Computing integral points on hyperelliptic curves using quadratic Chabauty

Abstract

We give a method for the computation of integral points on a hyperelliptic curve of odd degree over the rationals whose genus equals the Mordell-Weil rank of its Jacobian. Our approach consists of a combination of the $p$-adic approximation techniques introduced in previous work with the Mordell-Weil sieve

Minor revision. To appear in Math. Comp

References in corpus (3)

• Two-cover descent on hyperelliptic curves
• An explicit theory of heights for hyperelliptic Jacobians of genus three
• Explicit Coleman integration for hyperelliptic curves

Cited by in corpus (1)

• Solving S-unit, Mordell, Thue, Thue-Mahler and generalized Ramanujan-Nagell equations via Shimura-Taniyama conjecture