On translation lengths of Anosov maps on the curve graph of the torus

We show that an Anosov map has a geodesic axis on the curve graph of torus. The direct corollary our result is stable translation length always positive integer. As proof constructive, we also provide algorithm to calculate exact for any given map. application threefold: (a) determine which word realizes minimal within specific class words, (b) establish effective bound ratio lengths Teichm\"uller space, and (c) estimate overall growth number maps have sufficient with same length.