Rational torsion in elliptic curves and the cuspidal subgroup
نویسنده
چکیده
Let A be an elliptic curve over Q of square free conductor N . Suppose A has a rational torsion point of prime order r such that r does not divide 6N . We prove that then r divides the order of the cuspidal subgroup C of J0(N). If A is optimal, then viewing A as an abelian subvariety of J0(N), our proof shows more precisely that r divides the order of A ∩ C. Also, under the hypotheses above, we show that for some prime p that divides N , the eigenvalue of the Atkin-Lehner involution Wp acting on the newform associated to A is −1.
منابع مشابه
Rational torsion in optimal elliptic curves and the cuspidal subgroup
LetN be a square free integer, and let A be an optimal elliptic curve over Q of 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 J0(N).
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تاریخ انتشار 2007