%0 Journal Article %T Average Frobenius distribution for the degree two primes of a number field %A Kevin James %A Ethan Smith %J Mathematics %D 2011 %I arXiv %R 10.1017/S0305004112000631 %X 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 two prime ideals of $K$ with trace of Frobenius equal to $r$. Under certain restrictions on $K$, we show that "on average" the number of such prime ideals with norm less than or equal to $x$ satisfies an asymptotic identity that is in accordance with standard heuristics. This work is related to the classical Lang-Trotter conjecture and extends the work of several authors. %U http://arxiv.org/abs/1109.4007v2