The Weierstrass half‐periods can be represented through the complete elliptic integral and the inverse elliptic nome by the formula:
The Weierstrass invariants can be represented through the complete elliptic integral , the inverse elliptic nome , the modular lambda function , and the theta functions by the following formulas:
The Weierstrass function values at halfperiods can be represented through the complete elliptic integral , the modular lambda function , the Weierstrass sigma function , and the theta functions by the following formulas:
The Weierstrass zeta function values at halfperiods can be represented through the complete elliptic integrals and , the modular lambda function , and the theta functions by the following formulas:
The following formula shows that the Weierstrass half‐periods play the role of inverse functions to the Weierstrass invariants :
The Weierstrass half‐periods , the invariants , and the Weierstrass function values at halfperiods are connected by the following formulas:
