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The tangent from P is always vertical if

yP = 0.

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.

If one wanted to find 3P in this situation, one can add 2P + P. This becomes P + O = P Thus 3P = P.

3P = P, 4P = O, 5P = P, 6P = O, 7P = P, etc.



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