Chabauty-Coleman experiments for genus 3 hyperelliptic curves

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1805.03361 (2).pdf(299.03 KB)
Accepted manuscript
Date
2018-05-09
DOI
Authors
Balakrishnan, Jennifer
Bianchi, Francesca
Cantoral-Farfan, Victoria
Ciperiani, Mirela
Etropolski, Anastassia
Version
OA Version
Accepted manuscript
Citation
Jennifer Balakrishnan, Francesca Bianchi, Victoria Cantoral-Farfan, Mirela Ciperiani, Anastassia Etropolski. "Chabauty-Coleman experiments for genus 3 hyperelliptic curves." Women in Numbers 4 (WIN4). Banff International Research Station,
Abstract
We describe a computation of rational points on genus 3 hyperelliptic curves C defined over ℚ whose Jacobians have Mordell-Weil rank 1. Using the method of Chabauty and Coleman, we present and implement an algorithm in Sage to compute the zero locus of two Coleman integrals and analyze the finite set of points cut out by the vanishing of these integrals. We run the algorithm on approximately 17,000 curves from a forthcoming database of genus 3 hyperelliptic curves and discuss some interesting examples where the zero set includes global points not found in C(ℚ).
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