An elliptic function can be characterized by its real and imaginary half-periods ω_1 and ω_2, sometimes also denoted (ω, ω'). The Wolfram Language command WeierstrassHalfPeriods[{g2, g3}] gives the half-periods ω and ω' corresponding to the invariants g_2 and g_3 for a Weierstrass elliptic function. The notation ω_3 congruent - ω_1 - ω_2 is sometimes also defined, although Abramowitz and Stegun instead use the definition ω_3 congruent ω_2 - ω_1.

elliptic invariants | half-period ratio | ω_2 constant | Weierstrass elliptic function