William Arthur Stein

Explicit Approaches to Modular Abelian Varieties

PSfrag replacements

2 3

243A: y^{2} + y = x^{3} − 1 243B: y^{2} + y = x^{3} + 2

243C: dimension 2 243D: dimension 2 243E: dimension 3 243F: dimension 3

images of 81A: dimension 4

images of 27A (y^{2} + y = x^{3} − 7): dimension 3

A dissertation submitted in partial satisfaction of the requirements for the degree of

Doctor of Philosophy in Mathematics

Commitee in charge: Professor H. W. Lenstra Professor B. Poonen Professor B. Yu

Spring 2000

University of California, Berkeley