# This file lists 54 non-equivalent Belyi maps, in 44 Gal(Qbar/Q)-orbits.


# BranchPattern (3), (3), (1^3)  (in parametric Heun table)
Belyi_inf26_1 := 1/(1-x^3);

# BranchPattern (3), (1^3), (3)  (in parametric Heun table)
Belyi_inf26_2 := x^3;

# BranchPattern (1,2), (3), (1,2)  (in parametric Heun table)
Belyi_inf26_3 := (x-3)*x^2/(3*x-8)^2;

# BranchPattern (1^3), (3), (3)  (in parametric Heun table)
Belyi_inf26_4 := 1-x^3;

# BranchPattern (4), (1^2,2), (1,3)  (in parametric Heun table)
Belyi_inf26_5 := x^4/(4*x-3);

# BranchPattern (4), (1^2,2), (2^2)  (in parametric Heun table)
Belyi_inf26_6 := 1/(2*x^2-1)^2;

# BranchPattern (1,3), (1^2,2), (4)  (in parametric Heun table)
Belyi_inf26_7 := (4*x-3)/x^4;

# BranchPattern (2^2), (1^2,2), (4)  (in parametric Heun table)
Belyi_inf26_8 := (2*x^2-1)^2;

# BranchPattern (5), (1,2^2), (1^2,3)  (in parametric Heun table)
Belyi_inf26_9 := 64*x^5/(40*x^2+15*x+9);

# BranchPattern (5), (1,2^2), (1,2^2)  (in parametric Heun table)
Belyi_inf26_10 := (x+2)^5/(5*x^2-4)^2;

# BranchPattern (1,4), (1,2^2), (1,4)  (in parametric Heun table)
Belyi_inf26_11 := eval((5*x-1+2*_a)^4/((-7+24*_a)*(-x+1+2*_a)^4*x), _a=RootOf(_Z^2+1));

# BranchPattern (1,4), (1,2^2), (2,3)  (in parametric Heun table)
Belyi_inf26_12 := (5*x-1)^4/(4*(2*x+5)^3*x^2);

# BranchPattern (2,3), (1,2^2), (1,4)  (in parametric Heun table)
Belyi_inf26_13 := (3*x-10)^2*x^3/(60*x+16);

# BranchPattern (2,3), (1,2^2), (2,3)  (in parametric Heun table)
Belyi_inf26_14 := (5*x+4)^2/((4*x+5)^2*x^3);

# BranchPattern (1^2,3), (1,2^2), (5)  (in parametric Heun table)
Belyi_inf26_15 := (40*x^2+15*x+9)/(64*x^5);

# BranchPattern (1,2^2), (1,2^2), (5)  (in parametric Heun table)
Belyi_inf26_16 := (x^2-5*x+5)^2*x/4;

# BranchPattern (1^2,4), (1^2,2^2), (6)  (in non-parametric Heun table)
Belyi_inf26_17 := -27*(5*x^2+12*x+20)/x^6;
Belyi_inf26_18 := (3*x^2+2)/x^6;

# BranchPattern (1,2,3), (1^2,2^2), (6)
Belyi_inf26_19 := eval(3125*(x-1)^2*(6*_a^2+18*_a-25*x+4)*x^3/(681*_a^2+1968*_a-1196), _a=RootOf(_Z^3-2));

