%0 Journal Article
%T Rational Points on Genus 3 Real Hyperelliptic Curves
%A Brice M. Miayoka
%A Regis F. Babindamana
%A Basile G. R. Bossoto
%J Open Journal of Discrete Mathematics
%P 103-113
%@ 2161-7643
%D 2021
%I Scientific Research Publishing
%R 10.4236/ojdm.2021.114008
%X We
compute rational points on real hyperelliptic curves of genus 3 defined on <img src=\"Edit_ff1a2758-8302-45a6-8c7e-a73bd35f12bd.png\" width=\"20\" height=\"18\" alt=\"\" /> whose Jacobian have
Mordell-Weil rank <em>r=0</em>. We present an implementation in sagemath of an algorithm
which describes the birational transformation of real hyperelliptic curves into
imaginary hyperelliptic curves and <span>the
Chabauty-Coleman method to find <em>C </em>(<img src=\"Edit_243e29b4-1b26-469a-9e65-461ffac1e473.png\" width=\"20\" height=\"18\" alt=\"\" />)<span></span>. We run the algorithms in</span> Sage on 47 real
hyperelliptic curves of genus 3.
%K Hyperelliptic Curve
%K Jacobian
%K Coleman Integration
%K Rational Point
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=112538