VVZ API is not affiliated with ETH Zurich. Data might be outdated or incorrect. Please view the official ETHZ Vorlesungsverzeichnis for binding information.

401-3110-70L 4 Credits BSC , MSC D-MATH

Student Seminar in Number Theory: Elliptic Curves

Lecturers & Examiners: Dr. Markus Schwagenscheidt
Number of participants limited to 24.
VVZ CR n/a

Last Updated: 2026-02-05 16:14:48

Abstract

Seminar on the foundations of the theory of Elliptic Curves.

Objective

The participants learn the basics about elliptic curves, which will enable them to write a Bachelor's or Master's thesis in number theory. In addition to a talk, the writing of a short manuscript in latex will be required.

Content

We first study the basic properties of elliptic curves, such as the group law. Then we will proceed to study elliptic curves over the rationals and the question whether it has rational or integral points. One of the main goal of the seminar is the proof of the Mordell-Weil theorem, which states that the set of rational points of a rational elliptic curve is a finitely generated abelian group. Using the theory of elliptic functions we will show that an elliptic curve over the complex numbers can be viewed as a torus. As an outlook, we will sketch several deep results and conjectures about elliptic curves, such as Wiles' Modularity Theorem, which played an important role in the proof of Fermat's Last Theorem, and such as the Birch and Swinnerton-Dyer Conjecture.

Resources

Literature

Knapp: Elliptic Curves Koecher, Krieg: Elliptische Funktionen und Modulformen Milne: Elliptic Curves Silverman: The Arithmetic of Elliptic Curves Silverman, Tate: Rational Points on Elliptic Curves

General Information

Language
English
Levels
BSC , MSC

Examination

Type
ungraded semester performance

Registration & Places

Limited places (Special selection)
Signup Start
31.07.2023
Signup End
10.09.2023
Priority: Registration for the course unit is only possible for the primary target group

Course Components

Type Title Time & Place Hours
seminar Student Seminar in Number Theory: Elliptic Curves
  • Tue 14:15-16:00 (CHN D 42)
2 h weekly

Offered In

  • Mathematics Bachelor
    • Seminars (NOTICE: The number of seminar places is limited, and the special selection procedure should help to allocate the places not primarily according to the registration time. Everybody is waitlisted first when he/she tries to register for a seminar in myStudies. Moreover: Only one mathematics seminar can be chosen per semester. Notice also the course unit 401-0002-99L Generic Seminar - Second Priority / Third Priority.)
  • Mathematics Master
    • Seminars and Semester Papers
      • Seminars (NOTICE: The number of seminar places is limited, and the special selection procedure should help to allocate the places not primarily according to the registration time. Everybody is waitlisted first when he/she tries to register for a seminar in myStudies. Moreover: Only one mathematics seminar can be chosen per semester. In case you need to attend 2 seminars in this semester, please take contact with the Study Administration (email: ). Notice also the course unit 401-0002-99L Generic Seminar - Second Priority / Third Priority.)