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Christophe Delaunay; Xavier-François Roblot
Regulators of rank one quadratic twists
Journal de théorie des nombres de Bordeaux, 20 no. 3 (2008), p. 601-624, doi: 10.5802/jtnb.643
Article PDF | Reviews MR 2523310 | Zbl pre05572694

Résumé - Abstract

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.


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