{c}
{title2=2023}

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) \mod p> lets us define $N_r$ as the number of elements of the generated finite group

\Video[https://www.youtube.com/watch?v=84ig5cih4kI]


 Birch and Swinnerton-Dyer conjecture in two minutes by Ciro Santilli