REGULATORS OF RANK ONE QUADRATIC TWISTSReport as inadecuate




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1 ICJ - Institut Camille Jordan Villeurbanne

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.





Author: Christophe Delaunay - Xavier-François Roblot -

Source: https://hal.archives-ouvertes.fr/



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