Rational torsion in elliptic curves and the cuspidal subgroup

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/172674Let $A$ be an elliptic curve over $\Q$ of square free conductor $N$. We prove that if $A$ has a rational torsion point of prime order $r$ such that $r$ does not divide $6N$, then $r$ divides the order of the cuspidal subgroup of $J_0(N)$.Number TheoryAlgebraic Geometry11G05; 14G99Rational torsion in elliptic curves and the cuspidal subgrouptext