On the maximality of genus-3 nonhyperelliptic curves of Ciani type

Abstract

In this paper, we study a Ciani curve $C:x^4+y^4+z^4+r{x}^2{y}^2+s{y}^2{z}^2+t{z}^2{x}^2=0$ in positive characteristic $p\ge 3$. We will show that if $C$ is superspecial, then its standard form is maximal or minimal over ${\mathbb{F}}_{p^2}$ without taking its ${\mathbb{F}}_{p^2}$-form.

arXiv admin note: text overlap with arXiv:2112.11152