Reduction and isogenies of elliptic curves
Volume 215 / 2024
Acta Arithmetica 215 (2024), 179-192
MSC: Primary 11G07; Secondary 11G25
DOI: 10.4064/aa230929-17-4
Published online: 19 June 2024
Abstract
Let be a complete discrete valuation ring with fraction field K and perfect residue field k of characteristic p \gt 0. Let E/K be an elliptic curve with a K-rational isogeny of prime degree \ell . We study the possible Kodaira types of reduction that E/K can have. We also prove some related results for elliptic curves over \mathbb Q.
