Representations attached to elliptic curves with a non‐trivial odd torsion point. Issue 5 (16th May 2022)

• Record Type: Journal Article
• Authors: Barrios, Alexander J.; Roy, Manami
• Is Part Of: Bulletin of the London Mathematical Society. Volume 54:Issue 5(2022)
• Page Start: 1846
• Page End: 1861
• Publication Date: 2022-05-16
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1112/blms.12660
• Languages: English
• ISSNs: 0024-6093

Abstract

Abstract: We give a classification of the cuspidal automorphic representations attached to rational elliptic curves with a non‐trivial torsion point of odd order. Such elliptic curves are parameterizable, and in this paper, we find the necessary and sufficient conditions on the parameters to determine when split or non‐split multiplicative reduction occurs. Using this and the known results on when additive reduction occurs for these parametrized curves, we classify the automorphic representations in terms of the parameters.