Weierstrass points of modular curves at cusps
Volume 202 / 2022
Acta Arithmetica 202 (2022), 173-183
MSC: Primary 14H55.
DOI: 10.4064/aa201213-3-8
Published online: 31 January 2022
Abstract
We prove that all non-exact cusps on $X_1(N)$ of genus $\geq 2$ are Weierstrass points except for $X_1(18)$. Also, for any positive integer $N$ of the form $p^2M$ with a prime $p$ and a positive integer $M$, we obtain some results on when the cusps of $X_0(N)$ equivalent to $\bigl (\begin {smallmatrix} 1\\p \end {smallmatrix}\bigr )$ are Weierstrass points.
