  Let K be a field. Let A be a central simple algebra over K and let X be the
associated Brauer-Severi variety over K. It has recently been asked if there
exists a genus 1 curve C over K such that K(C) splits A. In other words, is
there a genus one curve C over K with a morphism to X? In this short note, we
explicitly construct such a curve in the case where X has dimension at most 4
(equivalently, when A has degree at most 5).
