Explicit Small Heights in Infinite Non-Abelian Extensions

2017/12/12 by Frey, Linda · 1 citation
#11G05 #11G50 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1712.04214

Abstract

Let E be an elliptic curve over the rationals. We will consider the infinite extension ℚ(E_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 ℚ(E_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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• Small points in radical extensions of number fields

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