本文简单地讨论下CSIDH型超奇异椭圆曲线同源图中的非退化环，或者说，\(t\)个线性无关的关系\(r_1,\cdots,r_t\)，使得 \[ \require{HTML} \newcommand{\rotateninety}[1]{\style{display: inline-block; transform: rotate(90deg)}{#1}} \newcommand{\ZZ}{\mathbb{Z}} \newcommand{\RR}{\mathbb{R}} \newcommand{\CC}{\mathbb{C}} \newcommand{\HH}{\mathbb{H}} \newcommand{\QQ}{\mathbb{Q}} \newcommand{\abs}[1]{\left\vert #1 \right\vert} \newcommand{\End}{\text{End}} \newcommand{\tens}[1]{\otimes_{#1}} \newcommand{\SL}{\text{SL}} \newcommand{\GL}{\text{GL}} \newcommand{\iso}{\mathop{\longrightarrow}\limits^{\sim}} \newcommand{\Tr}{\operatorname{T}} \newcommand{\Nm}{\operatorname{N}} \newcommand{\deg}{\operatorname{deg}} \newcommand{\gcd}{\mathop{\text{gcd}}} \newcommand{\lcm}{\mathop{\text{lcm}}} \newcommand{\Aut}{\text{Aut}} \newcommand{\diag}{\text{diag}} \newcommand{\ker}{\operatorname{ker}} \newcommand{\coker}{\operatorname{coker}} \newcommand{\PGL}{\text{PGL}} \newcommand{\OO}{\mathcal{O}} \newcommand{\cl}{\text{cl}} \newcommand{\FF}{\mathbb{F}} \newcommand{\PP}{\mathbb{P}} \newcommand{\disc}{\operatorname{disc}} \newcommand{\Gal}{\text{Gal}} \newcommand{\Im}{\operatorname{Im}} \newcommand{\Re}{\operatorname{Re}} \cl(\OO) = \left\langle [\mathfrak{l}_1],\cdots, [\mathfrak{l}_t]\mid r_1, \cdots, r_t,\quad [\mathfrak{l}_i][\mathfrak{l}_j][\mathfrak{l}_i]^{-1}[\mathfrak{l}_j]^{-1},\ i\ne j\right\rangle \]
其中，
\[ p = 4\prod\limits_{i=1}^t l_i - 1,\quad p,l_i\in\PP,\quad l_i > 2 \] \[ \OO = \ZZ\left[\sqrt{-p}\right],\quad \pi = \sqrt{-p} \] \[ \mathfrak{l}_i = (l_i, \pi - 1),\quad \bar{\mathfrak{l}}_i = (l_i, \pi + 1) \]