Article ID Journal Published Year Pages File Type
4595486 Journal of Number Theory 2008 18 Pages PDF
Abstract

Let E be an elliptic curve over a number field K which admits a cyclic p-isogeny with p⩾3 and semistable at primes above p. We determine the root number and the parity of the p-Selmer rank for E/K, in particular confirming the parity conjecture for such curves. We prove the analogous results for p=2 under the additional assumption that E is not supersingular at primes above 2.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory