Find all elliptic curves of conductor $\leq 234446$

Andrei Jorza, Jen Balakrishnan, and I verified that the Stein-Watkins tables

   http://modular.math.washington.edu/Tables/ecdb/

are complete for prime conductors $p<234446$ . This proved that the smallest conductor of a rank $4$ elliptic curve is not prime. Is the smallest conductor $234446$ ? To find out, one has to compute every elliptic curve (up to isogeny) of conductor $N\leq 234446$ . Cremona has computed every curve of conductor $\leq 130000$ , and much more about each curve (e.g., pretty much everything we know how to compute about a curve).

Problem 4.2.1   Determine all elliptic curves over $\mathbb{Q}$ of conductor $\leq 234446$ . By ``determine'' this could be man finding just the first few $a_p = p+1-\char93 E(\mathbb{F}_p)$ for each curve, not the actual equation.

The Stein-Watkins tables

   http://modular.math.washington.edu/Tables/ecdb/

contains a ``substantial chunk'' of the curves of conductor $\leq 234446$ . 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

$$130000 < N \leq 234446.$$