For rank 0 once-punctured elliptic curves, the quadratic Chabauty locus equals the p-adic points of a fixed finite subscheme of torsion points described explicitly by residues and local heights.
Balakrishnan, Amnon Besser, Francesca Bianchi, and J
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On a non-abelian analogue of a conjecture of Michael Stoll
For rank 0 once-punctured elliptic curves, the quadratic Chabauty locus equals the p-adic points of a fixed finite subscheme of torsion points described explicitly by residues and local heights.