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A note on pépin’s counter examples to the hasse principle for curves of genus 1

  • Franz Lemmermeyer
Article

Abstract

In a series of articles published in the C.R. Paris more than a century ago, T. PéPIN announced a list of “theorems” concerning the solvability of diophantine equations of the type ax4 +by 4 = z2. In this article, we show how to prove these claims using the structure of 2-class groups of imaginary quadratic number fields. We will also look at a few related results from a modern point of view.

Keywords

Elliptic Curve Rational Point Elliptic Curf Rational Solution Diophantine Equation 
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

© Mathematische Seminar 1999

Authors and Affiliations

  1. 1.Max-Planck-Institut für MathematikBonnGermany

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