Input and output files for Hurwitz classes

The links below lead to NETmap input and output files for exactly one representative from every modular group Hurwitz class of NET maps through degree 30. This information is organized first according to elementary divisors m and n. There is one web page of links for each choice of m and n with the product mn at least 2 and at most 30. For three of the classes, class 2 for m=2 and n=1, and classes 9 and 10 for m=2 and n=2, the maps have only three postcritical points for each choice of the translation vector and so don't give any NET maps.

Here is how the entries for a given ordered pair (m,n) are ordered. We use the fact that modular group Hurwitz classes of NET maps are classified by equivalence classes of Hurwitz structure sets. These Hurwitz structure sets are disjoint unions of four subsets of the form {±(α,β)} with (α,β) ∈ ℤ2m ⊕ ℤ2n. We represent α and β by nonnegative integers a and b. We define an ordering ≤ on ordered pairs of nonnegative integers so that (a,b) ≤ (c,d) if and only if either b<d or b=d and a≤c. This ordering of ordered pairs leads to an ordering of sets of four signed ordered pairs. This determines the ordering of the entries for (m,n). So the first entry always has structure set {(0,0),±(1,0),±(2,0),±(3,0)} except when m=2 ((1,0)=-(3,0) in ℤ2m ⊕ ℤ2n when m=2).

There are 46,245 Hurwitz classes of NET maps with degree at most 30.