Upper bound for the height of S-integral points on elliptic curves

Vincent Bosser (1) , Andrea Surroca (2)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 IMJ - Institut de Mathématiques de Jussieu

We establish new upper bounds for the height of the S-integral points of an elliptic curve. This bound is explicitly given in terms of the set S of places of the number field K involved, but also in terms of the degree of K, as well as the rank, the regulator and the height of a basis of the Mordell-Weil group of the curve. The proof uses the elliptic analogue of Baker's method, based on lower bounds for linear forms in elliptic logarithms.

Domains: Number Theory [math.NT]

Vincent Bosser, Andrea Surroca. Upper bound for the height of S-integral points on elliptic curves. Ramanujan Journal, 2013, 32 (1), ⟨10.1007/s11139-012-9440-4⟩. ⟨hal-02151921⟩