J-line
In the study of the arithmetic of elliptic curves, the j-line over a ring R is the coarse moduli scheme attached to the moduli problem sending a ring R {\displaystyle R} to the set of isomorphism classes of elliptic curves over R {\displaystyle R} . Since elliptic curves over the complex numbers are isomorphic (over an algebraic closure) if and only if their j {\displaystyle j} -invariants agree, the affine space A j 1 {\displaystyle \mathbb {A} _{j}^{1}} parameterizing j-invariants of elliptic curves yields a coarse moduli space.