Halving formulae for points on elliptic curves

TL;DR

This paper derives explicit halving formulas for points on elliptic curves over complex numbers, enabling the computation of points Q such that 2Q equals a given point P.

Contribution

It provides new explicit formulas for halving points on elliptic curves of specific forms over complex numbers.

Findings

Explicit formulas for halving points on elliptic curves of given forms

Applicable to elliptic curves over complex numbers

Enhances computational methods for elliptic curve points

Abstract

Let $P$ be an arbitrary point on an elliptic curve over the complex numbers of the form $y^2=x^3+a_4\,x+a_6$ or of the form $y^2=x^3+a_2\,x^2+a_4\,x$. We provide explicit formulae to compute the points $P/2$, i.e., the points $Q$ such that $2*Q=P$.