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Configurations on
elliptic curves
Andrin Halbeisen, Lorenz Halbeisen and Norbert Hungerbühler |
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Vol. 19 (2022), No. 3, 111–135
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Abstract |
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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. |
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Dedicated to the memory of Branko Grünbaum |
Keywords
configurations, elliptic curves
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Mathematical Subject Classification
Primary: 51A20
Secondary: 51A05
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Milestones
Received: 5 November 2021
Revised: 15 July 2022
Accepted: 7 August 2022
Published: 10 October 2022
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Authors |
| Andrin Halbeisen | |
| Winterthur Switzerland |
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| Lorenz Halbeisen | |
| Department of Mathematics ETH Zentrum Zürich Switzerland |
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| Norbert Hungerbühler | |
| Department of Mathematics ETH Zentrum Zürich Switzerland |
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