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)]:
![M([\Gamma(1)]) = \mathrm{Spec}(R[j]) \,](/2012-wikipedia_en_all_nopic_01_2012/I/96b27d42ddf4491d6f2ee0396e0b1249.png)
with the j-invariant normalized a la Tate; j = 0 has complex multiplication by Z[ζ3], and j = 1728 by Z[i].