Halving formulae for points on elliptic curves

2023/02/01 by Halbeisen, Lorenz, Hungerbuehler, Norbert
#11G05 94A60 11R16 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2302.00568

Abstract

Let P be an arbitrary point on an elliptic curve over the complex numbers of the form y²=x³+a₄ x+a₆ or of the form y²=x³+a₂ x²+a₄ x. We provide explicit formulae to compute the points P/2, i.e., the points Q such that 2*Q=P.

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