Essential welded pairs:

$S: BQ^4_{3} \quad U = (\iota , \iota , (2 4 3) , (2 3 4)) \quad D = (\iota , (3 4) , (3 4) , (3 4))$\hfil\break
$T: BQ^4_{9} \quad U = (\iota , (3 4) , (3 4) , (3 4)) \quad D = (\iota , (3 4) , (3 4) , (3 4))$\hfil\break

$S: BQ^4_{14} \quad U = (\iota , (3 4) , (1 4 3) , (1 3 4)) \quad D = ((3 4) , (3 4) , (3 4) , (3 4))$\hfil\break
$T: BQ^4_{30} \quad U = ((3 4) , (3 4) , (3 4) , (3 4)) \quad D = ((3 4) , (3 4) , (3 4) , (3 4))$\hfil\break

$S: BQ^4_{19} \quad U = (\iota , (1 3)(2 4) , (1 4)(2 3) , (1 2)(3 4)) \quad D = ((2 4 3) , (2 4 3) , (2 4 3) , (2 4 3))$\hfil\break
$T: BQ^4_{39} \quad U = ((2 3 4) , (2 3 4) , (2 3 4) , (2 3 4)) \quad D = ((2 4 3) , (2 4 3) , (2 4 3) , (2 4 3))$\hfil\break

$S: BQ^4_{29} \quad U = (\iota , (3 4) , \iota , \iota) \quad D = ((3 4) , (3 4) , (1 4) , (1 3))$\hfil\break
$T: BQ^4_{30} \quad U = ((3 4) , (3 4) , (3 4) , (3 4)) \quad D = ((3 4) , (3 4) , (3 4) , (3 4))$\hfil\break

$S: BQ^4_{37} \quad U = ((2 3 4) , (2 3) , (3 4) , (2 4)) \quad D = ((2 4 3) , (2 3 4) , (2 3 4) , (2 3 4))$\hfil\break
$T: BQ^4_{40} \quad U = ((2 3 4) , (2 4 3) , (2 4 3) , (2 4 3)) \quad D = ((2 4 3) , (2 3 4) , (2 3 4) , (2 3 4))$\hfil\break

$S: BQ^4_{54} \quad U = ((1 2)(3 4) , (1 2)(3 4) , (1 2)(3 4) , (1 2)(3 4)) \quad D = ((1 3 4 2) , (1 2 4 3) , (1 2 4 3) , (1 3 4 2))$\hfil\break
$T: Q^4_{1} \quad U = \iota \quad D = \iota$\hfil\break

$S: Q^4_{3} \quad U = ((2 4 3) , (1 3 4) , (1 4 2) , (1 2 3)) \quad D = \iota$\hfil\break
$T: Q^4_{1} \quad U = \iota \quad D = \iota$\hfil\break

$S: Q^4_{7} \quad U = ((2 4) , (1 4) , \iota , (1 2)) \quad D = \iota$\hfil\break
$T: Q^4_{1} \quad U = \iota \quad D = \iota$\hfil\break