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Rational Points on Genus 3 Real Hyperelliptic Curves

DOI: 10.4236/ojdm.2021.114008, PP. 103-113

Keywords: Hyperelliptic Curve, Jacobian, Coleman Integration, Rational Point

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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.

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