Let E be a fixed elliptic curve defined over the rational numbers. We prove that the number of primes p ≤ x such that E has supersingular reduction mod p is greater than for any positive δ and x sufficiently large. Here log k x is defined recursively as log(log k-1 x ) and log 1 x = log x . We also establish several results related to the Lang-Trotter conjecture.
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Fouvry et al. (1996) studied this question.