Let R be the ring of integers in $\displaystyle \mathbb {Q} [ \sqrt {-3} ] $. Determine the units in R.

Let $\displaystyle x = a + b \sqrt {-3}, \ \ \ a,b \in \mathbb {Z} $ be a unit of R, then the norm of x, that is, $\displaystyle N_{R} (x) = 1,-1 $

$\displaystyle N_{R} (x) = N_{R} (a+b \sqrt {-3} ) = a^2 + b^2 (-3) = =1, -1 $

I can only think of +1 and -1 being units in R, anything more?