Abstract
We prove that the number of elliptic curves E/ℚ with conductorN isO(N 1/2+e). More generally, we prove that the number of elliptic curves E/ℚ with good reduction outsideS isO(M 1/2+e), whereM is the product of the primes inS. Assuming various standard conjectures, we show that this bound can be improved toO(M c/loglogM ).
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