

Chabauty methods using elliptic curves
Abstract. In this article, we consider algebraic curves over Q that cover an elliptic curve over some extension of Q. We show how we can use the arithmetic on that elliptic curve to obtain information on the rational points on the cover. We apply this method to curves arising from the diophantine equations x^{2}+y^{4}=z^{5} and x^{2}y^{4}=z^{5}and determine all solutions with coprime, integral x,y,z. To do this, we determine the rational points on several curves of genus 5.
An archive of scripts for the algebraic number theory package KASH is available in the ASCIIfile 199914.sh. Instructions on how to unpack it can be found within.
Document: 199914.dvi (), 199914.ps (), 199914.ps.gz (), 199914.sh ()
Report printed: june 1999