Regulators of rank one quadratic twists

Details Regulators of rank one quadratic twists Regulators of rank one quadratic twists

2007-07-05

arxiv.org/abs/0707.0772v2

Mathematics

Number Theory

28 pages with 32 figures

Scientific paper

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 an odd 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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