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Elliptic Curves by Pete L. Clark
An elliptic curve is an object defined over a ground field K. This PDF covers the following topics related to Elliptic Curves : What is an elliptic curve?, Mordell-Weil Groups, Background on Algebraic Varieties, The Riemann-Roch Express, Weierstrass Cubics, The l-adic Tate module, Elliptic Curves Over Finite Fields, The Mordell-Weil Theorem I: Overview, The Mordell-Weil Theorem II: Weak Mordell-Wei, The Mordell-Weil Theorem III: Height Functions, The Mordell-Weil Theorem IV: The Height Descent Theorem, The Mordell-Weil Theorem V: Finale, More On Heights, Diophantine Approximation, Siegel’s Theorems on Integral Points.
Author(s): Pete L. Clark
90 Pages 
Lectures on Moduli Spaces of Elliptic Curves
The goal of these notes is to introduce orbifolds and stacks through the example of elliptic curves. This note contains below topics, Elliptic Curves and the Moduli Problem, Families of Elliptic Curves and the Universal Curve, The Orbifold and Modular Forms.
Author(s): Richard Hain
80 Pages
Park City lectures on elliptic curves over function fields
This note contains below topics, Background on curves and function fields, Elliptic curves over function fields, Surfaces and the Tate conjecture.
Author(s): Douglas Ulmer
72 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 EllipticCurve Cryptography, Efficient Implementation, Introduction to Pairing, PairingBased Cryptography, Sample ApplicationECDSA Batch Verification.
Author(s): Abhijit Das
137 Pages
Elliptic Functions An Elementary Text Book for Students of Mathematics
This note explains the following topics, Elliptic Integrals, Elliptic Functions, Periodicity of the Functions, Landens 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 Curve Cryptography by Christian Wuthrich
Ellipticcurve cryptography is an approach to publickey cryptography based on the algebraic structure of elliptic curves over finite fields.
Author(s): Christian Wuthrich
98 Pages
The elliptic modular functions associated with the elliptic norm curve E7
This note covers the following topics, The Groups Connected With E7, The Quadrigs On E7, The Interpretation Of The Forms F and F2, The Loci In S3.
Author(s): Roscoe Woods
106 Pages
Mathematical Foundations of Elliptic Curve Cryptography
This note covers the following topics, algebraic curves, elliptic curves, elliptic curves over special fields, more on elliptic divisibility sequences and elliptic nets, elliptic curve cryptography, computational aspects, elliptic curve discrete logarithm.
Author(s): Prof. Dipl-Ing, Dr. techn. Michael Drmota
113 Pages