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arXiv · 1712.04214

Explicit Small Heights in Infinite Non-Abelian Extensions

Linda Frey
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Abstract

Let $E$ be an elliptic curve over the rationals. We will consider the infinite extension $\mathbb{Q}(E_{\text{tor}})$ of the rationals where we adjoin all coordinates of torsion points of $E$. In this paper we will prove an explicit lower bound for the height of non-zero elements in $\mathbb{Q}(E_{\text{tor}})$ that are not a root of unity, only depending on the conductor of the elliptic curve. As a side result we will give an explicit bound for a small supersingular prime for an elliptic curve.

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Linda Frey. 2017-12-12. Explicit Small Heights in Infinite Non-Abelian Extensions. https://arxiv.org/abs/1712.04214

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