The Signs in Elliptic Nets

TL;DR

This paper generalizes a theorem about the signs in elliptic divisibility sequences to elliptic nets and explores their distribution and generation methods based on elliptic curve point denominators.

Contribution

It extends Silverman and Stephens' theorem to elliptic nets and applies it to analyze sign distribution and generate nets from elliptic curve point denominators.

Findings

Generalized sign theorem to elliptic nets

Described applications in sign distribution analysis

Presented methods to generate elliptic nets from elliptic curve points

Abstract

We give a generalization of a theorem of Silverman and Stephens regarding the signs in an elliptic divisibility sequence to the case of an elliptic net. We also describe applications of this theorem in the study of the distribution of the signs in elliptic nets and generating elliptic nets using the denominators of the linear combination of points on elliptic curves.