Elliptic curves over the rational numbers with semi-abelian reduction and two-division points

JOURNAL OF NUMBER THEORY

卷:231

Article

Schroeer, Stefan¹ 

[1] Heinrich Heine Univ, Math Inst, D-40204 Dusseldorf, Germany

关键词: Elliptic curves;    Rational points;    Global ground fields;   

DOI  :  10.1016/j.jnt.2020.11.019

来源: Elsevier

【 摘 要 】

We classify elliptic curves over the rationals whose Neron model over the integers is semi-abelian, with good reduction at p = 2, and whose Mordell-Weil group contains an element of order two that stays non-trivial at p = 2. Furthermore, we describe those curves where the element of order two is narrow, or where another element of order two exists, and also express our findings in terms of Deligne-Mumford stacks of pointed curves of genus one. (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free