  The "noncommutative geometry" of complex algebraic curves is studied. As
first step, we clarify a morphism between elliptic curves, or complex tori, and
C*-algebras T_t={u,v | vu=exp(2\pi it)uv}, or noncommutative tori. The main
result says that under the morphism isomorphic elliptic curves map to the
Morita equivalent noncommutative tori. Our approach is based on the rigidity of
the length spectra of Riemann surfaces.
