A note on certain maximal hyperelliptic curves
In this paper, the author gives necessary and sufficient conditions for a hyperelliptic curve of the form \(y^2=x^m+x\) to be maximal. More precisely, he proves that the curve \(y^2=x^{2g+1}+x\) is maximal over \(\mathbb{F}_{q^2}\) if and only if \(q\equiv -1\) or \(2g+1\pmod{4g}\), and the curve \(y^2=x^{2g+2}+x\) is maximal over the same field if and only if \(2g+1\) divides \(q+1\).
scientific article; zbMATH DE number 6092707