# BranchPattern (2^3), (1^2,2^2), (6)  (in parametric Heun table)
Belyi_inf26_20 := (3*x^2-4)^2/x^6;

# BranchPattern (6), (2^3), (1^3,3)  (in parametric Heun table)
Belyi_inf26_21 := x^6/(4*x^3-4);

# BranchPattern (6), (2^3), (1^2,2^2)  (in parametric Heun table)
Belyi_inf26_22 := 1/((x^2+1)*(4*x^2+1)^2);

# BranchPattern (1,5), (2^3), (1^2,4)  (in parametric Heun table)
Belyi_inf26_23 := (4*x-3)/((x^2+1)*(2*x-1)^4);

# BranchPattern (1,5), (2^3), (1,2,3)  (in parametric Heun table)
Belyi_inf26_24 := (x-6)^5*x/((3*x-50)*(5*x+2)^3);

# BranchPattern (2,4), (2^3), (1,2,3)  (in parametric Heun table)
Belyi_inf26_25 := (2*x+3)^4*x^2/((2*x-1)^3*(6*x+1)^2);

# BranchPattern (3^2), (2^3), (1^2,4)  (in parametric Heun table)
Belyi_inf26_26 := (4*x^2+1)^3/(3*x^2+1);

# BranchPattern (3^2), (2^3), (2^3)
Belyi_inf26_27 := -4*x^3/(x^3-1)^2;

# BranchPattern (1^2,4), (2^3), (1,5)  (in parametric Heun table)
Belyi_inf26_28 := (x^2+2*x+5)*x^4/(8*x-4);

# BranchPattern (1^2,4), (2^3), (3^2)  (in parametric Heun table)
Belyi_inf26_29 := (3*x^2+1)/(4*x^2+1)^3;

# BranchPattern (1,2,3), (2^3), (1,5)  (in parametric Heun table)
Belyi_inf26_30 := (3*x-50)*(5*x+2)^3/((x-6)^5*x);

# BranchPattern (1,2,3), (2^3), (2,4)  (in parametric Heun table)
Belyi_inf26_31 := (2*x-1)^3*(6*x+1)^2/((2*x+3)^4*x^2);

# BranchPattern (2^3), (2^3), (3^2)
Belyi_inf26_32 := -(x^3-1)^2/(4*x^3);

# BranchPattern (1^2,5), (1,2^3), (1,6)  (in non-parametric Heun table)
Belyi_inf26_33 := eval(2352980*(_a^2+_a*x+x^2+2)*(3*_a^2-7*_a-5*x+25)^5/((42*_a^2-72*_a+293)*(6*_a^2+4*_a+35*x+23)^6), _a=RootOf(_Z^3+3*_Z-1));

# BranchPattern (1,2,4), (1,2^3), (1,6)  (in non-parametric Heun table)
Belyi_inf26_34 := eval((2*_a^3-2*_a^2+9*x-11)^4*(8*_a^3-50*_a^2+102*_a+9*x-71)^2*x/((2*_a^3-6*_a^2+8*_a-9*x-5)^6*(x-1)), _a=RootOf(_Z^4-2*_Z^3+3));

# BranchPattern (1,3^2), (1,2^3), (1,6)  (in parametric Heun table)
Belyi_inf26_35 := eval(7*(x-1)*(6*_a*x+6*x^2-_a-3)^3/(3*(_a+9)*(7*x+2+6*_a)), _a=RootOf(_Z^2+3));

# BranchPattern (2^2,3), (1,2^3), (1,6)
Belyi_inf26_36 := (35*x^2-56*x+20)^2/((2*x+35)*x^6);

# BranchPattern (1^2,6), (2^4), (1^2,6)  (in non-parametric Heun table)
Belyi_inf26_37 := (8*x^2-4)/(x^6*(x^2+4));
Belyi_inf26_38 := (x^2+6*x+21)*x^6/(-756*x^2+1296*x-1296);

# BranchPattern (1,2,5), (2^4), (1^2,6)  (in non-parametric Heun table)
Belyi_inf26_39 := (x-4)*(5*x-14)^2*x^5/(-280*x^2-96*x-36);

# BranchPattern (1,3,4), (2^4), (1^2,6)  (in non-parametric Heun table)
Belyi_inf26_40 := eval(-64*(-21*x+27+4*_a)^4*(-12*x+15+2*_a)/(9*(-71+39*_a)*(-2*x^2+_a+3)*(-6*x+7+_a)^6), _a=RootOf(_Z^2+3));

# BranchPattern (2,3^2), (2^4), (1^2,6)  (in parametric Heun table)
Belyi_inf26_41 := 4*(2*x^2-1)^3/(x^6*(9*x^2-4));

# BranchPattern (1^2,2,4), (2^4), (2,6)  (in non-parametric Heun table)
Belyi_inf26_42 := -4*(x^2-4*x+6)*(x-1)^4*x^2/(4*x-1)^2;

# BranchPattern (1^2,3^2), (2^4), (2,6)  (in parametric Heun table)
Belyi_inf26_43 := -(x^2-1)*(x^2-9)^3/(64*x^6);

# BranchPattern (1,2^2,3), (2^4), (2,6)
Belyi_inf26_44 := -16*(x+2)^3*(2*x^2+6*x+3)^2*x/(4*x+9)^2;