Semi-Magic Squares and Elliptic Curves

TL;DR

This paper demonstrates a novel geometric arrangement of torsion points on elliptic curves in an N by N grid, where each row and column sums to the identity, revealing new structural insights.

Contribution

It introduces a new connection between elliptic curve torsion points and combinatorial grid arrangements for all odd natural numbers N.

Findings

For all odd N, torsion points can be arranged in an N x N grid with row and column sums equal to the identity.

Establishes a link between elliptic curve theory and combinatorial grid configurations.

Provides a constructive method for such arrangements for all odd N.

Abstract

We show that, for all odd natural numbers $N$, the $N$-torsion points on an elliptic curve may be placed in an $N \times N$ grid such that the sum of each column and each row is the point at infinity.