Families of Elliptic Curves and Geometric Properties of Torsion Points

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

Abstract

In this chapter we consider families of elliptic curves by studying cubics in normal form with coefficients depending on a parameter. The most important example is the Legendre family E: y 2 = x(x-1)(x-λ) over k(λ), where k is a field of characteristic unequal to 2. The points ·(0, 0), (1, 0), (λ, 0)× are the three 2-torsion points on E λ for each value of λk - ·0, 1×, and they are specified with a given ordering.

Keywords

Normal Form Elliptic Curve Elliptic Curf Tangent Line Double Point 
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

Authors and Affiliations

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

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