I'm reading/studying on my own a book about algebraic curves.

I'm trying to find a way for _Mathematica_ help me with the following (the book, ISBN: 038731802X, allows me to use any CAS / program.

Here is a question:

>How many times do the two given curves intersect at the origin? 

>$\quad(a)\quad y = x^3$ 

>which I can rewrite as $y-x^3 = 0$ 

>$\quad(b)\quad y^4 + 6x^3*y + x^8 == 0 $

I can view both curves using:

 ContourPlot[{y^4 + 6 x^3*y + x^8 == 0, y - x^3 == 0}, {x, -5, 5}, {y, -5, 5}]

However, I have no idea how to find the the multiplicity of the zeros at the origin. I'm really stuck.