INSTITUTE OF APPLIED MATHEMATICS
Last Updated:
28/08/2017 - 21:10

IAM601 - Elliptic Curves

Credit: 3(3-0); ECTS: 8.0
Instructor(s): Consent of IAM
Prerequisites: Consent of Instructor(s)

Course Catalogue Description

The Geometry of Elliptic Curves: Weirstrass equations, The group law, j-invariants, Isogenies, The dual isogeny, The Tate module, The Weil pairing. The Formal Group of an Elliptic Curve: Expansion around 0, Formal groups, Groups associated to formal groups, The invariant differential, The formal logarithm, Formal Groups over discrete valuation rings. Elliptic Curves over Finite Fields: Number of rational points, The Weil conjectures, The Endomorphism rings, Calculating Hasse invariant.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

The Geometry of Elliptic Curves: Weirstrass equations, The group law, j-invariants, Isogenies, The dual isogeny, The Tate module, The Weil pairing. The Formal Group of an Elliptic Curve: Expansion around 0, Formal groups, Groups associated to formal groups, The invariant differential, The formal logarithm, Formal Groups over discrete valuation rings. Elliptic Curves over Finite Fields: Number of rational points, The Weil conjectures, The Endomorphism rings, Calculating Hasse invariant.

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