On the explicit models of Shimura's elliptic curves
type: Item
instance of: scholarly article
title: On the explicit models of Shimura's elliptic curves
zbMATH Open document ID: 0608.14023
author: Ken-ichi Shiota
published in: Journal of the Mathematical Society of Japan
publication date: 1986-01-01T00:00:00Z
review text: The author studies the abelian varieties \(B_ N\), rational over the field \({\mathbb{Q}}(\sqrt{N})\), which \textit{G. Shimura} [J. Math. Soc. Japan 25, 523-544 (1973; Zbl 0266.14017)] has considered in relation with Nebentypus cusp forms of level N, in three cases (vis. \(N=29, 37, 41)\) where they have dimension \(1\). He computes their j-invariants by estimating their periods with sufficient accuracy, and deduces from known examples of elliptic curves over \({\mathbb{Q}}(\sqrt{N})\), with good reduction everywhere, explicit Weierstraß equations for the \(B_ N's\).
Mathematics Subject Classification ID: 14H25
Mathematics Subject Classification ID: 14G25
Mathematics Subject Classification ID: 14H52
Mathematics Subject Classification ID: 14H45
Mathematics Subject Classification ID: 11F67
zbMATH DE Number: 3983366
zbMATH Keywords: Nebentypus cusp forms
zbMATH Keywords: j-invariants
zbMATH Keywords: elliptic curves
zbMATH Keywords: Weierstraß equations
reviewed by: Daniel Bertrand
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/03840649
OpenAlex ID: W1967630621
DOI: 10.2969/JMSJ/03840649
description: scientific article; zbMATH DE number 3983366