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

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