Parity of ranks for elliptic curves with a cyclic isogeny
数论
2013-09-23 v3
摘要
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.
引用
@article{arxiv.math/0604149,
title = {Parity of ranks for elliptic curves with a cyclic isogeny},
author = {Tim Dokchitser and Vladimir Dokchitser},
journal= {arXiv preprint arXiv:math/0604149},
year = {2013}
}
备注
Minor corrections; 17 pages, to appear in J. Number Theory