  Let $k$ be a field, let ${\sf C}$ be a $k$-linear abelian category, let
$\underline{\mathcal{L}}:=\{\mathcal{L}_{i}\}_{i \in \mathbb{Z}}$ be a sequence
of objects in ${\sf C}$, and let $B_{\underline{\mathcal{L}}}$ be the
associated orbit algebra. We describe sufficient conditions on
$\underline{\mathcal{L}}$ such that there is a canonical morphism from the
noncommutative space ${\sf Proj }B_{\underline{\mathcal{L}}}$ to a
noncommutative projective line in the sense of \cite{abstractp1}, generalizing
the usual construction of a map from a scheme $X$ to $\mathbb{P}^{1}$ defined
by an invertible sheaf $\mathcal{L}$ generated by two global sections. We then
apply our results to construct, for every natural number $d>2$, a degree two
cover of Piontkovski's $d$th noncommutative projective line by a noncommutative
elliptic curve in the sense of Polishchuk.
