Isogeny classes are sets of elliptic curves that are related to each other through isogenies, which are non-constant morphisms that preserve the group structure of the curves. Each isogeny class contains curves that share the same number of points over a given finite field, highlighting deep connections in their algebraic structure. This concept plays a crucial role in understanding how elliptic curves can be transformed into one another while maintaining essential properties, and it connects to both the group laws on elliptic curves and the endomorphism algebras associated with these curves.
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