2.1.4 Doubling the point P if yP = 0 If a point P is such that yP = 0, then the tangent line to the elliptic curve at P is vertical and does not intersect the elliptic curve at any other point. By definition, 2P = O for such a point P.
The tangent from P is always vertical if yP = 0.	If one wanted to find 3P in this situation, one can add 2P + O. This becomes P + O = (-P), but here P = -P. Thus 3P = P. 3P = P, 4P = O, 5P = P, 6P = O, 7P = P, etc…
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