标题： 关于超椭圆曲线及其商曲线的水平$n$，我 显示英文标题

标题： On superelliptic curves of level $n$ and their quotients, I

摘要： 我们研究了具有固定自同构群的超椭圆曲线族。 此类族由用曲线系数表达的不变量来参数化。 这些不变量之间的代数关系决定了超椭圆曲线类别的包含格及其模域。 我们提供了一个 Maple 软件包，用于计算超椭圆曲线及其不变量的正规型。 完整列举任意特征为$\neq 2$的域上亏格为$g \leq 10$的所有超椭圆曲线的列表将在后续论文中给出。 显示英文摘要

摘要： We study families of superelliptic curves with fixed automorphism groups. Such families are parametrized with invariants expressed in terms of the coefficients of the curves. Algebraic relations among such invariants determine the lattice of inclusions among the loci of superelliptic curves and their field of moduli. We give a Maple package of how to compute the normal form of an superelliptic curve and its invariants. A complete list of all superelliptic curves of genus $g \leq 10$ defined over any field of characteristic $\neq 2$ is given in a subsequent paper.