Formulae for null curves deriving from elliptic curves

Any elliptic curve can be realised in the tangent bundle of the complex projective line as a double cover branched at four distinct points on the zero section. Such a curve generates, via classical osculation duality, a null curve in C³${\mathbb{C}}^3$ and thus an algebraic minimal surface in R³${\mathbb{R}}^3$. We derive simple formulae for the coordinate functions of such a null curve.