2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/109018We study modular fibers of elliptic differentials, which are roughly spaces of torus-coverings over a fixed base torus. For genus 2 torus covers with fixed degree we show, that the modular fibers F_d(1,1) are itself connected torus covers with Veech group SL_2(Z). Using results of Eskin, Masur and Schmoll we calculate the Euler Characteristic and the parity of the spin structure of the quadratic differential (F_d(1,1)/(-id),q_d). We state and apply formulas for the asymptotic quadratic growth rates of various types of geodesic segments on a surface S "contained" in F_d(1,1). The quadratic growth rates are expressed in terms of the SL_2(Z) orbit closure of S \in F_d(1,1) and the flat geometry of F_d(1,1).18 pages, 3 figures, published. Slightly improved version with updated referencesGeometric TopologyDynamical Systems14H15, 14H52, 30F30, 30F60, 37C35, 58D15, 58D27text