Dessins coming from the Miranda-Persson table

In R.Miranda-U.Persson, Configurations of In fibers on elliptic K3-surfaces, Math. Z. 201 (1989), 339-361 the authors study semi-stable elliptic fibrations over P^1 of K3-surfaces with 6 singular fibres. In their paper the authors give a list of possible fiber types for such fibrations. It turns out that there are 112 such cases.
The corresponding J-invariant is a so-called Belyi-function. More particularly, J is a rational function of degree 24, it ramifies of order 3 in every point above 0, it ramifies of order 2 in every point above 1, and the only other ramification occurs above infinity. To every such map we can associate a so-called 'dessin d'enfant' (coined by Grothendieck) which in its turn uniquely determines the Belyi map. If f: C -> P^1 is a Belyi map, the dessin is the inverse image under f of the real segment [0,1].
Recently (2004) H.Montanus and F.Beukers computed all J-invariants corresponding to the Miranda-Persson list. Below is the collection of dessins d'enfant. An entry like 14-3-2-2-2-1 means that one finds there all dessins of J-maps with ramification orders 14,3,2,2,2,1 above infinity. Alternative one can say that the special elliptic fibers are of type In with n=14,3,2,2,2,1. If to a partition there corresponds only one picture, this means that J is a rational function with coefficients in Q. If there are several pictures, the corresponding fields of definition are indicated.

Furthermore, we compiled the list of all J-maps with coefficients in Q. The other J-maps can be defined over quadratic or cubic fields except one which is defined over a quartic field. An explicit list is under preparation.

Page 1
19-1-1-1-1-1
18-2-1-1-1-1
17-3-1-1-1-1
17-2-2-1-1-1

Page 2
16-4-1-1-1-1
16-3-2-1-1-1
16-2-2-2-1-1
15-5-1-1-1-1


Page 3
15-4-2-1-1-1
15-3-3-1-1-1
15-3-2-2-1-1
14-6-1-1-1-1

Page 4
14-5-2-1-1-1
14-4-3-1-1-1
14-4-2-2-1-1
14-3-3-2-1-1


Page 5
14-3-2-2-2-1
13-7-1-1-1-1
13-6-2-1-1-1
13-5-3-1-1-1


Page 6
13-5-2-2-1-1
13-4-3-2-1-1
13-3-3-2-2-1
12-7-2-1-1-1

Page 7
12-6-3-1-1-1
12-6-2-2-1-1
12-5-3-2-1-1
12-5-2-2-2-1

Page 8
12-4-4-2-1-1
12-4-3-3-1-1
12-4-3-2-2-1
12-3-3-3-2-1


Page 9
12-3-3-2-2-2
11-9-1-1-1-1
11-8-2-1-1-1
11-7-3-1-1-1


Page 10
11-7-2-2-1-1
11-6-4-1-1-1
11-6-3-2-1-1
11-5-5-1-1-1

Page 11
11-5-4-2-1-1
11-5-3-3-1-1
11-5-3-2-2-1
11-4-4-3-1-1

Page 12
11-4-3-3-2-1
10-10-1-1-1
10-9-2-1-1-1
10-8-3-1-1-1


Page 13
10-7-4-1-1-1
10-7-3-2-1-1
10-7-2-2-2-1
10-6-5-1-1-1


Page 14
10-6-4-2-1-1
10-6-3-2-2-1
10-5-5-2-1-1
10-5-4-2-2-1


Page 15
10-5-3-2-2-2
10-4-4-3-2-1
10-4-3-3-2-2
9-9-2-2-1-1


Page 16
9-8-3-2-1-1
9-7-5-1-1-1
9-7-4-2-1-1
9-7-3-2-2-1

Page 17
9-6-5-2-1-1
9-6-4-3-1-1
9-6-3-3-2-1
9-5-5-2-2-1


Page 18
9-5-4-3-2-1
9-5-3-3-3-1
9-4-3-3-3-2
8-8-4-2-1-1


Page 19
8-8-3-3-1-1
8-8-2-2-2-2
8-7-6-1-1-1
8-7-5-2-1-1


Page 20
8-7-4-3-1-1
8-7-4-2-2-1
8-7-3-3-2-1
8-6-6-2-1-1


Page 21
8-6-5-3-1-1
8-6-5-2-2-1
8-6-4-3-2-1
8-6-4-2-2-2


Page 22
8-5-4-3-3-1
8-5-4-3-2-2
8-4-4-4-3-1
8-4-4-4-2-2


Page 23
7-7-7-1-1-1
7-7-5-3-1-1
7-7-4-4-1-1
7-7-3-3-2-2


Page 24
7-6-6-2-2-1
7-6-5-4-1-1
7-6-5-3-2-1
7-6-4-4-2-1


Page 25
7-5-5-4-2-1
7-5-5-3-2-2
7-5-4-4-3-1
7-5-4-3-3-2

Page 26
6-6-6-4-1-1
6-6-6-2-2-2
6-6-5-5-1-1
6-6-5-4-2-1


Page 27
6-6-5-3-3-1
6-6-4-4-2-2
6-6-4-3-3-2
6-6-3-3-3-3


Page 28
6-5-4-4-3-2
5-5-5-5-2-2
5-5-4-4-3-3
4-4-4-4-4-4