A remarkable eelliptic curve

2024/04/08 by Duco van Straten, van Straten, Duco · 1 voice
Mathematics · #00A18 #FOS: Mathematics #History and Overview (math.HO) #History and Theory of Mathematics #Number Theory (math.NT) #math.HO #math.NT

paper · pdf · doi:10.48550/arxiv.2404.05852

openalex publication_date 2024/04/08 · arxiv published 2024/04/08 · arxiv updated 2024/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe a system of plane algebraic curves defined over \Z, attached naturally to the exponential function. On of these is a remarkable curve of degree 6 that has genus equal to 1. As the sectic curve has rational points, it is an elliptic curveand can be tranformed over \Q into the curve 1584.j1 of the LMFDB. One is left to wonder what the number 11, appearing in the factorisation 1584=2⁴.3².11 has to do with the exponential function.

Discussions

• I have used the first nodal cubic twice in my course already (and did one more patch to cover all the curve). Now trying to find a way to incorporate this cute singular sextic a friend came up with. a [bsky, 1 points, 1 comments]

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