It can be tricky to trust elliptic curves standardized in a non-transparent way. To rectify this, we propose a systematic methodology for analyzing curves and statistically comparing them to the expected values of a large number of generic curves with the aim of identifying any deviations in the standard curves. For this purpose, we put together the largest publicly available database of standard curves. To identify unexpected properties of standard generation methods and curves, we simulate over 250 000 curves by mimicking the generation process of four standards. We compute 22 different properties of curves and analyze them with automated methods to pinpoint deviations in standard curves, pointing to possible weaknesses.