  We present a database of rational elliptic curves, up to Q-isomorphism, with
good reduction outside {2,3,5,7,11,13}. We provide a heuristic involving the
abc and BSD conjectures that the database is likely to be the complete set of
such curves. Moreover, proving completeness likely needs only more computation
time to conclude. We present data on the distribution of various quantities
associated to curves in the set. We also discuss the connection to S-unit
equations and the existence of rational elliptic curves with maximal conductor.
