Could you provide a source proving you claims about form factor?
All bullets with a pointed tip have a parabolic form, that's not how form factor is defined.
The ogive is the curve of the bullet's surface from the shank to the tip.
A parabola is a curved line with a point to it.
All bullets with a pointed tip have a parabolic shape with a an ogive. The shape of the ogive will exist even if the point of the bullet is large and flat, as long as the bullet tapers toward the tip it has an ogive.
Mea culpa, I was careless in my terminology. I was referring to a power series curve which looks like a classic parabola, while a parabolic nose is actually only a portion of a parabola rotated about its axis. Most bullets have a tangent ogive nose profile (although it's generally not
really an ogive, since it is not a spherical curve, but we'll call it an ogive because everyone else does), blunted to some degree for several reasons: 1. Heat dissipation- a sharp point produces much more friction heating at supersonic velocities than a point blunted to some extent. 2. Durability- pointed tips (particularly in exposed lead) are fragile. 3. Ease of manufacturing- It is virtually impossible to draw a really sharp point, even in a full metal jacket, without variations in concentricity that make it unacceptable for high precision shooting.
The ideal shape for supersonic flight is a Von Kármán curve, a specific instance of the Sears-Haack Series providing minimum drag for a given length and diameter. It looks like a power series curve but is subtly different. Of course, there are tradeoffs. A Von Kármán profile is less efficient at high transonic velocities (~M 1.4) than several other shapes. In the fully supersonic region, it is superior. Since it is not derived from simple geometric shapes, it is a bit more difficult (or was until modern CNC equipment came along) to design and produce.
All that being said, the actual ballistic differences between a really well-designed tangent ogive bullet and a true Von Kármán are very small.
Ashley and Landahl:
Aerodynamics of Wings and Bodies, (Dover Publications Inc New York 1985)
Carlo Ferrari: Bodies of Revolution having Minimum Pressure Drag. In:
Theory of Optimum Aerodynamic Shapes, ed by Angelo Miele (Academic Press Inc, New York 1965) pp 103–124