Half-period values of the Weierstrass elliptic function ($e_1,e_2,e_3$)

At the three nonzero two-torsion points $z_i$ of $\mathbb{C}/\Lambda$, put $e_i=\wp (z_i)$. The values are distinct because $\wp (z)=\wp (w)$ exactly when $z\equiv \pm w(\mathrm{mod}\Lambda )$.

A two-torsion point satisfies $2z\in \Lambda$. The three nonzero classes are represented by half-periods $\lambda /2$, $\mu /2$, and $(\lambda +\mu )/2$.