  We study Heegner points on elliptic curves, or more generally modular abelian
varieties, coming from uniformization by Shimura curves attached to a rather
general type of quaternionic or- ders closely related to those introduced by
Hijikata{Pizer{Shemanske in the 80's. We address several questions arising from
the Birch and Swinnerton-Dyer (BSD) conjecture in this general context. In par-
ticular, under mild technical conditions, we show the existence of non-torsion
Heegner points on elliptic curves in all situations in which the BSD conjecture
predicts their existence.
