Modular degrees of Elliptic curves : On a conjecture of Watkins

Language: English

Published by LAP Lambert Academic Publishing, 2013

3659349410 / 9783659349416

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nach der Bestellung gedruckt Neuware - Printed after ordering - 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.…

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Title
Modular degrees of Elliptic curves : On a conjecture of Watkins
Author
Srilakshmi Krishnamoorthy
Publisher
LAP Lambert Academic Publishing
Publication year
2013
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
3659349410
ISBN 13
9783659349416
Item weight
156 grams
Dimensions
220x150x7 mm

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