  We establish an explicit formula for the number $C_n(q)$ of ideals of
codimension $n$ of the algebra ${\mathbb F}_q[x,y,x^{-1}, y^{-1}]$ of Laurent
polynomials in two variables over a finite field of cardinality $q$. This
number is a palindromic polynomial of degree $2n$ in $q$. Moreover, $C_n(q) =
(q-1)^2 P_n(q)$, where $P_n(q)$ is another palindromic polynomial; the latter
is a $q$-analogue of the sum of divisors of $n$, which happens to be the number
of subgroups of ${\mathbb Z}^2$ of index $n$.
