= A complex lattice is determined by its fourth and sixth Eisenstein sums
{title2=$G_4(\Lambda)=G_4(\Lambda'),\ G_6(\Lambda)=G_6(\Lambda')\Rightarrow\Lambda=\Lambda'$}
Equal sums give equal <Klein j-invariants>, hence the <complex lattices> are homothetic. If both sums are nonzero, the scaling factor obeys $a^4=a^6=1$ and is $\pm1$. If only $G_6$ vanishes, the lattice is homothetic to the square lattice and the possible fourth roots of unity already preserve it. If only $G_4$ vanishes, it is homothetic to the hexagonal lattice and the possible sixth roots of unity preserve it. The two sums cannot vanish together because the elliptic discriminant is nonzero.
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