n-torsion in the Jacobian of an m-gonal curve yields n-torsion in the class group of an associated number field K via branched covers of the projective line.
Kishi, Note on the divisibility of the class number of certain imaginary quadratic fields , Glasgow Math
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Branched covers of $\mathbb{P}^1$ and divisibility in class group
n-torsion in the Jacobian of an m-gonal curve yields n-torsion in the class group of an associated number field K via branched covers of the projective line.