## Math 997 Topics in Number Theory: Elliptic Curves

### Spring 2008

1:05 PM TR in 122 Cardwell Hall

Course Information ----- Homework ----- Lecture Notes

## Course Information

Instructor: Jennifer Paulhus

Office Hours: By appointment

Office: 125 Cardwell Hall

e-mail: paulhus [at] math [dot] ksu [dot] edu

web site: www.math.ksu.edu/~paulhus/ma997ec.html

Recommended Text: *The Arithmetic of Elliptic Curves*, Silverman

On Reserve:

*Commutative algebra with a view toward algebraic geometry*, Eisenbud

*Algebraic Geometry*, Hartshorne

*Intro to Elliptic Curves and Modular Forms*, Koblitz

*Algebraic Curves and Riemann Surfaces*, Miranda

## Homework

Below will be posted any homework problems I recommend during the lectures.

- Lecture 2: Exercise 1.12
- Lecture 5: Prove Proposition 2 in the notes (in particular Exercise 2.2).
- Lecture 5: Convince yourself of Example II.3.3 (in particular the poles at infinity).
- Lecture 8: Exercise 3.5
- Lecture 11: Exercise 3.13
- Lecture 14: Exercise 5.5
- Lecture 18: Exercise 6.2
- Lecture 25: Exercise 8.4
- Lecture 27: Show that the height on
**P**^N(K) agrees with the height function we defined when K=**Q**.
- Lecture 29: Prove rk(E(
**Q**)+rk(E^(d)(**Q**))=rk(E(**Q**(\sqrt(d))).

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## Lecture Notes

If you were a student in this class and you would like a copy of the notes, please e-mail me. My primary source for these notes was Silverman's *Arithmetic of Elliptic Curves*.

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