
| reface to the second editionreface to the fit editionacknowledgments to the second editionacknowledgments to the fit editionintroduction to rational oints on lane curves i rational lines in the rojective lane 2 rational oints on conics 3 ythagoras, diohantus, and fermat 4 rational cubics and mordeli’s theorem 5 the grou law on cubic curves and ellitic curves 6 rational oints on rational curves. faltings and the mordellconjecture 7 real and comlex oints on euiticcurves 8 the ellitic cu~e. grou law on the inteection of two quadricsin rojective.three sace1 elementary roerties of the chord-tangent grou law on a cubiccurve2 lane algebraic curves 3 ellitic curves and their isomorhisms4 families of ellitic curves and geometric roertiesof toionoints5 reduction mod and toion oints6 roof of mordell’s finite generation theorem.7 galois cohomology and isomorhism classification of elliticcurves over arbitrary fields8 descent and galois cohomology9 ellitic and hyergeometric functio10 theta functio11 modular functio.12 endomorhisms of ellitic curves13 ellitic curves over finite fields14 ellitic curves over local fields15 ellitic curves over global fields and e-adic reresentatio 16 l.function of an,ellitic curve and its analytic continuation 17 remarks on the birch and swinnerton-dyer conjecture18 remarks on the modular ellitic curves conjecture and fermat’slast theorem19 higher dimeional analogs of ellitic curves: calabi-yauvarieties20 families of ellitic curvesaendixreferenceslist of notationindex |
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