… computational problems for supersingular elliptic curves, their … isomorphic to the endomorphism
ring of a supersingular … algebra an isomorphism class of supersingular elliptic curves. …

… ℓ-isogeny graph is the graph whose vertex set is the isomorphism classes of supersingular
elliptic curves2 defined over F𝑝2 (labelled by the j-invariants) and two vertices are connected …

… to the number of isomorphism classes of supersingular elliptic curves over k. Let {El }1=1.2,...,h
be a set of representatives of isomorphism classes of supersingular elliptic curves. P. …

… on a supersingular elliptic curve (which is defined over Fp2 ) always have coordinates in
Fp2 . Because the j-invariant of a supersingular curve lies in Fp2 , El is isomorphic to a curve E: …

… ▶ vertices are isomorphism classes of K-oriented supersingular elliptic … EFFECTIVE CLASS
GROUP ACTIONS We consider an elliptic curve E0 with an effective endomorphism ring (eg…

… the endomorphism rings of elliptic curves. We also present the ideal class group action over
… Then there exists a unique elliptic curve E′ (up to K-isomorphism) and a unique separable …

… Note that for each D, however, there are only finitely many isomorphism classes of elliptic
curves over Qwith complex multiplication by OD. Furthermore, the j-invariants of these …

… set of isomorphism classes of supersingular elliptic curves over Fp, and for each point xi ∈
S we let Ei denote a supersingular curve representing the isomorphism class corresponding …

… From Lemma 1 it follows that the CTP curves split into two equivalence classes under the …
that there are exactly two isomorphism classes of supersingular elliptic curves over GF(p2) …

… of supersingular elliptic curves over F 2 equipped with a -isogeny to their Galois conjugate.
These curves … we can show that the isomorphism class of any Z[√− ]-oriented supersingular …