The Manin Constant, Congruence Primes, and the Modular Degree
نویسندگان
چکیده
We obtain relations between the modular degree and congruence modulus of elliptic curves, and answer a question raised in a paper of Frey and Müller about whether or not the congruence number and modular degree of elliptic curves are always equal; they are not, but we give a conjectural relation between them. We also prove results and make conjectures about Manin constants of quotients of J1(N) of arbitrary dimension. For optimal elliptic curve, we prove that if 2 exactly divides N and the congruence number of E is odd, then the Manin constant of E is also odd.
منابع مشابه
The Modular Degree , Congruence Primes
The modular degree and congruence number are two fundamental invariants of an elliptic curve over the rational field. Frey and Müller have asked whether these invariants coincide. We find that the question has a negative answer, and show that in the counterexamples, multiplicity one (defined below) does not hold. At the same time, we prove a theorem about the relation between the two invariants...
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تاریخ انتشار 2005