(6,7),(1,7)(2,5,4,6,3),(1,2,7,4,6).png "(1,2,3,4,5)(6,7)_(1,7)(2,5,4,6,3)_(1,2,7,4,6)")
A
(6,7),(1,2,3,6,7)(4,5),(1,4,2,7,3).png "(1,2,3,4,5)(6,7)_(1,2,3,6,7)(4,5)_(1,4,2,7,3)")
B
(6,7),(1,7)(2,5,4,3,6),(1,2,7,3,6).png "(1,2,3,4,5)(6,7)_(1,7)(2,5,4,3,6)_(1,2,7,3,6)")
B
(6,7),(1,7)(2,6,3,4,5),(1,6,3,7,2).png "(1,5,4,3,2)(6,7)_(1,7)(2,6,3,4,5)_(1,6,3,7,2)")
B
(6,7),(1,2,5,6,7)(3,4),(1,2,7,5,3).png "(1,2,3,4,5)(6,7)_(1,2,5,6,7)(3,4)_(1,2,7,5,3)")
C
(6,7),(1,7,6,5,2)(3,4),(1,3,5,7,2).png "(1,5,4,3,2)(6,7)_(1,7,6,5,2)(3,4)_(1,3,5,7,2)")
C
(6,7),(1,6,5,7,2)(3,4),(1,6,5,3,7).png "(1,2,3,4,5)(6,7)_(1,6,5,7,2)(3,4)_(1,6,5,3,7)")
C
(6,7),(1,2,7,5,6)(3,4),(1,7,3,5,6).png "(1,5,4,3,2)(6,7)_(1,2,7,5,6)(3,4)_(1,7,3,5,6)")
C
(6,7),(1,3)(2,5,4,6,7),(1,2,3,7,4).png "(1,2,3,4,5)(6,7)_(1,3)(2,5,4,6,7)_(1,2,3,7,4)")
C
(6,7),(1,3)(2,7,6,4,5),(1,4,7,3,2).png "(1,5,4,3,2)(6,7)_(1,3)(2,7,6,4,5)_(1,4,7,3,2)")
C
In this puzzle, the passport decomposes as 10 = 6 + 3 + 1. This means that one of the Belyi maps is defined over \(\mathbb{Q}\). This map is defined on the ellipt curve with LMFDB label 490.f2.