The Birch and Swinnerton Dyer Conjecture The Birch and Swinnerton Dyer conjecture is a conjecture about the relationship between the zeta function of an elliptic curve and the behavior of the points on that curve An elliptic curve is a type of curve that has many interesting mathematical properties The Birch and Swinnerton Dyer conjecture states that if the zeta function of an elliptic curve has a zero at a particular point then there are infinitely many points on that curve that have that same number as their x coordinate