Download this article
Download this article For screen
For printing
Recent Issues
Volume 18
Volume 16
Volume 15
Volume 14
Volume 13
Volume 12
Volume 11
Volume 10
Volume 9
Volume 8
Volume 6+7
Volume 5
Volume 4
Volume 3
Volume 2
Volume 1
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 2640-7345
ISSN (print): 2640-7337
Author Index
To Appear
 
Other MSP Journals
Configurations on elliptic curves

Andrin Halbeisen, Lorenz Halbeisen and Norbert Hungerbühler

Vol. 19 (2022), No. 3, 111–135
Abstract

An elliptic configuration is a configuration with all its points on a cubic curve, or more precisely, where all points are in the torsion group of an elliptic curve. We investigate the existence of elliptic (3r4,4r3) configurations for r 5. In particular, we construct elliptic ((p 1)3) configurations for every prime p > 7 and show that there are (3r4,4r3) configurations whenever 3r = p 1 for some prime p > 7. Furthermore, we show that for every k 2 there is an elliptic (9k4,12k3) configuration with a rotational symmetry of order 3, where we introduce a new normal form for D3-symmetric elliptic curves.

Dedicated to the memory of Branko Grünbaum

Keywords
configurations, elliptic curves
Mathematical Subject Classification
Primary: 51A20
Secondary: 51A05
Milestones
Received: 5 November 2021
Revised: 15 July 2022
Accepted: 7 August 2022
Published: 10 October 2022
Authors
Andrin Halbeisen
Winterthur
Switzerland
Lorenz Halbeisen
Department of Mathematics
ETH Zentrum
Zürich
Switzerland
Norbert Hungerbühler
Department of Mathematics
ETH Zentrum
Zürich
Switzerland