Non-divisible point on a two-parameter family of elliptic curves

Point non divisible sur une famille de courbe elliptique à deux paramètres

Valentin Petit (1)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

Let n be a positive integer and t a non-zero integer. We consider the elliptic curve over Q given by E : y 2 = x 3 + tx 2 − n 2 (t + 3n 2)x + n 6. It is a special case of an elliptic surface studied recently by Bettin, David and Delaunay [2] and it generalizes Washington's family. The point (0, n 3) belongs to E(Q) and we obtain some results about its nondivisibility in E(Q). Our work extends to this two-parameter family of elliptic curves a previous study of Duquesne (mainly stated for n = 1 and t > 0).

Mots clés: Elliptic curves; Integral points; Heights

Domaines: Théorie des nombres [math.NT]

Valentin Petit. Non-divisible point on a two-parameter family of elliptic curves. 2021. ⟨hal-03115452v2⟩