On Darboux-Treibich-Verdier potentials

It is shown that the four-parameter family of elliptic functions $$u_D(z)=m_0(m_0+1)\mathrm{\wp }(z)+\sum _{i=1}^3{m}_i(m_i+1)\mathrm{\wp }(z-{\omega }_i)$$ introduced by Darboux and rediscovered a hundred years later by Treibich and Verdier, is the most general meromorphic family containing infinitely many finite-gap potentials.