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arXiv · 2005.10025

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

Stefan Schröer
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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.

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Stefan Schröer. 2020-05-20. Elliptic curves over the rational numbers with semi-abelian reduction and two-division points. https://arxiv.org/abs/2005.10025

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