  We provide an ultimately fine-grained analysis of the data complexity and
rewritability of ontology-mediated queries (OMQs) based on an EL ontology and a
conjunctive query (CQ). Our main results are that every such OMQ is in AC0,
NL-complete, or PTime-complete and that containment in NL coincides with
rewritability into linear Datalog (whereas containment in AC0 coincides with
rewritability into first-order logic). We establish natural characterizations
of the three cases in terms of bounded depth and (un)bounded pathwidth, and
show that every of the associated meta problems such as deciding wether a given
OMQ is rewritable into linear Datalog is ExpTime-complete. We also give a way
to construct linear Datalog rewritings when they exist and prove that there is
no constant Datalog rewritings.
