Families of Elliptic Curves and Geometric Properties of Torsion Points

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


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.


Normal Form Elliptic Curve Elliptic Curf Tangent Line Double Point 
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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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