Space Elliptic Curves

  • Takashi Ono
Part of the The University Series in Mathematics book series (USMA)

Abstract

In Chapter 3, we found a group structure on the plane cubic C(M, N) by a geometric construction (the cord-and-tangent method), which depends on properties peculiar to plane cubics. Since the space curve E(M, N), the solution space of equations of the Fibonacci-Fermat type, is biregularly equivalent to C(M, N), it carries a group structure, too. It certainly is nice to recognize a group structure on the set of solutions of a system of Diophantine equations. However, we soon find that it is extremely impractical to try to copy the group structure of C(M, N) on E(M, N) via the biregular equivalence.

Keywords

Group Structure Elliptic Curf Elliptic Function Theta Function Abelian Variety 
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

© Takashi Ono 1994

Authors and Affiliations

  • Takashi Ono
    • 1
  1. 1.The Johns Hopkins UniversityBaltimoreUSA

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