# Elliptic curve defined with parameter

For example, I want to create and study the curve y^2 = x^3 + (u)x^2 + (16*u)x over finite fields. This curve parameterizes all elliptic curves with rational 2-torsion subgroups. I get errors when I try to use "u" when defining the curve. Is it possible to define a curve in this way and study it as a family of curves?