http://modular.math.washington.edu/Tables/ecdb/are complete for prime conductors . This proved that the smallest conductor of a rank elliptic curve is

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