Neville's primitive elliptic functions: the case ${\mathbf{g}}_{\mathbf{3}}=\mathbf{0}$

The vanishing of the invariant $g_3$ attached to a lattice $\mathrm{\Lambda }$ singles out a midpoint lattice and yields a square-root of the associated Weierstrass function ${\mathrm{\wp }}_{\mathrm{\Lambda }}$.