… Hence the number of isomorphism classes of superspecial genus 2 curves over 𝑘 is given
… (𝑝, 1) is the number of isomorphism classes of supersingular elliptic curves over 𝑘, see [23, …

Let L be a number field and let E∕ L be an elliptic curve with potentially supersingular reduction
at a prime ideal℘ of L above a rational prime p. In this article we describe a formula for …

… Next we define an action of the ring class group, Cl(O) on the set of isomorphism classes
of elliptic curves defined over C with complex multiplication by O, which we call ELLC(O), and …

… for the supersingular elliptic curves in characteristic 3, … isomorphism classes of elliptic curves
in terms of endomorphism rings structure. A more refined analysis of the supersingular case …

… Among all curves Er,s, parameterized by coefficients (r, s) ∈ 3, we study… isomorphism classes
which are represented and, finally, the number of curves lying in a given isomorphism class…

… elliptic curve is supersingular when ϵ = 1 or when p ≡ 3 (mod 4). These distinguished
isomorphism classes of elliptic curves … isomorphism classes when we consider them as elliptic …

… supersingular elliptic curves. In Section 7, we discuss Schoof’s original algorithm for point-counting
on elliptic curves. … Firstly, all isomorphism classes of supersingular elliptic curves …

… −p] on the set of isomorphism classes of supersingular elliptic curves defined over Fp.
This is the basic mathematical structure underlying the CSIDH isogeny-based cryptosystem. …

… 2 -isomorphism class [ E ] of supersingular elliptic curves defined … and ϕ 2 are equivalent if
there exist isomorphisms ρ 1 : E 1 → E … Then an edge in the graph is an equivalent class of ℓ-…

… is supersingular, there are up to isomorphism … isomorphism classes of elliptic curves which
are isogenous to E. We say that two vertices are adjacent if the corresponding elliptic curves …