Khawaja, M. (2024) Torsion primes for elliptic curves over degree 8 number fields. Research in Number Theory, 10. 48. ISSN 2363-9555
Abstract
Let d ≥ 1 be an integer and let p be a rational prime. Recall thatp is a torsion prime of degree d if there exists an elliptic curve E over a degree d number field K such that E has a K-rational point of order p. Derickx, Kamienny, Stein and Stoll [5] have computed the torsion primes of degrees 4, 5, 6 and 7. We verify that the techniques used in [5] can be extended to determine the torsion primes of degree 8.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © The Author(s) 2024. Open Access: This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
Keywords: | Modular curves; Elliptic curves; Rational points; Abelian varieties |
Dates: |
|
Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Funding Information: | Funder Grant number Engineering and Physical Sciences Research Council EP/T517835/1 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 15 Apr 2024 14:00 |
Last Modified: | 26 Apr 2024 08:12 |
Status: | Published |
Publisher: | Springer |
Refereed: | Yes |
Identification Number: | 10.1007/s40993-024-00533-6 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:211212 |