English

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

Algebraic Geometry 2020-12-14 v2

Abstract

We classify elliptic curves over the rationals whose N\'eron 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.

Keywords

Cite

@article{arxiv.2005.10025,
  title  = {Elliptic curves over the rational numbers with semi-abelian reduction and two-division points},
  author = {Stefan Schröer},
  journal= {arXiv preprint arXiv:2005.10025},
  year   = {2020}
}

Comments

19 pages, minor changes, to appear in J. Number Theory