= Nonvanishing discriminant of a complex lattice
{title2=$g_2^3-27g_3^2=16\prod_{i<j}(e_i-e_j)^2\ne0$}
The three nonzero half-period classes make the odd derivative of the <Weierstrass elliptic function> vanish. Their values are distinct: two equal values would force at least four zeros for a function with only one double pole. Thus they are three distinct roots of $4X^3-g_2X-g_3$, whose monic discriminant gives the displayed factor. This lattice discriminant differs by $(2\pi)^{12}$ from the normalized <modular discriminant> for the lattice $\mathbb Z+\mathbb Z\tau$.
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