j-line

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Not to be confused with J (New York City Subway service).


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]) \,

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