The equation y² = x³ - ax + 3, where a is a parameter, defines a well-known family of elliptic curves. 

a. Verify that if a = 3, the graph consists of a single curve.

b. Verify that if a = 4, the graph consists of two distinct curves.

c. By experimentation, determine the value of a (3 < a < 4) at which the graph separates into two curves.