The map in the Galois orbit of size 1 is defined on the elliptic curve with LMFDB label 490.e2. The maps in the orbit of size 2 are defined on an elliptic curve over Q(21) with conductor norm 2940.
,(1,3,5,2,6,4,7),(1,2)(3,4).png "(1,7,3,2,5,4,6)_(1,3,5,2,6,4,7)_(1,2)(3,4)")
,(1,3,2,7,6,5,4),(1,2)(3,4).png "(1,3,2,4,5,6,7)_(1,3,2,7,6,5,4)_(1,2)(3,4)")
,(1,7,3,2,6,5,4),(1,2)(3,4).png "(1,3,7,2,4,5,6)_(1,7,3,2,6,5,4)_(1,2)(3,4)")