When singular points determine quadratic systems

When one considers a quadratic differential system, one realizes that it depends on 12 parameters of which one can be fixed by means of a time change. One also can notice that fixing 4 finite real singular points plus 3 infinite real ones (all its possible singular points) implies to fix 11 conditions, that is, 11 equations that the parameters must satisfy. Since these conditions are linear with respect to the parameters, it is obvious to think that the system will be determined, except that the fixed conditions are incompatible with a quadratic differential system having finitely many singular points.