  We give a mathematical foundation for, and numerical demonstration of, the
existence of mean curvature 1 surfaces of genus 1 with either two elliptic ends
or two hyperbolic ends in de Sitter 3-space. An end of a mean curvature 1
surface is an ``elliptic end'' (resp. a ``hyperbolic end'') if the monodromy
matrix at the end is diagonalizable with eigenvalues in the unit circle (resp.
in the reals). Although the existence of the surfaces is numerical, the types
of ends are mathematically determined.
