We reduced the unsolved problem of Evans triangles to
the problem of nding rational points on a class of elliptic curves,
the twisted Edwards curves En. We proved that the set of all Evans
triangles with a given ratio is isomorphic to a quotient group of En(Q).
After this, using Sage, we can solve the Evans problem for an amount
of cases within the capacity of computer. Even without the help of
a computer, we can still obtain a large class of new Evans triangles,
and nd an e ective way to test if the rank of an Edwards curve is
positive or not.