亏格3的Ciani型非超椭圆曲线的极大值
On the maximality of genus-3 nonhyperelliptic curves of Ciani type
摘要：
本文研究了正特性$p \geq 3$的Ciani曲线$C: x^4 + y^4 + z^4 + rx^2y^2 + sy^2z^2 + tz^2x^2 = 0$.我们将证明，如果$C$是超特殊的，那么它的标准式是最大或最小的$\mathbb{F}_{p^2}$，而不采取其$\mathbb{F}_{p^2}$ -形式。
英文摘要：
In this paper, we study a Ciani curve $C: x^4 + y^4 + z^4 + rx^2y^2 + sy^2z^2 + tz^2x^2 = 0$ in positive characteristic $p \geq 3$. 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
