Math 997 Topics in Number Theory: Elliptic Curves
1:05 PM TR in 122 Cardwell Hall
Course Information ----- Homework ----- Lecture Notes
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
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
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))).
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.