Summary:

- overview of the formula of the BSD Conjecture
- definition of elliptic curve
- domain of an elliptic curve. Prerequisite: field
- elliptic curve group. Prerequisite: group
- Mordell's theorem lets us define the rank of an elliptic curve over the rational numbers, which is the $r$. Prerequisite: generating set of a group
- reduction of an elliptic curve from $E(Q)$ to $E(F_{p})modp$ lets us define $N_{r}$ as the number of elements of the generated finite group