Tamagawa Numbers of Elliptic Curves with an $\ell$-isogeny
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911980403556352 |
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| author | Barrios, Alexander Cullinan, John |
| author_facet | Barrios, Alexander Cullinan, John |
| contents | Let $\ell$ be an odd prime, and suppose $E$ is an elliptic curve defined over the rational numbers $\mathbb{Q}$. If $E$ has an $\ell$-torsion point, then there has been significant work done on characterizing the $\ell$-divisibility of the global Tamagawa number of $E$. In this paper, we consider elliptic curves that are $\ell$-isogenous to elliptic curves with an $\ell$-torsion point and study the $\ell$-divisibility of their global Tamagawa numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_03419 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tamagawa Numbers of Elliptic Curves with an $\ell$-isogeny Barrios, Alexander Cullinan, John Number Theory Let $\ell$ be an odd prime, and suppose $E$ is an elliptic curve defined over the rational numbers $\mathbb{Q}$. If $E$ has an $\ell$-torsion point, then there has been significant work done on characterizing the $\ell$-divisibility of the global Tamagawa number of $E$. In this paper, we consider elliptic curves that are $\ell$-isogenous to elliptic curves with an $\ell$-torsion point and study the $\ell$-divisibility of their global Tamagawa numbers. |
| title | Tamagawa Numbers of Elliptic Curves with an $\ell$-isogeny |
| topic | Number Theory |
| url | https://arxiv.org/abs/2408.03419 |