Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 14 (2018), 102, 13 pages      arXiv:1708.09745      https://doi.org/10.3842/SIGMA.2018.102
Contribution to the Special Issue on Modular Forms and String Theory in honor of Noriko Yui

Hesse Pencils and 3-Torsion Structures

Ane S.I. Anema, Jaap Top and Anne Tuijp
Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen, P.O. Box 407, 9700 AK Groningen, The Netherlands

Received May 08, 2018, in final form September 18, 2018; Published online September 21, 2018

Abstract
This paper intends to focus on the universal property of this Hesse pencil and of its twists. The main goal is to do this as explicit and elementary as possible, and moreover to do it in such a way that it works in every characteristic different from three.

Key words: Hesse pencil; Galois representation; torsion points; elliptic curves.

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