Computing integral points on hyperelliptic curves using quadratic Chabauty

DOI10.1090/mcom/3130zbMath1376.11053arXiv1504.07040OpenAlexW2100212459MaRDI QIDQ2967970

Jan Steffen Müller, Jennifer S. Balakrishnan, Amnon Besser

Publication date: 9 March 2017

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.07040

zbMATH Keywords

integer solutionMordell-Weil sievehyperelliptic equationsChabauty-Coleman methodquadratic Chabauty method

Mathematics Subject Classification ID

Computer solution of Diophantine equations (11Y50) Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80) [https://portal.mardi4nfdi.de/w/index.php?title=+Special%3ASearch&search=%22Curves+of+arbitrary+genus+or+genus+%28%0D%0Ae+1%29+over+global+fields%22&go=Go Curves of arbitrary genus or genus ( e 1) over global fields (11G30)] Arithmetic varieties and schemes; Arakelov theory; heights (14G40)

Related Items (12)

"Equation missing" -Integral Points on a Mordell Curve ⋮ Quadratic Chabauty and 𝑝-adic Gross–Zagier ⋮ Explicit Vologodsky integration for hyperelliptic curves ⋮ Quadratic Chabauty for modular curves: algorithms and examples ⋮ M_{0, 5}: Toward the Chabauty–Kim method in higher dimensions ⋮ A Chabauty-Coleman bound for surfaces ⋮ Solving 𝑆-unit, Mordell, Thue, Thue–Mahler and Generalized Ramanujan–Nagell Equations via the Shimura–Taniyama Conjecture ⋮ Rational motivic path spaces and Kim's relative unipotent Section conjecture ⋮ Quadratic Chabauty and rational points. I: \(p\)-adic heights ⋮ Explicit quadratic Chabauty over number fields ⋮ Explicit Chabauty-Kim for the split Cartan modular curve of level 13 ⋮ Two Recent p-adic Approaches Towards the (Effective) Mordell Conjecture

Uses Software

• Magma
• SageMath

Cites Work

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