 
Summary: arXiv:1012.0094v1[math.NT]1Dec2010
Periods of quadratic twists of elliptic curves
Vivek Pal
with an appendix by Amod Agashe
Abstract
In this paper we prove a relation between the period of an elliptic curve
and the period of its real and imaginary quadratic twists. This relation is
often misstated in the literature.
1 Introduction
One of the central conjectures in Number Theory is the Birch and Swinnerton
Dyer Conjecture, which predicts how one can obtain arithmetic information
from the Lfunction. A simpler questions is to ask:
(*) if an elliptic curve satisfies the Birch and SwinnertonDyer Con
jecture then will its (quadratic) twist also satisfy the Birch and
SwinnertonDyer Conjecture.
Part two of the Birch and SwinnertonDyer Conjecture involves many ellip
tic curve invariants, namely the order of the TateShafarevich group, the period
and the order of the torsion subgroup among other important invariants. In this
paper we relate the period of an elliptic curve with the period of its quadratic
twists. A relation between the orders of the torsion subgroups has already been
