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Elliptic Functions An Elementary Text Book for Students of Mathematics
This note explains the following topics: Elliptic Integrals, Elliptic Functions, Periodicity of the Functions, Landen’s Transformation, Complete Functions, Development of Elliptic Functions into Factors, Elliptic Integrals of the Second Order, Numerical Calculations.
Author(s): Arthur L. Bake
147 Pages 
Elliptic Curves An Introduction
This note describes the following topics: Solving cubic equations in two variables, Group law on the cubic curve, Theta functions, Rank two vector bundles on elliptic curves.
Author(s): University of Limerick
99 Pages
Elliptic Curves by Zhiyuan Bai
This note covers fermats method of infinite descent, Some remarks on algebraic curves, Weierstrass equations, The group law, Isogeny, The invariant differential, Elliptic curves over finite fields, Formal groups, Elliptic curves over local fields, Elliptic curves over number fields, Kummer theory, Mordell weil theorem, Heights, Dual isogenies and weil pairing, Galois cohomology, Descent by cyclic isogeny.
Author(s): Zhiyuan Bai
41 Pages
Elliptic Curve Cryptography by Abhijit Das
This note explains the following topics: Arithmetic of Elliptic Curves, Classical Elliptic-Curve Cryptography, Efficient Implementation, Introduction to Pairing, Pairing-Based Cryptography, Sample Application—ECDSA Batch Verification.
Author(s): Abhijit Das
137 Pages
Elliptic Curve Cryptography by Christian Wuthrich
Elliptic-curve cryptography is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields.
Author(s): Christian Wuthrich
98 Pages