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Let $K$ be a number field and $r$ an integer. Given an elliptic curve $E$,defined over $K$, we consider the problem of counting the number of degree twoprime ideals of $K$ with trace of Frobenius equal to $r$. Under certainrestrictions on $K$, we show that "on average" the number of such prime idealswith norm less than or equal to $x$ satisfies an asymptotic identity that is inaccordance with standard heuristics. This work is related to the classicalLang-Trotter conjecture and extends the work of several authors.

Average Frobenius distribution for the degree two primes of a number field