2-adic Galois images of non-CM isogeny-torsion graphs
| Autor: | Chiloyan, Garen |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | Let $\mathcal{E}$ be a $\mathbb{Q}$-isogeny class of elliptic curves defined over $\mathbb{Q}$ without CM. The isogeny graph associated to $\mathcal{E}$ is a graph which has a vertex for each elliptic curve in $\mathcal{E}$ and an edge for each $\mathbb{Q}$-isogeny of prime degree that maps one elliptic curve in $\mathcal{E}$ to another elliptic curve in $\mathcal{E}$, with the degree recorded as a label of the edge. An isogeny-torsion graph is an isogeny graph where, in addition, we label each vertex with the abstract group structure of the torsion subgroup over $\mathbb{Q}$ of the corresponding elliptic curve. Then, the main statement of the article is a classification of the $2$-adic image of Galois that occurs at each vertex of all isogeny-torsion graphs consisting of elliptic curves defined over $\mathbb{Q}$ without CM. Comment: 48 pages, 19 tables, comments welcome. arXiv admin note: text overlap with arXiv:2208.11649 |
| Databáze: | arXiv |
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