On the points of order 3 of the period parallelogram of the Weierstrass elliptic function

Abstract

We examine the significance of the values of the Weierstrass ℘ function at the points of order three in the period parallelogram. Based upon the well-known duplication formulae and the differential equation of the Weierstrass ℘ function, we derive a set of identities involving the values of ℘ at these points.