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1. Introduction 2. Modular Symbol Algorithms 3. Elliptic Curve Algorithms 4. The Tables
"Algorithms for Modular Elliptic Curves" by "John E. Cremona" is a classic text that brings together theory and computation in modern number theory. The book focuses on elliptic curves over the rational numbers and shows how deep theoretical results can be turned into practical algorithms. It is written for readers who want to understand both the mathematics and the computations behind it. The book explains how "elliptic curves" are connected to "modular forms" and how this relationship allows mathematicians to compute important invariants. Cremona presents clear methods for calculating conductors, ranks, torsion groups, and L-functions. These algorithms form the backbone of much work in "computational number theory" and are explained with precision and clarity. Overall, the book is widely used by graduate students and researchers working in "arithmetic geometry". It is especially valued for showing how abstract ideas can be implemented through "algorithms", making it a key reference for anyone studying the computational side of modern number theory.
Title: Algorithms for Modular Elliptic Curves by John Cremona Publisher: Cambridge University Press Year: 1992 Pages: 351 Type: PDF Language: English ISBN-10 #: 0521418135 ISBN-13 #: 978-0521418133 License: External Educational Resource Amazon: Amazon
The author John E. Cremona is a leading British mathematician known for his influential work in number theory and elliptic curves. He has spent much of his academic career at the University of Warwick, where he helped advance computational approaches in modern mathematics. Cremona is especially recognized for developing algorithms to study "elliptic curves" and their links to "modular forms". His research has shaped "computational number theory" and strengthened understanding in "arithmetic geometry", making his work essential for both researchers and advanced students.
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