  In this paper we show how we can transform quadratic systems into new
quadratic systems after some kind of birational transformations, the quadratic
plane Cremona maps. We afterwards apply these transformations to the families
of quadratic differential systems having an algebraic limit cycle. As a
consequence, we provide a new family of quadratic systems having an algebraic
limit cycle of degree 5. Moreover we show how the known families of quadratic
differential systems having an algebraic limit cycle of degree greater than
four are obtained using these transformations. We also provide the phase
portraits on the Poincar\'e disk of all the families of quadratic differential
systems having algebraic limit cycles.
