… meaningful for students with a background in elliptic curves (though the relevant concepts are
… studying quaternion algebras with an eye to applications with supersingular elliptic curves, …

… unrelated quaternion algebras and el1iptic curves, We recall … definitions of a supersingular
elliptic curve E on page 32: we … use quaternion algebras to derive properties of elliptic curves…

… of the classical modular curves as moduli spaces of elliptic curves with level structure and
sheds … We provide tables of quaternion algebras and tables of Eichler orders for small ramified …

… (4.3.2)) for the situation considered here we prove that two qua.ternion algebras over a …
construction for quaternion algebras over lorally ringrd spaces by which all quaternion algebras: …

… in terms of quaternion algebras. We provide algorithms which compute an embedding of a
fixed imaginary quadratic order into a maximal order of the quaternion algebra ramified at p …

… A link between elliptic curves, isogenies, and quaternion algebras, another family of objects
inherited from number theory, was discovered by the German mathematician Max Deuring (…

… theory of a quaternion algebra. Using a … quaternion algebras and their ideal theory, and
follow in section three with a discussion of the equivalence between supersingular elliptic curves …

… quaternion algebras and their application to Shimura curves. Let A be a quaternion algebra
… X 0 ([special characters omitted]) and to find nontorsion points on some elliptic curves over …

… For certain sections, further experience with objects in arithmetic geometry, such as elliptic
curves, is useful; however, we have endeavored to present the material in a way that is …

… from a special elliptic curve E0. We construct this algorithm using a quaternion technique
and the … to a supersingular elliptic curve, the product of two supersingular elliptic curves, or a …