http://modular.math.washington.edu/Tables/ecdb/are complete for prime conductors . This proved that the smallest conductor of a rank elliptic curve is not prime. Is the smallest conductor ? To find out, one has to compute every elliptic curve (up to isogeny) of conductor . Cremona has computed every curve of conductor , and much more about each curve (e.g., pretty much everything we know how to compute about a curve).
The Stein-Watkins tables
http://modular.math.washington.edu/Tables/ecdb/contains a ``substantial chunk'' of the curves of conductor . Challenge 4.2.1 amounts to finding the number (and some info about) the curves that are missing from Stein-Watkins in the range of conductors