There exist holomorphic maps from a torus $T$ to the sphere $S$ of all degree $\geq 2$

Question

While reading through "Restrictions on harmonic maps of surfaces" by J. Eells and J. C. Wood I came across the lines:

We know that there are holomorphic maps from a torus $T$ to the sphere $S$ of all degrees $\geq 2$. These provide harmonic maps $\phi: (T,g) \to (S,h)$ with degree $\geq 2$, whatever the metrics $g$ and $h$; and are essentially the only ones with those degrees.

I basically have two questions:

1. How would I go about proving that there are holomorphic maps from a torus $T$ to the sphere $S$ of all degrees $\geq 2$.
2. Why are they essentially the only ones with those degrees?