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Torsion of rational elliptic curves over the [formula omitted]-extensions of quadratic fields.

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Title: Torsion of rational elliptic curves over the [formula omitted]-extensions of quadratic fields.
Authors: Avcı, Ömer1 (AUTHOR) oavci@uottawa.ca
Source: Journal of Number Theory. Mar2026, Vol. 280, p153-170. 18p.
Subjects: Elliptic curves, Quadratic fields, Torsion theory (Algebra), Number theory, Mathematics
Abstract: Let E be an elliptic curve defined over Q. For a quadratic number field K and an odd prime number p , let L be a Z p -extension of K. We prove that E (L) tors = E (K) tors when p > 5. It enables us to classify the groups that can be realized as the torsion subgroup E (L) tors , by using the classification of torsion subgroups over the quadratic fields. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Number Theory is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 188782698
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Torsion of rational elliptic curves over the [formula omitted]-extensions of quadratic fields.
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  Data: <searchLink fieldCode="AR" term="%22Avcı%2C+Ömer%22">Avcı, Ömer</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> oavci@uottawa.ca</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Number+Theory%22">Journal of Number Theory</searchLink>. Mar2026, Vol. 280, p153-170. 18p.
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  Data: <searchLink fieldCode="DE" term="%22Elliptic+curves%22">Elliptic curves</searchLink><br /><searchLink fieldCode="DE" term="%22Quadratic+fields%22">Quadratic fields</searchLink><br /><searchLink fieldCode="DE" term="%22Torsion+theory+%28Algebra%29%22">Torsion theory (Algebra)</searchLink><br /><searchLink fieldCode="DE" term="%22Number+theory%22">Number theory</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics%22">Mathematics</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: Let E be an elliptic curve defined over Q. For a quadratic number field K and an odd prime number p , let L be a Z p -extension of K. We prove that E (L) tors = E (K) tors when p > 5. It enables us to classify the groups that can be realized as the torsion subgroup E (L) tors , by using the classification of torsion subgroups over the quadratic fields. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Number Theory is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1016/j.jnt.2025.08.009
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 18
        StartPage: 153
    Subjects:
      – SubjectFull: Elliptic curves
        Type: general
      – SubjectFull: Quadratic fields
        Type: general
      – SubjectFull: Torsion theory (Algebra)
        Type: general
      – SubjectFull: Number theory
        Type: general
      – SubjectFull: Mathematics
        Type: general
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      – TitleFull: Torsion of rational elliptic curves over the [formula omitted]-extensions of quadratic fields.
        Type: main
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            NameFull: Avcı, Ömer
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          Dates:
            – D: 01
              M: 03
              Text: Mar2026
              Type: published
              Y: 2026
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              Value: 280
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            – TitleFull: Journal of Number Theory
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