A remarkable eelliptic curve
Duco van Straten
Journal of Singularities
volume 30 (2026), 300-309
Received: 30 September 2025. In revised form: 19 April 2026
Abstract:
We describe a system of plane algebraic curves defined over Z, attached naturally to the exponential function. One of these is a remarkable curve of degree 6 that has genus equal to 1.
As this sextic curve has rational points, it is an elliptic curve and can be transformed over Q into the curve 1584.j1 of the L-functions and modular forms database. One is left to wonder what the number 11, appearing in the factorisation 1584=(2^4)(3^2)(11), has to do with the exponential function.
Author(s) information:
Duco van Straten
Johannes Gutenberg University
Institut für Mathematik
Staudingerweg 9
55128 Mainz, Germany