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What is Elliptic Curve? What do elliptic curves look like? Basically it is plan algebraic curve that describes a type of cubic curve with two variables. Does this sound hard? Well it is actually the most powerful yet least understood type of curve.

Well this course will let you know all about Elliptic Curves. The main purpose is to prove Mazur’s theorem. You will also know about abelian varieties, moduli of elliptic curves.

### Assessment

This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.

### Certification

Edukite courses are free to study. To successfully complete a course you must submit all the assignment of the course as part of the assessment. Upon successful completion of a course, you can choose to make your achievement formal by obtaining your Certificate at a cost of £49.

Having an Official Edukite Certification is a great way to celebrate and share your success. You can:

• Show it to prove your success

Course Credit: Open Michigan

### Course Curriculum

 Module: 01 Math 679 / Lecture 1: Overview 00:48:00 Math 679 / Lecture 1: Overview 00:00:00 Math 679 / Lecture 2: Elliptic curves 01:17:00 Math 679 / Lecture 2: Elliptic curves 01:17:00 Math 679 / Lecture 3: Abelian varieties (analytic theory) 01:21:00 Math 679 / Lecture 3: Abelian varieties (analytic theory) 01:20:00 Module: 02 Math 679 / Lecture 4: Abelian varieties (algebraic theory) 01:18:00 Math 679 / Lecture 4: Abelian varieties (algebraic theory) 01:27:00 Math 679 / Lecture 5: Group schemes 1 01:21:00 Lecture 05: Group schemes 1 01:22:00 Math 679 / Lecture 6: Group schemes 2 01:18:00 Math 679 / Lecture 6: Group schemes 2 01:27:00 Math 679 / Lecture 7: Raynaud’s theorem 00:00:00 Module: 03 Math 679 / Lecture 8: Elliptic curves over DVRs 01:14:00 Math 679 / Lecture 8: Elliptic curves over DVRs 01:14:00 Math 679 / Lecture 9: Néron models 01:12:00 Math 679 / Lecture 9: Néron models 01:12:00 Math 679 / Lecture 10: Jacobians 01:17:00 Math 679 / Lecture 10: Jacobians 01:17:00 Module: 04 Math 679 / Lecture 11: Criterion for rank 0 00:00:00 Math 679 / Lecture 11: Criterion for rank 0 01:11:00 Math 679 / Lecture 12: Modular curves over C 01:06:00 Math 679 / Lecture 12: Modular curves over C 01:06:00 Math 679 / Lecture 13: Modular forms 01:21:00 Lecture 13: Modular forms 01:21:00 Math 670 / Lecture 15: Modular curves over Z 01:08:00 Math 679 / Lecture 17: Eichler–Shimura 01:17:00 Module: 05 Math 679 / Lecture 18: Criterion for non-existence of torsion points 01:11:00 Math 679 / Lecture 19: J_0(N) mod N 01:19:00 Math 679 / Lecture 20: Proof of Mazur’s theorem (part 1) 01:10:00 Math 679 / Lecture 21: Proof of Mazur’s theorem (part 2) 01:22:00 Math 679 / Lecture 22: 13 torsion 01:12:00 Math 679 / Lecture 23: Finishing up 00:52:00 Assessment Submit Your Assignment 00:00:00 Certification 00:00:00

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