  Let $\mathbb{F}_q$ denote the finite field with $q$ elements. In this work,
we use characters to give the number of rational points on suitable curves of
low degree over $\mathbb{F}_q$ in terms of the number of rational points on
elliptic curves. In the case where $q$ is a prime number, we give a way to
calculate these numbers. As a consequence of these results, we characterize
maximal and minimal curves given by equations of the forms $ax^3+by^3+cz^3=0$
and $ax^4+by^4+cz^4=0$.
