J line

In the study of the arithmetic of elliptic curves, the j-line over any ring R is the coarse moduli scheme attached to the moduli problem Γ(1)]:

with the j-invariant normalized a la Tate: j = 0 has complex multiplication by Z[ζ₃], and j = 1728 by Z[i].

The j-line can be seen as giving a coordinatization of the classical modular curve of level 1, X₀(1), which is isomorphic to the complex projective line.