Minimal torsion curves in geometric isogeny classes
Abstract
Abstract In this paper, we introduce the study of minimal torsion curves within a fixed geometric isogeny class. For a double struck upper Q overbar Q ¯ $\overline{{\mathbb{Q}}}$ -isogeny class script upper E E $\mathcal{E}$ of elliptic curves and upper N element of double struck upper Z Superscript plus N ∈ Z + $N \in {\mathbb{Z}}^+$ , we wish to determine the least degree of a point on the modular curve upper X 1 left parenthesis upper N right parenthesis X 1 ( N ) $X_1(N)$ associated to any upper E element of script upper E E ∈ E $E \in \mathcal{E}$ . We consider the cases where script upper E E $\mathcal{E}$ is rational , i.e., contains an elliptic curve with rational j -invariant, or where script upper E E $\mathcal{E}$ consists of elliptic curves with complex multiplication (CM). If upper N equals script l Superscript k
Fields of Study & Subjects
Advanced Numerical Analysis Techniques
Digital Image Processing Techniques
Geometric and Algebraic Topology
Publication details
- Journal / source
- Mathematical Proceedings of the Cambridge Philosophical Society
- Publisher
- Cambridge University Press (CUP)
- Volume
- 181
- Issue
- 2
- Pages
- 1049–1078
- Publication date
- 16 April 2026
- Language
- EN