The 12-th roots of the discriminant of an elliptic curve and the torsion points; a survey (Algebraic Number Theory and Related Topics 2013)

Abstract

This article is a survey of [2], which is a joint work with K. Fukuda. Given an elliptic curve over a scheme with 6 invertible, its discriminant defines a canonical $mu$_{12}-torsor over the base scheme. In this article, we give an explicit description of this $mu$_{12}-torsor in terms of the 3-torsion points and of the 4-torsion points of the given elliptic curve. We refer our paper [2] for the detail.