Elliptic Curves pp 22-42 | Cite as

# Elementary Properties of the Chord-Tangent Group Law on a Cubic Curve

Chapter

## Abstract

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.

## Keywords

Normal Form Elliptic Curve Rational Point Elliptic Curf Tangent Line
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer Science+Business Media New York 1987