# Weierstrass points on $X_0^+(p)$ and supersingular $j$-invariants

## TL;DR

This paper investigates the arithmetic properties of Weierstrass points on the modular curves $X_0^+(p)$ and establishes a relationship with supersingular elliptic curve $j$-invariants in characteristic $p$, revealing new insights into their interplay.

## Contribution

It introduces a novel connection between Weierstrass points on $X_0^+(p)$ and supersingular $j$-invariants, advancing understanding of modular curve arithmetic.

## Key findings

- Weierstrass points are related to supersingular $j$-invariants.
- Established a new relationship between geometric and arithmetic properties.
- Enhanced understanding of modular curve structures in characteristic $p$.

## Abstract

We study the arithmetic properties of Weierstrass points on the modular curves $X_0^+(p)$ for primes $p$. In particular, we obtain a relationship between the Weierstrass points on $X_0^+(p)$ and the $j$-invariants of supersingular elliptic curves in characteristic $p$.