 Elliptic-curve addition formula

ID: elliptic-curve-addition-formula

y^{2} = x^{3} + a_{2} x^{2} + a_{4} x + a_{6}

, let

λ

be the secant slope through distinct points

P, Q

, or the tangent slope when

P = Q

. Then

x (P + Q) = λ^{2} - a_{2} - x (P) - x (Q), y (P + Q) = - y (P) + λ (x (P) - x (P + Q)) .

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