The Moduli Space of Elliptic Curves is parametrized by a single complex number, the j-invariant. There is a space, and every point in it has a single complex number called the j-invariant. Every point represents a family (infinite members) of elliptic curves that have the same j-invariant. You might notice that this moduli space must necessarily be isomorphic to the complex plane C.
Elliptic curves are one of the most studied objects in modern mathematics. They are famously related to modular forms, were used to prove Fermat's Last Theorem and are part of the Langlands Program.
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