For arithmetic lattices in products of PGL2(R) and PGL2(C), Zariski-dense subgroups have normalized height bounded below by a constant times log(covolume) divided by the square of the field degree.
Borel , Commensurability classes and volumes of hyperbolic 3-manifolds, Ann
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A strong height gap theorem for $PGL_2$
For arithmetic lattices in products of PGL2(R) and PGL2(C), Zariski-dense subgroups have normalized height bounded below by a constant times log(covolume) divided by the square of the field degree.