Division Polynomials and Intersection of Projective Torsion Points

TL;DR

This paper explores how the images of torsion points from two elliptic curves intersect when mapped onto projective space, providing insights into their algebraic and geometric relationships.

Contribution

It introduces a novel analysis of the intersection patterns of projective torsion point images from two elliptic curves, expanding understanding of their algebraic structure.

Findings

Characterization of intersection points of projective torsion images

Conditions for finite versus infinite intersections

Connections to elliptic curve torsion subgroup structures

Abstract

Given two elliptic curves, each of which is associated with a projection map that identifies opposite elements with respect to the natural group structure, we investigate how their corresponding projective images of torsion points intersect.