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

  • Dale Husemöller
Part of the Graduate Texts in Mathematics book series (GTM, volume 111)


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.


Normal Form Elliptic Curve Rational Point Elliptic Curf Tangent Line 
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Copyright information

© Springer Science+Business Media New York 1987

Authors and Affiliations

  • Dale Husemöller
    • 1
  1. 1.Department of MathematicsHaverford CollegeHaverfordUSA

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