On the 2-part of the class number of \(\mathbb{Q}(\sqrt{\pm D})\) for a congruent number \(D\)
type: Item
instance of: scholarly article
title: On the 2-part of the class number of \(\mathbb{Q}(\sqrt{\pm D})\) for a congruent number \(D\)
author: Shamik Das
author: Anupam Saikia
published in: Research in Number Theory
publication date: 2022-10-13T00:00:00Z
review text: When \(D\) is a congruent number which is a product of two primes \(p\) and \(q\) both congruent to 5 modulo 8, and which satisfy the Legendre symbol \((q/p)=-1\), the authors, assuming some condition on the Tate-Shafarevich group, proved that the class number of \(\mathbb{Q}(\sqrt{D})\) is divisible by 4. Assuming some extra hypotheses involving the representations of \(p\) band \(q\) by certain binary quadratic forms, they also proved that the class number of \(\mathbb{Q}(\sqrt{- D})\) is congruent to 8 modulo 16. Some other properties and comments are made. This is a nice contribution to the problem of characterizing congruent numbers.
reviewed by: Claude Levesque
Mathematics Subject Classification ID: 11G05
Mathematics Subject Classification ID: 11R29
Mathematics Subject Classification ID: 11A15
zbMATH DE Number: 7600670
zbMATH Keywords: congruent number
zbMATH Keywords: elliptic curve
zbMATH Keywords: class number
describes a project that uses: SageMath
MaRDI profile type: Publication
full work available at URL: s40993-022-00382-1
OpenAlex ID: W4298393599
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DOI: 10.1007/S40993-022-00382-1
description: scientific article; zbMATH DE number 7600670