# Elliptic Curves with Large Intersection of Projective Torsion Points

## TL;DR

This paper constructs pairs of elliptic curves over number fields that share a large number of projective torsion points, highlighting new intersections in their torsion structures.

## Contribution

It introduces a method to explicitly construct elliptic curve pairs with significantly large intersections of their projective torsion points.

## Key findings

- Pairs of elliptic curves with large torsion point intersections constructed
- Demonstrates the existence of elliptic curves with unexpectedly large shared torsion structures
- Provides explicit examples over number fields

## Abstract

We construct pairs of elliptic curves over number fields with large intersection of projective torsion points.