  The Katz-Sarnak philosophy predicts that statistics of zeros of families of
L-functions are strikingly universal. However, subtle arithmetical differences
between families of the same symmetry type can be detected by calculating
lower-order terms of the statistics of interest. In this paper we calculate
lower-order terms of the 1-level density of some families of elliptic curves.
We show that there are essentially two different effects on the distribution of
low-lying zeros. First, low-lying zeros are more numerous in families of
elliptic curves E with relatively large numbers of points (mod p). Second, and
somewhat surprisingly, a family with a relatively large number of primes of bad
reduction has relatively fewer low-lying zeros.
  We also show that the lower order term can grow arbitrarily large by taking a
biased family with a relatively large number of points (mod p) for all small
primes p.
