Noam Elkies (Harvard) and Matthew Greenberg (University of Calgary): Mod p representations associated to elliptic curves
Background reading:
Silverman, "The arithmetic of elliptic curves", Chapters 3 and 7
Diamond and Shurman, "A first course in modular forms, Chapter 9
Neukirch, "Algebraic number theory", Chapter 2, Section 10 and Chapter 5, Section 6
Ribet and Stein, "Lectures on Serre's conjecture", Chapter 1