Elliptic curves with missing Frobenius traces · arXivDeskAbstract
Let E be an elliptic curve defined over Q. In 1976, Lang and Trotter conjectured an asymptotic formula for the number πE,r(X) of primes p≤X
of good reduction for which the Frobenius trace at
associated to
is equal to a given fixed integer
. We investigate elliptic curves
over
that have a missing Frobenius trace, i.e. for which the counting function
πE,r(X) remains bounded as
X→∞ , for some
. In particular, we classify all elliptic curves
over
that have a missing Frobenius trace.