(3,4),(1,4,5,3,6)(2,7),(1,2,3)(4,5,6).png "(1,5,6,2,7)(3,4)_(1,4,5,3,6)(2,7)_(1,2,3)(4,5,6)")
A
(3,4),(1,4,7,5,3)(2,6),(1,2,3)(4,5,6).png "(1,2,5,7,6)(3,4)_(1,4,7,5,3)(2,6)_(1,2,3)(4,5,6)")
B
(6,7),(1,6,7,3,4)(2,5),(1,2,7)(3,4,5).png "(1,3,2,4,5)(6,7)_(1,6,7,3,4)(2,5)_(1,2,7)(3,4,5)")
C
(3,4),(1,4,2,7,6)(3,5),(1,2,3)(4,5,6).png "(1,5,2,6,7)(3,4)_(1,4,2,7,6)(3,5)_(1,2,3)(4,5,6)")
D
(3,4),(1,4)(2,5,3,7,6),(1,2,3)(4,5,6).png "(1,6,7,2,5)(3,4)_(1,4)(2,5,3,7,6)_(1,2,3)(4,5,6)")
D
(3,4),(1,4)(2,6,7,3,5),(1,3,2)(4,6,5).png "(1,5,2,7,6)(3,4)_(1,4)(2,6,7,3,5)_(1,3,2)(4,6,5)")
D
In this puzzle, the passport decomposes as 6 = 3 + 1 + 1 + 1, yielding three Belyi maps defined over \(\mathbb{Q}\). Two of these three maps are defined on the elliptic curve with LMFDB label 735.b1, and the other on the elliptic curve with LMFDB label 7350.cr2.