A criterion to rule out torsion groups for elliptic curves over number fields
We present a criterion for proving that certain groups of the form \(\mathbb {Z}/m\mathbb {Z}\oplus \mathbb {Z}/n\mathbb {Z}\) do not occur as the torsion subgroup of any elliptic curve over suitable (families of) number fields. We apply this criterion to eliminate certain groups as torsion groups o...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer International Publishing
2017
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| Online Access: | http://hdl.handle.net/1721.1/106205 |
| _version_ | 1826191290415448064 |
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| author | Bruin, Peter Najman, Filip |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Bruin, Peter Najman, Filip |
| author_sort | Bruin, Peter |
| collection | MIT |
| description | We present a criterion for proving that certain groups of the form \(\mathbb {Z}/m\mathbb {Z}\oplus \mathbb {Z}/n\mathbb {Z}\) do not occur as the torsion subgroup of any elliptic curve over suitable (families of) number fields. We apply this criterion to eliminate certain groups as torsion groups of elliptic curves over cubic and quartic fields. We also use this criterion to give the list of all torsion groups of elliptic curves occurring over a specific cubic field and over a specific quartic field. |
| first_indexed | 2024-09-23T08:53:55Z |
| format | Article |
| id | mit-1721.1/106205 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T08:53:55Z |
| publishDate | 2017 |
| publisher | Springer International Publishing |
| record_format | dspace |
| spelling | mit-1721.1/1062052022-09-30T12:01:16Z A criterion to rule out torsion groups for elliptic curves over number fields Bruin, Peter Najman, Filip Massachusetts Institute of Technology. Department of Mathematics Najman, Filip We present a criterion for proving that certain groups of the form \(\mathbb {Z}/m\mathbb {Z}\oplus \mathbb {Z}/n\mathbb {Z}\) do not occur as the torsion subgroup of any elliptic curve over suitable (families of) number fields. We apply this criterion to eliminate certain groups as torsion groups of elliptic curves over cubic and quartic fields. We also use this criterion to give the list of all torsion groups of elliptic curves occurring over a specific cubic field and over a specific quartic field. 2017-01-05T17:54:02Z 2017-01-05T17:54:02Z 2016-01 2015-06 2016-05-23T09:38:32Z Article http://purl.org/eprint/type/JournalArticle 2363-9555 http://hdl.handle.net/1721.1/106205 Bruin, Peter, and Filip Najman. “A Criterion to Rule out Torsion Groups for Elliptic Curves over Number Fields.” Research in Number Theory 2.1 (2016): n. pag. en http://dx.doi.org/10.1007/s40993-015-0031-5 Research in Number Theory Creative Commons Attribution http://creativecommons.org/licenses/by/4.0/ The Author(s) application/pdf Springer International Publishing Springer International Publishing |
| spellingShingle | Bruin, Peter Najman, Filip A criterion to rule out torsion groups for elliptic curves over number fields |
| title | A criterion to rule out torsion groups for elliptic curves over number fields |
| title_full | A criterion to rule out torsion groups for elliptic curves over number fields |
| title_fullStr | A criterion to rule out torsion groups for elliptic curves over number fields |
| title_full_unstemmed | A criterion to rule out torsion groups for elliptic curves over number fields |
| title_short | A criterion to rule out torsion groups for elliptic curves over number fields |
| title_sort | criterion to rule out torsion groups for elliptic curves over number fields |
| url | http://hdl.handle.net/1721.1/106205 |
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