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In 2009, W. D. Banks and I. E. Shparlinski studied the average densities ofprimes $p \leq x$ for which the reductions of elliptic curves of small heightmodulo $p$ satisfy certain geometric properties, namely cyclicity anddivisibility of the number of points by a fixed integer $m$. In this paper, werefine their results, restricting the primes $p$ under consideration to lie inan arithmetic progression $k \bmod{n}$. Furthermore, for a fixed modulus $n$,we investigate statistical biases among the different congruence classes $k\bmod{n}$ of primes satisfying the aforementioned properties.

On the average congruence class bias for cyclicity and divisibility of the groups of $\mathbb{F}_p$-points of elliptic curves