Recently Thorsten Kleinjung and Benjamin Wesolowski published https://arxiv.org/abs/1906.10668 There is the definition of an elliptic curve model of a finite field extension:

Definition 2.1 (Elliptic curve model). Consider a prime power $q$ and an integer $n > 1$. Suppose there is an ordinary elliptic curve $E$ defined over $\mathbb F_q$, a rational point $Q\in E(\mathbb F_q)$ and an irreducible divisor $I$ of degree $n$ over $\mathbb F_q$ such that for any $f\in \mathbb F_q(E)$, one has $f\circ \phi_q\equiv f\circ \tau_Q \mod I$, where $\phi_q$ is the q-Frobenius and $\tau_Q$ is the translation by $Q$. Then, $\mathbb F_q[I]\cong \mathbb F_{q^n}$, and we call $(E,Q,I)$ a $(q,n)$-elliptic curve model of the field $\mathbb F_{q^n}$.

Tell me what is the meaning of maps equivalence modulo divisor, please. And in what book can I find the detailed presentation of the topic. Thanks.