Rational torsion in elliptic curves and the cuspidal subgroup
classification
🧮 math.NT
math.AG
keywords
cuspidalellipticorderrationalsubgrouptorsionconductorcurve
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Let $A$ 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 $J_0(N)$.
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