The Group of Rational Points

  • Joseph H. Silverman
  • John Tate
Part of the Undergraduate Texts in Mathematics book series (UTM)


In this chapter we will prove Mordell’s theorem that the group of rational points on a non-singular cubic is finitely generated. There is a tool used in the proof called the height. In brief, the height of a rational point measures how complicated the point is from the viewpoint of number theory.


Abelian Group Rational Number Elliptic Curve Rational Point Quotient Group 
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Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Joseph H. Silverman
    • 1
  • John Tate
    • 2
  1. 1.Department of MathematicsBrown UniversityProvidenceUSA
  2. 2.Department of MathematicsUniversity of Texas at AustinAustinUSA

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