Let
M be a curve of genus 2 over $\mathbb{C}$, and let
V be the hyperelliptic involution of
M. Assume Aut(
M)$\supsetneqq \left\langle V \right\rangle$. Then Aut(
M)/$\left\langle V \right\rangle$ is a non-trivial finite subgroup of Aut($\mathbb{P}^1$). It is well-known that finite subgroups
H of Aut($\mathbb{P}^1$) are classified into five types. In [8], we determined the defining equations of
M with
H = Aut(
M)/$\left\langle V \right\rangle$ for each type of
H. In this paper we study invariants of
M derived from these equations.
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