The idea of degree is a fundamental concept, which will take us several chapters to explore in depth. We begin by explaining what an algebraic curve is, and offer two different definitions of the degree of an algebraic curve. Our job in the next few chapters will be to show that these two different definitions, suitably interpreted, agree.
During our journey of discovery, we will often use elliptic curves as typical examples of algebraic curves. Often, we’ll use y2 = x3 − x or y2 = x3 + 3x as our examples.
In this chapter, we will begin exploring the concept of the degree of an algebraic ...