Please use this identifier to cite or link to this item:
Title: An Elliptic Curve over Q has an Isogenous Quadratic Twist if and Only if it has complex Multiplication
Author: B.Langlois, Marie-Andree
Advisor: Cunningham, Clifton
Keywords: Mathematics
Issue Date: 23-Sep-2014
Abstract: In this thesis we prove that, for every elliptic curve E over the rational numbers, E is isogenous to a quadratic twist if and only if E admits complex multiplication. To prove this, we use a famous result of Faltings comparing local and global isogenies of elliptic curves over number fields, and a famous theorem proven by Serre on the density of supersingular primes for elliptic curves over the rational numbers. While the result of this thesis is certainly known to experts, a proof seems to not appear in the literature. The thesis includes background on elliptic curves, isogenies, twists and complex multiplication.
Appears in Collections:Electronic Theses

Files in This Item:
File Description SizeFormat 
ucalgary_2014_Blanglois_MarieAndree.pdf772.27 kBAdobe PDFView/Open

Items in The Vault are protected by copyright, with all rights reserved, unless otherwise indicated.