A modular-period-map variant of Chabauty computes all S-integral points on elliptic-fibred curves, including Y1(N) and the S-unit equation, in seconds.
On the modularity of elliptic curves overQ: wild 3-adic exercises
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Modular Chabauty: Effective S-Integral Point Computation On Curves with Elliptic Fibrations
A modular-period-map variant of Chabauty computes all S-integral points on elliptic-fibred curves, including Y1(N) and the S-unit equation, in seconds.