Rational Points on Genus 3 Real Hyperelliptic Curves

Abstract

We compute rational points on real hyperelliptic curves of genus 3 defined on  whose Jacobian have Mordell-Weil rank 0 r = . We present an implementation in sagemath of an algorithm which describes the birational transformation of real hyperelliptic curves into imaginary hyperelliptic curves and the Chabauty-Coleman method to find ( ) C  . We run the algorithms in Sage on 47 real hyperelliptic curves of genus 3.