Parity of ranks for elliptic curves with a cyclic isogeny

被引：24

作者：

Dokchitser, Tim ^{[1
]}

Dokchitser, Vladimir ^{[2
]}

机构：

[1] Robinson Coll, Cambridge CB3 9AN, England

[2] Max Planck Inst Math, D-53111 Bonn, Germany

来源：

JOURNAL OF NUMBER THEORY | 2008年 / 128卷 / 03期

关键词：

parity conjecture; elliptic curves; selmer rank; root numbers;

D O I：

10.1016/j.jnt.2007.02.008

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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. (c) 2007 Elsevier Inc. All rights reserved.

引用

页码：662 / 679

页数：18

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