In 1965 Harvey Cohn presented an algorithm for the numerical
approximation of low-points for the Hilbert modular group of real
quadratic number fields with . It turns out that in fact the
low-points correspond to extreme Humbert forms of real quadratic
number fields. For extreme Humbert forms we use the theory of
Voronoï and Coulangeon for characterization. In this talk we combine
the advantages of known algorithms and Cohn's algorithm to obtain
new examples of extreme Humbert forms. We are able to compute
extreme Humbert forms for the fields , and
.