 There is exactly 1 cubic polynomial 
going through the four points 
Note here that it could be possible that for example formula_385, hence we must take multiplicities into account.Putting formula_386 we find that 
and hence 
As formula_389 is a polynomial of degree 6, we have that formula_390 has six zeroes and hence formula_391 has besides formula_384 two more intersection points with formula_70, call them formula_394 and formula_395, with formula_396.Now, formula_397 are intersection points of formula_70 with an algebraic curve.