Number of rational points (reviewed)

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.