MATH Seminar
| Title: Minimal Torsion Curves in Geometric Isogeny Classes |
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| Seminar: Algebra |
| Speaker: Abbey Bourdon of Wake Forest University |
| Contact: Santiago Arango-Piñeros, santiago.arango@emory.edu |
| Date: 2024-09-17 at 4:00PM |
| Venue: MSC W303 |
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| Abstract: Let $E/\mathbb{Q}$ be a non-CM elliptic curve and let $\mathcal{E}$ denote the collection of all elliptic curves geometrically isogenous to $E$. That is, for every $E' \in \mathcal{E}$, there exists an isogeny $\varphi: E \rightarrow E'$ defined over $\overline{\mathbb{Q}}$. We will discuss the problem of identifying minimal torsion curves in $\mathcal{E}$, which are elliptic curves $E' \in \mathcal{E}$ attaining a point of prime-power order in least possible degree. Using recent classification results of Rouse, Sutherland, and Zureick-Brown, we obtain an answer to this question in many cases, including a complete characterization for points of odd degree.\\ \\ This is joint work with Nina Ryalls and Lori Watson. |
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