In mathematics, and in particular the study of Weierstrass elliptic functions, the equianharmonic case occurs when the Weierstrass invariants satisfy g2=0 and g3=1. This page follows the terminology of Abramowitz and Stegun; see also the lemniscatic case. (These are special examples of complex multiplication.)

In the equianharmonic case, the minimal half period 2 is real and equal to

is the Gamma function. The half period is

Here the period lattice is a real multiple of the Eisenstein integers.

The constantss e1, e2 and e3 are given by

The case g2 = 0, g3 = a may be handled by a scaling transformation.

References