Обложка Modular degrees of Elliptic curves
Название книги:

Modular degrees of Elliptic curves

On a conjecture of Watkins

LAP LAMBERT Academic Publishing (2013-02-21 )

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ISBN-13:

978-3-659-34941-6

ISBN-10:
3659349410
EAN:
9783659349416
Язык Книги:
Английский
Краткое описание:
Modular degree is an interesting invariant of elliptic curves. It is computed by variety of methods. After computer calculations, Watkins conjectured that given E over the rational numbers of rank R, 2^R divides (\Phi), where (Phi) : X_0(N) to E is the optimal map (up to isomorphism of E) and degree of (Phi) is the modular degree of E. In fact he observed that 2^{R+K} divides the degree of the modular degree and 2^K depends on {W}, where {W}is the group of Atkin-Lehner involutions, the cardinality of {W}=2^{omega(N)}, N is the conductor of the elliptic curve and omega(N) counts the number of distinct prime factors of N. The goal of this thesis is to study this conjecture. We have proved that 2^{R+K} divides the degree of (Phi) would follow from an isomorphism of complete intersection of a universal deformation ring and a Hecke ring, where 2^K is the cardinality of W^{\prime}, the cardinality of a certain subgroup of the group of Atkin-Lehner involutions. I attempt to verify 2^{R+K} divides the degree of ({\Phi}) for certain Ellipitic Curves E by using a computer algebra package Magma. I have verified when N is squarefree. Computations are in chapter 5.
Издательский Дом:
LAP LAMBERT Academic Publishing
Веб-сайт:
https://www.lap-publishing.com/
By (author) :
Srilakshmi Krishnamoorthy
Количество страниц:
104
Опубликовано:
2013-02-21
Акции:
В наличии
Категория:
Математика
Цена:
49.00 €
Ключевые слова:
elliptic curves, Modular degrees, watkins' conjecture, Deformation rings

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