Regulators of rank one quadratic twists

Christophe Delaunay (1) , Xavier-François Roblot (1)

1 ICJ - Institut Camille Jordan

We investigate the regulators of elliptic curves with rank 1 in some families of quadratic twists of a fixed elliptic curve. In particular, we formulate some conjectures on the average size of these regulators. We also describe an efficient algorithm to compute explicitly some of the invariants of a rank one quadratic twist of an elliptic curve (regulator, order of the Tate-Shafarevich group, etc.) and we discuss the numerical data that we obtain and compare it with our predictions.

Domaines: Théorie des nombres [math.NT]

Christophe Delaunay, Xavier-François Roblot. Regulators of rank one quadratic twists. Journal de Théorie des Nombres de Bordeaux, 2008, pp.601-624. ⟨hal-00863572⟩