Planar, rational curves over ${\mathbb{F}}_2$ whose only singularity is a double point

Abstract

We exhibit planar, rational curves of large degree over ${\mathbb{F}}_2$ that have a unique singular point, which has multiplicity 2. In characteristic 0 such curves exist only for degrees up to $6$. v.2: references updated and examples of supersingular double planes added. v.3: references updated.