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"["ζ"3], and "j" = 1728 by "Z"["i"].
The "j"-line can be seen as giving a coordinatization of the classical modular curve of level 1, "X"0(1), which is isomorphic to the complex projective line.