  We show the existence of families of elliptic curves over Q whose generic
rank is at least 2 for the torsion groups Z/8Z and Z/2Z x Z/6Z. Also in both
cases we prove the existence of infinitely many elliptic curves, which are
parameterized by the points of an elliptic curve with positive rank, with such
torsion group and rank at least 3. These results represent an improvement of
previous results by Campbell, Kulesz, Lecacheux, Dujella and Rabarison where
families with rank at least 1 were constructed in both cases.

Number Theory