,(1,2,5,3,7),(1,2,3)(4,5)(6,7).png "(1,6,7,2,3,4,5)_(1,2,5,3,7)_(1,2,3)(4,5)(6,7)")
A
,(1,2,7,5,3),(1,2,3)(4,5)(6,7).png "(1,2,3,4,5,6,7)_(1,2,7,5,3)_(1,2,3)(4,5)(6,7)")
B
,(3,7,4,6,5),(1,2,3)(4,5)(6,7).png "(1,3,4,6,5,7,2)_(3,7,4,6,5)_(1,2,3)(4,5)(6,7)")
B
,(2,7,5,3,6),(1,2,3)(4,5)(6,7).png "(1,3,4,5,6,2,7)_(2,7,5,3,6)_(1,2,3)(4,5)(6,7)")
B
,(2,6,3,5,7),(1,3,2)(4,5)(6,7).png "(1,7,2,6,5,4,3)_(2,6,3,5,7)_(1,3,2)(4,5)(6,7)")
B
,(1,4,7,3,6),(1,2,3)(4,5)(6,7).png "(1,7,5,4,3,6,2)_(1,4,7,3,6)_(1,2,3)(4,5)(6,7)")
B
,(1,6,3,7,4),(1,3,2)(4,5)(6,7).png "(1,2,6,3,4,5,7)_(1,6,3,7,4)_(1,3,2)(4,5)(6,7)")
B
Just as in the first puzzle, one of the maps stands alone and is defined over the rational numbers, while the other six are related by Galois symmetries.
The map in the Galois orbit of size 1 is defined on the elliptic curve with LMFDB label 7350.ck1.