# Belyi maps downloaded from the LMFDB on 11 September 2026.
# Search link: https://www.lmfdb.org/Belyi/4T5/[4,4,3]
# Query "{'a_s': 3, 'b_s': 4, 'c_s': 4, 'group': '4T5'}" returned 1 maps, sorted by degree.

# Each entry in the following data list has the form:
#    [Label, Degree, Group, abc, Ramification type, Genus, Orbit Size, Base field]
# For more details, see the definitions at the bottom of the file.



"4T5-4_4_3.1-a"	4	"4T5"	[4, 4, 3]	[[4], [4], [3, 1]]	1	1	["1.1.1.1", [-1, 1]]


# Label --
#    The **label** of a Belyi map $\phi$ has the form $d$T$G$-$\lambda_0\_\lambda_1\_\lambda_\infty$-m encoding the following data.

#    - $d$T$G$ is the transitive group label of the monodromy group of $\phi$. Here $d$ is the degree of $\phi$.

#    - $\lambda_i$ are partitions of $d$ specifying the ramification type of $\phi$, each written using `.` as a separator between the parts of the partition.

#    - m is the Galois orbit label, a non-negative integer written in base 26 using the 26 symbols a, b, ..., z.


#Degree (deg) --
#    The **degree** of a Belyi map $\phi:X\to\mathbb{P}^1$ is the degree of $\phi$ as a finite map of curves.


# Group --
#    The **monodromy group** of a Belyi map $\phi \colon X \to \mathbb{P}^1$ of degree $d$ is the transitive subgroup of $S_d$ generated by its associated transitive permutation triple $\sigma$.  This group is the geometric monodromy group of the branched cover $\phi$, or equivalently it is the geometric Galois group of the corresponding extension of function fields $K(X) \supseteq K(\phi) \simeq K(\mathbb{P}^1)$.


# abc --
#    The **$(a,b,c)$ triple** for a Belyi map is obtained by taking the orders of the elements in the corresponding transitive permutation triple.


#Ramification type (lambdas) --
#    The **ramification type** of a Belyi map $\phi \colon X \to \mathbb{P}^1$ is the triple of partitions $\lambda_0,\lambda_1,\lambda_\infty$ giving the ramification orders of the preimages of $0,1,\infty$, respectively.


#Genus (g) --
#    The **genus** of a Belyi map $\phi:X\to\mathbb{P}^1$ is the genus of the source $X$.


#Orbit Size (orbit_size) --
#    The **orbit size** is the number of isomorphism classes of Belyi maps contained in a given Galois orbit.


#Base field (field) --
#    The **base field** of a Belyi map $\phi:X\to\mathbb{P}^1$ is the field $X$ and $\phi$ are defined over.
#    (In the database, we take this base field to be the field of moduli whenever possible.)