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By a celebrated theorem of Faltings, the number of rational points on a curve of genus $g\ge 2$ defined over a number field is finite. Faltings' theorem is unfortunately ineffective, and computing this finite set is a difficult problem, in general.

For curves of genus $g\ge 2$ in the LMFDB, we store all known rational points, and we indicate cases where this is provably all rational points.

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  • Review status: reviewed
  • Last edited by Jennifer Paulhus on 2019-04-20 15:09:59
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