  With the assistance of one fold Darboux transformation formula, we derive
rogue wave solutions of the complex modified Korteweg-de Vries equation on an
elliptic function background. We employ an algebraic method to find the
necessary squared eigenfunctions and eigenvalues. To begin we construct the
elliptic function background. Then, on top of this background, we create a
rogue wave. We demonstrate the outcome for three distinct elliptic modulus
values. We find that when we increase the modulus value the amplitude of rogue
waves on the dn-periodic background decreases whereas it increases in the case
of cn-periodic background.
