Elliptic curves with a point of order 13 defined over cyclic cubic fields
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866917796563124224 |
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| author | Bruin, Peter Derickx, Maarten Stoll, Michael |
| author_facet | Bruin, Peter Derickx, Maarten Stoll, Michael |
| contents | We show that there is essentially a unique elliptic curve $E$ defined over a cubic Galois extension $K$ of $\mathbb Q$ with a $K$-rational point of order 13 and such that $E$ is not defined over $\mathbb Q$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_05557 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Elliptic curves with a point of order 13 defined over cyclic cubic fields Bruin, Peter Derickx, Maarten Stoll, Michael Number Theory 11G05, 14G05, 14G25, 14H52 We show that there is essentially a unique elliptic curve $E$ defined over a cubic Galois extension $K$ of $\mathbb Q$ with a $K$-rational point of order 13 and such that $E$ is not defined over $\mathbb Q$. |
| title | Elliptic curves with a point of order 13 defined over cyclic cubic fields |
| topic | Number Theory 11G05, 14G05, 14G25, 14H52 |
| url | https://arxiv.org/abs/2101.05557 |