Let d≥1 be fixed. Let F be a number field of degree d, and let E/F be an elliptic curve. Let E(F)
tors be the torsion subgroup of E(F). In 1996, Merel proved the uniform boundedness …

… Let p be an odd prime number, and E an elliptic curve defined over a number field. Suppose
that E has good reduction at any prime lying above p, and has supersingular reduction at …

… So far we have restricted the discussion to non-supersingular elliptic curves. However,
supersingular curves may also … We consider the case of supersingular curves over F2m, m odd. …

… Let E/K be an elliptic curve with additive reduction. … curve E/K has potentially good
supersingular reduction. We also analyze the possible reduction types of two isogenous elliptic …

… , a new multiparty protocol that generates supersingular elliptic curves defined over \(\mathbb …
secure curve returned by CSIDH-SCG to generate a random supersingular elliptic curve of …

The Main Conjecture of Iwasawa theory for an elliptic curve is a prime of supersingular
reduction. The foundational study of supersingular main conjectures carried out by Perrin-Riou, …

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 …

… Cryptographic algorithms built on isogenies between supersingular elliptic curves have, for
… theory of supersingular curves and utilize walks on a specific supersingular isogeny graph. …

… that new families of elliptic curves are modular. Consider a … its applicability to the study of
elliptic curves is worked out. The … and their connection to the study of elliptic curves over Q. …

… In this note, we shall work on the supersingular elliptic curves with j -invariants … elliptic curve
defined over F p 2 . Consequently, we may and will assume the supersingular elliptic curve …