For a given integer $A$ and various families of elliptic curves over finite fields, we compare the number of occurrences of $A$ with the number of occurrences of $-A$ as the trace of Frobenius in the family.
"2, 3, 5, Legendre: ± Trace Ratios in Families of Elliptic Curves." Experiment. Math. 19 (3) 267 - 277, 2010.