  There are 26 possibilities for the torsion group of elliptic curves defined
over quadratic number fields. We present examples of high rank elliptic curves
with given torsion group which give the current records for most of the torsion
groups. In particular, we show that for each possible torsion group, except
maybe for Z/15Z, there exist an elliptic curve over some quadratic field with
this torsion group and with rank >= 2.
