Define q congruent e^(2π i τ) (cf. the usual nome), where τ is in the upper half-plane. Then the modular discriminant is defined by Δ(τ) congruent (2π)^12 q product_(r = 1)^∞ (1 - q^r)^24. However, some care is needed as some authors omit the factor of (2π)^12 when defining the discriminant. If g_2(ω_1, ω_2) and g_3(ω_1, ω_2) are the elliptic invariants of a Weierstrass elliptic function ℘(z|ω_1, ω_2) = ℘(z;g_2, g_3) with periods ω_1 and ω_2, then the discriminant is defined by Δ(ω_1, ω_2) = g_2^3 - 27g_3^2.

Dedekind eta function | elliptic invariants | Klein's absolute invariant | nome | tau function | Weierstrass elliptic function