28 research outputs found
Chabauty-Coleman experiments for genus 3 hyperelliptic curves
We describe a computation of rational points on genus 3 hyperelliptic curves
defined over 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 .Comment: 18 page
Cwatset Isomorphism and its Consequences
We explore the consequences of cwatset isomorphism (there are a finite number of non-isomorphic cwatsets of each order) and consider parallels between the theory of groups and the theory of cwatsets (cwatsets of prime order are cyclic but direct sums of isomorphic cwatsets aren\u27t necessarily isomorphic)