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- catalog contributor b3837339.
- catalog contributor b3837340.
- catalog created "c1992.".
- catalog date "1992".
- catalog date "c1992.".
- catalog dateCopyrighted "c1992.".
- catalog description "Ch. I. Geometry and Arithmetic -- 1. Rational Points on Conics -- 2. The Geometry of Cubic Curves -- 3. Weierstrass Normal Form -- 4. Explicit Formulas for the Group Law -- Ch. II. Points of Finite Order -- 1. Points of Order Two and Three -- 2. Real and Complex Points on Cubic Curves -- 3. The Discriminant -- 4. Points of Finite Order Have Integer Coordinates -- 5. The Nagell-Lutz Theorem and Further Developments -- Ch. III. The Group of Rational Points -- 1. Heights and Descent -- 2. The Height of P + P[subscript 0] -- 3. The Height of 2P -- 4. A Useful Homomorphism -- 5. Mordell's Theorem -- 6. Examples and Further Developments -- 7. Singular Cubic Curves -- Ch. IV. Cubic Curves over Finite Fields -- 1. Rational Points over Finite Fields -- 2. A Theorem of Gauss -- 3. Points of Finite Order Revisited -- 4. A Factorization Algorithm Using Elliptic Curves -- Ch. V. Integer Points on Cubic Curves -- 1. How Many Integer Points? -- 2. Taxicabs and Sums of Two Cubes -- 3. Thue's Theorem and Diophantine Approximation -- 4. Construction of an Auxiliary Polynomial -- 5. The Auxiliary Polynomial Is Small -- 6. The Auxiliary Polynomial Does Not Vanish -- 7. Proof of the Diophantine Approximation Theorem -- 8. Further Developments -- Ch. VI. Complex Multiplication -- 1. Abelian Extensions of Q -- 2. Algebraic Points on Cubic Curves -- 3. A Galois Representation -- 4. Complex Multiplication -- 5. Abelian Extensions of Q(i). Appendix A: Projective Geometry -- 1. Homogeneous Coordinates and the Projective Plane -- 2. Curves in the Projective Plane -- 3. Intersections of Projective Curves -- 4. Intersection Multiplicities and a Proof of Bezout's Theorem -- 5. Reduction Modulo p.".
- catalog description "Includes bibliographical references (p. [259]-262) and index.".
- catalog extent "x, 281 p. :".
- catalog hasFormat "Rational points on elliptic curves.".
- catalog identifier "0387978259 (Springer-Verlag New York)".
- catalog identifier "3540978259 (Springer-Verlag Berlin)".
- catalog isFormatOf "Rational points on elliptic curves.".
- catalog isPartOf "Undergraduate texts in mathematics".
- catalog issued "1992".
- catalog issued "c1992.".
- catalog language "eng".
- catalog publisher "New York : Springer-Verlag,".
- catalog relation "Rational points on elliptic curves.".
- catalog subject "516.3/52 20".
- catalog subject "Curves, Elliptic.".
- catalog subject "Diophantine analysis.".
- catalog subject "QA567.2.E44 S55 1992".
- catalog subject "Rational points (Geometry)".
- catalog tableOfContents "Ch. I. Geometry and Arithmetic -- 1. Rational Points on Conics -- 2. The Geometry of Cubic Curves -- 3. Weierstrass Normal Form -- 4. Explicit Formulas for the Group Law -- Ch. II. Points of Finite Order -- 1. Points of Order Two and Three -- 2. Real and Complex Points on Cubic Curves -- 3. The Discriminant -- 4. Points of Finite Order Have Integer Coordinates -- 5. The Nagell-Lutz Theorem and Further Developments -- Ch. III. The Group of Rational Points -- 1. Heights and Descent -- 2. The Height of P + P[subscript 0] -- 3. The Height of 2P -- 4. A Useful Homomorphism -- 5. Mordell's Theorem -- 6. Examples and Further Developments -- 7. Singular Cubic Curves -- Ch. IV. Cubic Curves over Finite Fields -- 1. Rational Points over Finite Fields -- 2. A Theorem of Gauss -- 3. Points of Finite Order Revisited -- 4. A Factorization Algorithm Using Elliptic Curves -- Ch. V. Integer Points on Cubic Curves -- 1. How Many Integer Points? -- 2. Taxicabs and Sums of Two Cubes -- 3. Thue's Theorem and Diophantine Approximation -- 4. Construction of an Auxiliary Polynomial -- 5. The Auxiliary Polynomial Is Small -- 6. The Auxiliary Polynomial Does Not Vanish -- 7. Proof of the Diophantine Approximation Theorem -- 8. Further Developments -- Ch. VI. Complex Multiplication -- 1. Abelian Extensions of Q -- 2. Algebraic Points on Cubic Curves -- 3. A Galois Representation -- 4. Complex Multiplication -- 5. Abelian Extensions of Q(i). Appendix A: Projective Geometry -- 1. Homogeneous Coordinates and the Projective Plane -- 2. Curves in the Projective Plane -- 3. Intersections of Projective Curves -- 4. Intersection Multiplicities and a Proof of Bezout's Theorem -- 5. Reduction Modulo p.".
- catalog title "Rational points on elliptic curves / Joseph H. Silverman, John Tate.".
- catalog type "text".