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This book presents an extensive set of tables giving information about elliptic curves.
Book Synopsis Algorithms for Modular Elliptic Curves Full Canadian Binding by : J. E. Cremona
Download or read book Algorithms for Modular Elliptic Curves Full Canadian Binding written by J. E. Cremona and published by CUP Archive. This book was released on 1997-05-15 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an extensive set of tables giving information about elliptic curves.
This book presents a thorough treatment of many algorithms concerning the arithmetic of elliptic curves with remarks on computer implementation. It is in three parts. First, the author describes in detail the construction of modular elliptic curves, giving an explicit algorithm for their computation using modular symbols. Second, a collection of algorithms for the arithmetic of elliptic curves is presented; some of these have not appeared in book form before. They include: finding torsion and nontorsion points, computing heights, finding isogenies and periods, and computing the rank. Finally, an extensive set of tables is provided giving the results of the author's implementations of the algorithms. These tables extend the widely used "Antwerp IV Tables" in two ways, the range of conductors (up to 1000) and the level of detail given for each curve. In particular the quantities relating to the Birch-Swinnerton-Dyer conjecture have been computed in each case and are included.
Book Synopsis Algorithms for Modular Elliptic Curves by : J. E. Cremona
Download or read book Algorithms for Modular Elliptic Curves written by J. E. Cremona and published by . This book was released on 1992 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a thorough treatment of many algorithms concerning the arithmetic of elliptic curves with remarks on computer implementation. It is in three parts. First, the author describes in detail the construction of modular elliptic curves, giving an explicit algorithm for their computation using modular symbols. Second, a collection of algorithms for the arithmetic of elliptic curves is presented; some of these have not appeared in book form before. They include: finding torsion and nontorsion points, computing heights, finding isogenies and periods, and computing the rank. Finally, an extensive set of tables is provided giving the results of the author's implementations of the algorithms. These tables extend the widely used "Antwerp IV Tables" in two ways, the range of conductors (up to 1000) and the level of detail given for each curve. In particular the quantities relating to the Birch-Swinnerton-Dyer conjecture have been computed in each case and are included.
This book constitutes the refereed proceedings of the 8th International Algorithmic Number Theory Symposium, ANTS 2008, held in Banff, Canada, in May 2008. The 28 revised full papers presented together with 2 invited papers were carefully reviewed and selected for inclusion in the book. The papers are organized in topical sections on elliptic curves cryptology and generalizations, arithmetic of elliptic curves, integer factorization, K3 surfaces, number fields, point counting, arithmetic of function fields, modular forms, cryptography, and number theory.
Book Synopsis Algorithmic Number Theory by : Alf J. van der Poorten
Download or read book Algorithmic Number Theory written by Alf J. van der Poorten and published by Springer. This book was released on 2008-05-07 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 8th International Algorithmic Number Theory Symposium, ANTS 2008, held in Banff, Canada, in May 2008. The 28 revised full papers presented together with 2 invited papers were carefully reviewed and selected for inclusion in the book. The papers are organized in topical sections on elliptic curves cryptology and generalizations, arithmetic of elliptic curves, integer factorization, K3 surfaces, number fields, point counting, arithmetic of function fields, modular forms, cryptography, and number theory.
The book surveys some recent developments in the arithmetic of modular elliptic curves. It places a special emphasis on the construction of rational points on elliptic curves, the Birch and Swinnerton-Dyer conjecture, and the crucial role played by modularity in shedding light on these two closely related issues. The main theme of the book is the theory of complex multiplication, Heegner points, and some conjectural variants. The first three chapters introduce the background and prerequisites: elliptic curves, modular forms and the Shimura-Taniyama-Weil conjecture, complex multiplication and the Heegner point construction. The next three chapters introduce variants of modular parametrizations in which modular curves are replaced by Shimura curves attached to certain indefinite quaternion algebras. The main new contributions are found in Chapters 7-9, which survey the author's attempts to extend the theory of Heegner points and complex multiplication to situations where the base field is not a CM field. Chapter 10 explains the proof of Kolyvagin's theorem, which relates Heegner points to the arithmetic of elliptic curves and leads to the best evidence so far for the Birch and Swinnerton-Dyer conjecture.
Book Synopsis Rational Points on Modular Elliptic Curves by : Henri Darmon
Download or read book Rational Points on Modular Elliptic Curves written by Henri Darmon and published by American Mathematical Soc.. This book was released on 2004 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book surveys some recent developments in the arithmetic of modular elliptic curves. It places a special emphasis on the construction of rational points on elliptic curves, the Birch and Swinnerton-Dyer conjecture, and the crucial role played by modularity in shedding light on these two closely related issues. The main theme of the book is the theory of complex multiplication, Heegner points, and some conjectural variants. The first three chapters introduce the background and prerequisites: elliptic curves, modular forms and the Shimura-Taniyama-Weil conjecture, complex multiplication and the Heegner point construction. The next three chapters introduce variants of modular parametrizations in which modular curves are replaced by Shimura curves attached to certain indefinite quaternion algebras. The main new contributions are found in Chapters 7-9, which survey the author's attempts to extend the theory of Heegner points and complex multiplication to situations where the base field is not a CM field. Chapter 10 explains the proof of Kolyvagin's theorem, which relates Heegner points to the arithmetic of elliptic curves and leads to the best evidence so far for the Birch and Swinnerton-Dyer conjecture.
