Opposing Average Congruence Class Biases in the Cyclicity and Koblitz Conjectures for Elliptic Curves

Sung Min Lee, Jacob Mayle, Tian Wang

The cyclicity and Koblitz conjectures ask about the distribution of primes of cyclic and prime-order reduction, respectively, for elliptic curves over $\mathbb{Q}$. In 1976, Serre…