The purpose of this paper is to determine morphisms and algebraic points of low degree on the quotients of the Fermat quintic. An algebraic point of degree at most $3$ is called an algebraic point of low degree. The quotients of the Fermat quintic is a family curves $\mathcal{C}_{rs}(5) : v^5 =u^r(u-1)^s$ where $r$ and $s$ are integers such that: $1< r, s, r+s< 5$. We determine explicitly the morphisms between the curves $\mathcal{C}_{rs}(5)$. By applying Abel Jacobi's theorem and using Riemann-Roch spaces, we give a parametrization of algebraic points of low degree on the special curve $\mathcal{C}_{1,1}(5)$. Birational morphisms allow us to determine the set of algebraic points of low degree on each curve of the family curves $\mathcal{C}_{rs}(5)$.
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