  We give an analytical description of the locus of the two-gap elliptic
potentials associated with the corresponding flow of the Calogero--Moser
system. We start with the description of Treibich--Verdier two--gap elliptic
potentials. The explicit formulae for the covers, wave functions and Lam\'e
polynomials are derived, together with a new Lax representation for the
particle dynamics on the locus. Then we consider more general potentials within
the Weierstrass reduction theory of theta functions to lower genera. The
reduction conditions in the moduli space of the genus two algebraic curves are
given. This is some subvariety of the Humbert surface, which can be singled out
by the condition of the vanishing of some theta constants.
