The torsion order of a finitely-generated abelian group such as the Mordell-Weil group of the Jacobian of a curve over a number field is the cardinality of its torsion subgroup. The torsion primes are the primes that divide the torsion order, equivalently, the primes $\ell$ for which the Jacobian has a rational point of order $\ell$.
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