… supersingular elliptic curve is a curve which is enhanced with the information of an
endomorphism. Computing the full endomorphism ring of a supersingular elliptic curve … elliptic …

… the quaternionic endomorphism rings of supersingular elliptic curves in more detail; we use
Waterhouse [Wate69, §3] as our main reference. Let E be a supersingular elliptic curve over \…

… In section two, we discuss quaternion algebras and their ideal theory, and follow in section …
equivalence between supersingular elliptic curves and certain ideals over a maximal order. In …

… between the seemingly unrelated quaternion algebras and el1iptic curves, We recall that …
of a supersingular elliptic curve E on page 32: we then ha<! that "End(E) is a maximal order in …

… We present a deterministic and explicit algorithm for the computation of the
endomorphism rings of supersingular elliptic curves. Given any prime characteristic p, the …

… both forms arise from maximal orders in the same quaternion algebra. Our work … supersingular
elliptic curves. One problem is, given a maximal order O in Bp, to compute an elliptic curve …

… In Chapter 2 we review the general theory of elliptic curves, … of supersingular curves; in it
we consider rational quaternion … with the study of supersingular curves. The main result we …

… of supersingular elliptic curves, and in this work we extend these tools to supersingular elliptic
curves … rings O(E,G) are Eichler orders of level-N in the quaternion algebra End(E) ⊗Z Q. …

… either to an order in a quaternion algebra or to an order in an imaginary … elliptic curves are
used in an isogeny-based system, we propose using supersingular curves of smooth order to …

… 1.3 Definition of a supersingular curve. As alluded to before, a supersingular elliptic curve
is one that has the maximum number of symmetries: End(E) is an order in the quaternion …