We will give an introduction to the basic objects involved in the MTT conjecture; namely, we will discuss p-adic L-functions L_p(E, s) and important invariants of elliptic curves E over the rationals. Under certain assumptions on the prime p and curve E, the p-adic L-function satisfies L_p(E, 1) = 0. We will state the MTT conjecture, which is a formula for the value of the derivative at s = 1.