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Contents

1Fermat’s Method of Infinite Descent
1.1A variant for polynomials
2Some Remarks on Plane Curves
2.1The degree of a morphism
3Weierstrass Equations
4The Group Law
5Isogenies
6The Invariant Differential
7Elliptic Curves over Finite Fields
7.1Zeta functions
8Formal Groups
9Elliptic Curves over Local Fields
10Elliptic Curves over Number Fields: The torsion subgroup
11Kummer Theory
12Elliptic Curves over Number Fields: The weak Mordell-Weil Theorem
13Heights
14Dual isogenies and the Weil pairing
15Galois Cohomology
16Descent by Cyclic Isogeny
16.1Descent by 2-isogeny
16.2Birch Swinnerton Dyer Conjecture
Index

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