TITLE:
Rational Points on Genus 3 Real Hyperelliptic Curves
AUTHORS:
Brice M. Miayoka, Regis F. Babindamana, Basile G. R. Bossoto
KEYWORDS:
Hyperelliptic Curve, Jacobian, Coleman Integration, Rational Point
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.11 No.4,
October
19,
2021
ABSTRACT: We
compute rational points on real hyperelliptic curves of genus 3 defined on whose Jacobian have
Mordell-Weil rank r=0. 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.