000			03104nam a2200385 i 4500
001			19978
005			20260309164435.0
008			920210s1992 nyua b 001 0 eng
010			_a92004669
020			_a0387978259 _qSpringer-Verlag New York
020			_a9780387978253 _qSpringer-Verlag New York
020			_a3540978259 _qSpringer-Verlag Berlin
020			_a9783540978251 _qSpringer-Verlag Berlin
040			_aDLC _beng _cDLC _dFPU _dMUQ _dBAKER _dNLGGC _dBTCTA _dYDXCP _dOCLCG _dGBVCP _dZWZ _dOCLCQ _dNMC _dBDX _dOCLCO _dOCLCF _dBAUN
041	0		_aeng
049			_aBAUN_MERKEZ
050	0	4	_aQA567.2.E44 _bS55 1992
100	1		_aSilverman, Joseph H., _d1955- _978636 _eaut
245	1	0	_aRational points on elliptic curves / _cJoseph H. Silverman, John Tate.
264		1	_aNew York : _bSpringer-Verlag, _c[1992]
264		4	_c©1992
300			_ax, 281 pages : _billustrations ; _c24 cm.
336			_atext _btxt _2rdacontent
337			_aunmediated _bn _2rdamedia
338			_avolume _bnc _2rdacarrier
490	0		_aUndergraduate texts in mathematics
504			_aIncludes bibliographical references (pages [259]-262) and index.
505	0	0	_tCh. I. Geometry and Arithmetic _t-- 1. Rational Points on Conics _t-- 2. The Geometry of Cubic Curves _t-- 3. Weierstrass Normal Form _t-- 4. Explicit Formulas for the Group Law _t-- Ch. II. Points of Finite Order _t-- 1. Points of Order Two and Three _t-- 2. Real and Complex Points on Cubic Curves _t-- 3. The Discriminant _t-- 4. Points of Finite Order Have Integer Coordinates _t-- 5. The Nagell-Lutz Theorem and Further Developments _t-- Ch. III. The Group of Rational Points _t-- 1. Heights and Descent _t-- 2. The Height of P + P[subscript 0] _t-- 3. The Height of 2P _t-- 4. A Useful Homomorphism _t-- 5. Mordell's Theorem _t-- 6. Examples and Further Developments _t-- 7. Singular Cubic Curves _t-- Ch. IV. Cubic Curves over Finite Fields _t-- 1. Rational Points over Finite Fields _t-- 2. A Theorem of Gauss _t-- 3. Points of Finite Order Revisited _t-- 4. A Factorization Algorithm Using Elliptic Curves _t-- Ch. V. Integer Points on Cubic Curves _t-- 1. How Many Integer Points? _t-- 2. Taxicabs and Sums of Two Cubes _t-- 3. Thue's Theorem and Diophantine Approximation _t-- 4. Construction of an Auxiliary Polynomial _t-- 5. The Auxiliary Polynomial Is Small _t-- 6. The Auxiliary Polynomial Does Not Vanish _t-- 7. Proof of the Diophantine Approximation Theorem _t-- 8. Further Developments _t-- Ch. VI. Complex Multiplication _t-- 1. Abelian Extensions of Q _t-- 2. Algebraic Points on Cubic Curves _t-- 3. A Galois Representation _t-- 4. Complex Multiplication _t-- 5. Abelian Extensions of Q(i). Appendix A: Projective Geometry _t-- 1. Homogeneous Coordinates and the Projective Plane _t-- 2. Curves in the Projective Plane _t-- 3. Intersections of Projective Curves _t-- 4. Intersection Multiplicities and a Proof of Bezout's Theorem _t-- 5. Reduction Modulo pages.
650		0	_aCurves, Elliptic. _916659
650		0	_aRational points (Geometry)
650		0	_aDiophantine analysis.
700	1		_aTate, John Torrence, _d1925- _eaut
900			_bsatın
942			_2lcc _cKT
999			_c16838 _d16838