokyo Journal of Mathematics
publication date: 2002-07-24T00:00:00Z
review text: Let \(K\) be a quadratic field, i.e. a quadratic extension of \(\mathbb Q\), with ring of integers \(O_K\). This paper gives an algorithm for finding all elliptic curves with given \(j\)-invariant \(j \in O_K\) and good reduction at every finite place of \(K\). A table of all such curves with rational \(j\)-invariant is given. This contains a correction to an earlier table [see \textit{B. Setzer}, Ill. J. Math. 25, 233--245 (1981; Zbl 0471.14019)].
Mathematics Subject Classification ID: 11G05
Mathematics Subject Classification ID: 14H52
Mathematics Subject Classification ID: 14Q05
Mathematics Subject Classification ID: 14H25
zbMATH DE Number: 1744157
zbMATH Keywords: elliptic curve
zbMATH Keywords: good reduction
zbMATH Keywords: quadratic field
zbMATH Keywords: rational \(j\)-invariant
reviewed by: T. G. Berry
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1255958193
OpenAlex ID: W2090767833
DOI: 10.3836/TJM/1255958193
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description: scientific article; zbMATH DE number 1744157