Elementary Properties of the Chord-Tangent Group Law on a Cubic Curve
In this chapter we illustrate how, by using simple analytic geometry, a large number of numerical calculations are possible with the group law on a cubic curve. The cubic curves in x and y will be in normal form, that is, without x 2 y, xy 2, or y 3 terms. In this form the entire curve lies in the affine x, y-plane with the exception of 0:0:1 which is to be zero in the group law. The lines through O are exactly the vertical lines in the x, y-plane, and all other lines used are of the form y = λx + β. We use the definition of P + Q as given in §5 of the Introduction.
KeywordsNormal Form Elliptic Curve Rational Point Elliptic Curf Tangent Line
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