Twists of Elliptic Curves
In this note we extend the theory of twists of elliptic curves as presented in various standard texts for characteristic not equal to two or three to the remaining characteristics. For this, we make explicit use of the correspondence between the twists and the Galois cohomology set H¹(GK¯/K,AutK¯(E)...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2017 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2017
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149277 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Twists of Elliptic Curves / M. Kronberg, M.A. Soomro, J. Top // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 24 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862712473175457792 |
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| author | Kronberg, M. Soomro, M.A. Top, J. |
| author_facet | Kronberg, M. Soomro, M.A. Top, J. |
| citation_txt | Twists of Elliptic Curves / M. Kronberg, M.A. Soomro, J. Top // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 24 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In this note we extend the theory of twists of elliptic curves as presented in various standard texts for characteristic not equal to two or three to the remaining characteristics. For this, we make explicit use of the correspondence between the twists and the Galois cohomology set H¹(GK¯/K,AutK¯(E)). The results are illustrated by examples.
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| first_indexed | 2025-12-07T17:37:37Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-149277 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:37:37Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Kronberg, M. Soomro, M.A. Top, J. 2019-02-19T19:45:04Z 2019-02-19T19:45:04Z 2017 Twists of Elliptic Curves / M. Kronberg, M.A. Soomro, J. Top // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 24 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 11G05; 11G25; 14G1 DOI:10.3842/SIGMA.2017.083 https://nasplib.isofts.kiev.ua/handle/123456789/149277 In this note we extend the theory of twists of elliptic curves as presented in various standard texts for characteristic not equal to two or three to the remaining characteristics. For this, we make explicit use of the correspondence between the twists and the Galois cohomology set H¹(GK¯/K,AutK¯(E)). The results are illustrated by examples. This paper is a contribution to the Special Issue on Modular Forms and String Theory in honor of Noriko
 Yui. The full collection is available at http://www.emis.de/journals/SIGMA/modular-forms.html.
 It is a pleasure to thank Joe Silverman, John Cremona, Nurdag¨ul Anbar Meidl, and Jan Stef fen
 M¨uller for helpful comments, advise, and support while preparing this paper. We are especially
 grateful for the many useful suggestions of the two referees of the first draft of this, which we
 hope have improved the readability of the text a lot. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Twists of Elliptic Curves Article published earlier |
| spellingShingle | Twists of Elliptic Curves Kronberg, M. Soomro, M.A. Top, J. |
| title | Twists of Elliptic Curves |
| title_full | Twists of Elliptic Curves |
| title_fullStr | Twists of Elliptic Curves |
| title_full_unstemmed | Twists of Elliptic Curves |
| title_short | Twists of Elliptic Curves |
| title_sort | twists of elliptic curves |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149277 |
| work_keys_str_mv | AT kronbergm twistsofellipticcurves AT soomroma twistsofellipticcurves AT topj twistsofellipticcurves |