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

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 $p$.