Periods of Quadratic Twists of Elliptic Curves

TL;DR

This paper establishes a precise relation between the periods of elliptic curves and their quadratic twists, clarifying a common misconception in existing literature.

Contribution

It provides a corrected and rigorous relation between the periods of elliptic curves and their quadratic twists, addressing a frequent misstatement.

Findings

Derived an exact formula relating periods of elliptic curves and their quadratic twists

Clarified misconceptions in the literature about these period relations

Enhanced understanding of the structure of elliptic curve periods

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.