Question: Rule (5) for doing arithmetic in elliptic curves over real numbers states that to double a point (Q_{2}), draw the tangent line and find the

Rule (5) for doing arithmetic in elliptic curves over real numbers states that to double a point \(Q_{2}\), draw the tangent line and find the other point of intersection \(S\). Then \(Q+Q=2 Q=-S\). If the tangent line is not vertical, there will be exactly one point of intersection. However, suppose the tangent line is vertical? In that case, what is the value \(2 Q\) ? What is the value \(3 Q\) ?

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