How can I find $E(\mathbb F_{17})$ for the elliptic curve $E:$ $y^2=x^3+c$ where $c$ is any element in $\mathbb F_{17}^*$?

Question

This was left as an exercise in a seminar in my college. I tried to figure it out myself, but haven't been able to make any progress thus far. I don't think it should need any non-trivial result (or should it?) like Mordell's theorem, but I really have no clue. Any help will be appreciated.

Answer 1

Hint: the map $\mathbb F_{17}^*\to\mathbb F_{17}^*$ which sends $x\mapsto x^3$ is a bijection.