This book constitutes the refereed proceedings of the 8th International Algorithmic Number Theory Symposium, ANTS 2008, held in Banff, Canada, in May 2008. The 28 revised full papers presented together with 2 invited papers were carefully reviewed and selected for inclusion in the book. The papers are organized in topical sections on elliptic curves cryptology and generalizations, arithmetic of elliptic curves, integer factorization, K3 surfaces, number fields, point counting, arithmetic of function fields, modular forms, cryptography, and number theory.
Book Synopsis Algorithmic Number Theory by : Alf J. van der Poorten
Download or read book Algorithmic Number Theory written by Alf J. van der Poorten and published by Springer Science & Business Media. This book was released on 2008-04-25 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 8th International Algorithmic Number Theory Symposium, ANTS 2008, held in Banff, Canada, in May 2008. The 28 revised full papers presented together with 2 invited papers were carefully reviewed and selected for inclusion in the book. The papers are organized in topical sections on elliptic curves cryptology and generalizations, arithmetic of elliptic curves, integer factorization, K3 surfaces, number fields, point counting, arithmetic of function fields, modular forms, cryptography, and number theory.
The theory of elliptic curves and modular forms provides a fruitful meeting ground for such diverse areas as number theory, complex analysis, algebraic geometry, and representation theory. This book starts out with a problem from elementary number theory and proceeds to lead its reader into the modern theory, covering such topics as the Hasse-Weil L-function and the conjecture of Birch and Swinnerton-Dyer. This new edition details the current state of knowledge of elliptic curves.
Book Synopsis Introduction to Elliptic Curves and Modular Forms by : Neal I. Koblitz
Download or read book Introduction to Elliptic Curves and Modular Forms written by Neal I. Koblitz and published by Springer. This book was released on 2012-11-21 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of elliptic curves and modular forms provides a fruitful meeting ground for such diverse areas as number theory, complex analysis, algebraic geometry, and representation theory. This book starts out with a problem from elementary number theory and proceeds to lead its reader into the modern theory, covering such topics as the Hasse-Weil L-function and the conjecture of Birch and Swinnerton-Dyer. This new edition details the current state of knowledge of elliptic curves.
The book surveys some recent developments in the arithmetic of modular elliptic curves. It places a special emphasis on the construction of rational points on elliptic curves, the Birch and Swinnerton-Dyer conjecture, and the crucial role played by modularity in shedding light on these two closely related issues. The main theme of the book is the theory of complex multiplication, Heegner points, and some conjectural variants. The first three chapters introduce the background and prerequisites: elliptic curves, modular forms and the Shimura-Taniyama-Weil conjecture, complex multiplication and t.
Book Synopsis Rational Points on Modular Elliptic Curves by : Henri Darmon
Download or read book Rational Points on Modular Elliptic Curves written by Henri Darmon and published by . This book was released on 2003 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book surveys some recent developments in the arithmetic of modular elliptic curves. It places a special emphasis on the construction of rational points on elliptic curves, the Birch and Swinnerton-Dyer conjecture, and the crucial role played by modularity in shedding light on these two closely related issues. The main theme of the book is the theory of complex multiplication, Heegner points, and some conjectural variants. The first three chapters introduce the background and prerequisites: elliptic curves, modular forms and the Shimura-Taniyama-Weil conjecture, complex multiplication and t.
Book Synopsis Elliptic Curves and Modular Forms in Algebraic Topology by : Peter S. Landweber
Download or read book Elliptic Curves and Modular Forms in Algebraic Topology written by Peter S. Landweber and published by . This book was released on 2014-01-15 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Elliptic Curves, Modular Forms, and Fermat's Last Theorem by : John Henry Coates
Download or read book Elliptic Curves, Modular Forms, and Fermat's Last Theorem written by John Henry Coates and published by . This book was released on 1997 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Many problems in number theory have simple statements, but their solutions require a deep understanding of algebra, algebraic geometry, complex analysis, group representations, or a combination of all four. This book is an introduction to some of these problems.
Book Synopsis Elliptic Curves, Modular Forms, and Their L-functions by : Alvaro Lozano-Robledo
Download or read book Elliptic Curves, Modular Forms, and Their L-functions written by Alvaro Lozano-Robledo and published by American Mathematical Soc.. This book was released on with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many problems in number theory have simple statements, but their solutions require a deep understanding of algebra, algebraic geometry, complex analysis, group representations, or a combination of all four. This book is an introduction to some of these problems.
