Algorithms for Modular Elliptic Curves by John E. Cremona
About this book :-
This text is a comprehensive resource in computational number theory, with numerous applications in such areas as cryptography, primality testing and factorisation. It focusing on algorithms for studying elliptic curves over the rationals. The book is divided into three main sections:
Modular Symbol Algorithms section explains how to compute modular elliptic curves using modular symbols, covering topics like Hecke operators and Fourier coefficients.
Elliptic Curve Algorithms discusses algorithms for studying the arithmetic of elliptic curves, including methods for determining the rank, computing canonical heights, and finding isogenies.
Tables: The final section presents tables of all modular elliptic curves of conductor less than 1000, including coefficients, L-series, generators, and quantities related to the Birch–Swinnerton–Dyer conjecture.
Researchers and graduate students of number theory will find this book useful particularly those interested in computation. That aspect will make it appeal also to computer scientists and coding theorists.
Book Detail :-
Title:
Algorithms for Modular Elliptic Curves by John E. Cremona
Publisher:
Cambridge University Press
Year:
1992
Pages:
351
Type:
PDF
Language:
English
ISBN-10 #:
0521418135
ISBN-13 #:
978-0521418133
License:
Linked Content Owned by Author
Amazon:
Amazon
About Author :-
The author
John E. Cremona
is a British mathematician renowned for his contributions to number theory and algebraic geometry, particularly in the study of elliptic curves. He is well known for his seminal work, Algorithms for Modular Elliptic Curves. His work continues to be a cornerstone in the study of modular elliptic curves and their applications in number theory.
Book Contents :-
1. Introduction
2. Modular Symbol Algorithms
3. Elliptic Curve Algorithms
4. The Tables
Similar
Abstract Algebra
Books