Regulators of rank one quadratic twists

Christophe Delaunay[1]; Xavier-François Roblot[1]

  • [1] Université de Lyon Université Lyon 1 INSA de Lyon, F-69621 École Centrale de Lyon CNRS, UMR5208, Institut Camille Jordan 43 blvd du 11 novembre 1918 F-69622 Villeurbanne-Cedex, France

Journal de Théorie des Nombres de Bordeaux (2008)

  • Volume: 20, Issue: 3, page 601-624
  • ISSN: 1246-7405

Abstract

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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.

How to cite

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Delaunay, Christophe, and Roblot, Xavier-François. "Regulators of rank one quadratic twists." Journal de Théorie des Nombres de Bordeaux 20.3 (2008): 601-624. <http://eudml.org/doc/10853>.

@article{Delaunay2008,
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.},
affiliation = {Université de Lyon Université Lyon 1 INSA de Lyon, F-69621 École Centrale de Lyon CNRS, UMR5208, Institut Camille Jordan 43 blvd du 11 novembre 1918 F-69622 Villeurbanne-Cedex, France; Université de Lyon Université Lyon 1 INSA de Lyon, F-69621 École Centrale de Lyon CNRS, UMR5208, Institut Camille Jordan 43 blvd du 11 novembre 1918 F-69622 Villeurbanne-Cedex, France},
author = {Delaunay, Christophe, Roblot, Xavier-François},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {elliptic curves; quadratic twists},
language = {eng},
number = {3},
pages = {601-624},
publisher = {Université Bordeaux 1},
title = {Regulators of rank one quadratic twists},
url = {http://eudml.org/doc/10853},
volume = {20},
year = {2008},
}

TY - JOUR
AU - Delaunay, Christophe
AU - Roblot, Xavier-François
TI - Regulators of rank one quadratic twists
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2008
PB - Université Bordeaux 1
VL - 20
IS - 3
SP - 601
EP - 624
AB - 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.
LA - eng
KW - elliptic curves; quadratic twists
UR - http://eudml.org/doc/10853
ER -

References

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