Doubly Transitive Parabolic Ovals in Affine Planes of Even Order \(n \leq 64\)

Abstract

All parabolic ovals in affine planes of even order \(q \leq 64\) which are preserved by a collineation group isomorphic to \(\mathrm{A\Gamma L}(1,q)\) are determined. They are either parabolas or translation ovals.