Regulators of rank one quadratic twists

Christophe Delaunay, Xavier-François Roblot
2008 Journal de Théorie des Nombres de Bordeaux  
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.
doi:10.5802/jtnb.643 fatcat:baqhv7xgcrctrhkjzk24j5pwzm