Parity of ranks for elliptic curves with a cyclic isogeny
Tim Dokchitser, Vladimir Dokchitser
Abstract
Let E be an elliptic curve over a number field K which admits a cyclic p-isogeny with p odd 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.
Create a lesson
Related papers
Rational points on loxodromic K3 surfaces and complex dynamics
Damián Gvirtz-Chen, Zhizhong Huang, Zhuchao Ji et al.
Ramanujan-type congruences for the smallest parts function
Larry Rolen
Some instances of modularity for residually reducible representations in the mixed case
Luis V. Dieulefait
Classification of torsion of elliptic curves over sextic fields
Filip Najman
A generalization of the Dirichlet approximation theorem for affine actions on the real line
Mohammad Javaheri
On ill-distributed B3 and B4 sets
André Hisatsuga, Rafael Miyazaki, Cosmin Pohoata