I am confused by some lecture I heard. It was stated that the elliptic curve over a finite field $\mathbb{F}_{q^k}$ would be a subset of the elliptic curve over the finite field $\mathbb{F}_{q}$. But isn't it exactly the other way arround that $ E(\mathbb{F}_{q}) \subset E(\mathbb{F}_{q^k})$ for some $k\geq 1$?
Thanks guys :)