Constructing families of 3-Selmer companions
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911020798181376 |
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| author | Spencer, Harry |
| author_facet | Spencer, Harry |
| contents | Mazur and Rubin introduced the notion of $n$-Selmer companion elliptic curves and gave several examples of pairs of non-isogenous Selmer companions. We construct several pairs of families of elliptic curves, each parameterised by $t\in\ZZ$, such that the two curves in a pair corresponding to a given $t$ are non-isogenous $3$-Selmer companions, possibly provided that $t$ satisfies a simple congruence condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_01351 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Constructing families of 3-Selmer companions Spencer, Harry Number Theory Mazur and Rubin introduced the notion of $n$-Selmer companion elliptic curves and gave several examples of pairs of non-isogenous Selmer companions. We construct several pairs of families of elliptic curves, each parameterised by $t\in\ZZ$, such that the two curves in a pair corresponding to a given $t$ are non-isogenous $3$-Selmer companions, possibly provided that $t$ satisfies a simple congruence condition. |
| title | Constructing families of 3-Selmer companions |
| topic | Number Theory |
| url | https://arxiv.org/abs/2502.01351 |