Elliptic equation
In mathematics, an elliptic curve (EC) is a smooth, projective algebraic curve of genus one, on which there is a specified point O. An elliptic curve is in fact an abelian variety – that is, it has a ...
Elliptic equation - Wikipedia
Birch and Swinnerton-Dyer conjecture
In mathematics, the Birch and Swinnerton-Dyer conjecture is an open problem in the field of number theory. It is widely recognized as one of the most challenging mathematical problems; the conjecture ...
Modularity theorem
In mathematics, the modularity theorem (formerly called the Taniyama–Shimura–Weil conjecture and several related names) states that elliptic curves over the field of rational numbers are related to m...
Modularity theorem - Wikipedia
Isogeny
In mathematics, an isogeny is a morphism of algebraic groups that is surjective and has a finite kernel.If the groups are abelian varieties, then any morphism f : A → B of the unde...
Arithmetic of abelian varieties
In mathematics, the arithmetic of abelian varieties is the study of the number theory of an abelian variety, or family of those. It goes back to the studies of Fermat on what are now recognised as ell...