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 C-3 and thus an algebraic minimal surface in R-3. We derive simple formulae for the coordinate functions of such a null curve. (c) 2008 Elsevier B.V. All rights reserved.