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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. 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 there anyway to do this in sage?

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. (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 there anyway it possible to do define a curve in this in sage?way and study it as a family of curves?