Papers › Computing rational points on rank 0 genus 3 hyperelliptic curves
Computing rational points on rank 0 genus 3 hyperelliptic curves
María Inés de Frutos-Fernández, Sachi Hashimoto
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We compute rational points on genus $3$ odd degree hyperelliptic curves C over ℚ that have Jacobians of Mordell-Weil rank $0$. The computation applies the Chabauty-Coleman method to find the zero set of a certain system of p-adic integrals, which is known to be finite and include the set of rational points C(ℚ). We implemented an algorithm in Sage to carry out the Chabauty-Coleman method on a database of $5870$ curves.
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