# This file lists 121 non-equivalent Belyi maps, in 84 Gal(Qbar/Q)-orbits.


# BranchPattern (3), (3), (1^3)  (in parametric Heun table)
Belyi_inf24_1 := 1/(1-x^3);

# BranchPattern (3), (1^3), (3)  (in parametric Heun table)
Belyi_inf24_2 := x^3;

# BranchPattern (1,2), (3), (1,2)  (in parametric Heun table)
Belyi_inf24_3 := (x-3)*x^2/(3*x-8)^2;

# BranchPattern (1^3), (3), (3)  (in parametric Heun table)
Belyi_inf24_4 := 1-x^3;

# BranchPattern (4), (1^4), (4)  (in parametric Heun table)
Belyi_inf24_5 := 1/x^4;

# BranchPattern (1^2,2), (1,3), (4)  (in parametric Heun table)
Belyi_inf24_6 := (6*x^2-8*x+3)/x^4;

# BranchPattern (4), (1^2,2), (1,3)  (in parametric Heun table)
Belyi_inf24_7 := x^4/(4*x-3);

# BranchPattern (4), (1^2,2), (2^2)  (in parametric Heun table)
Belyi_inf24_8 := 1/(2*x^2-1)^2;

# BranchPattern (5), (1^3,2), (1,4)  (in non-parametric Heun table)
Belyi_inf24_9 := x^5/(5*x-4);

# BranchPattern (1^2,3), (2,3), (1,4)  (in non-parametric Heun table)
Belyi_inf24_10 := eval(-625*(-x^2+_a+x+2)*(3*x-39+5*_a)^3/((-29+6*_a)*(-15*x+3+7*_a)^4), _a=RootOf(_Z^2-6));

# BranchPattern (1,2^2), (2,3), (1,4)  (in parametric Heun table)
Belyi_inf24_11 := -x*(96*x^2+80*x+15)^2/(15*x+8);

# BranchPattern (5), (1,2^2), (1^2,3)  (in parametric Heun table)
Belyi_inf24_12 := 64*x^5/(40*x^2+15*x+9);

# BranchPattern (5), (1,2^2), (1,2^2)  (in parametric Heun table)
Belyi_inf24_13 := (x+2)^5/(5*x^2-4)^2;

# BranchPattern (1,4), (1,2^2), (2,3)  (in parametric Heun table)
Belyi_inf24_14 := (5*x-1)^4/(4*(2*x+5)^3*x^2);

# BranchPattern (2,3), (1,2^2), (2,3)  (in parametric Heun table)
Belyi_inf24_15 := (5*x+4)^2/((4*x+5)^2*x^3);

# BranchPattern (1^2,3), (1,2^2), (5)  (in parametric Heun table)
Belyi_inf24_16 := (9*x^2+15*x+40)*x^3/64;

# BranchPattern (1,2^2), (1,2^2), (5)  (in parametric Heun table)
Belyi_inf24_17 := (x^2-5*x+5)^2*x/4;

# BranchPattern (6), (1^2,2^2), (1^2,4)  (in non-parametric Heun table)
Belyi_inf24_18 := -432/((5*x^2+18*x+45)*x^4);
Belyi_inf24_19 := 1/(x^4*(2*x^2+3));

# BranchPattern (1,5), (1^2,2^2), (2,4)  (in non-parametric Heun table)
Belyi_inf24_20 := eval((-2*x-9+3*_a)^5*x/(16200*_a*(x-1)^4), _a=RootOf(_Z^2+15));

# BranchPattern (2,4), (1^2,2^2), (2,4)
Belyi_inf24_21 := eval(-243*(x-1)^2/((45+26*_a)*(-x-9+6*_a)^2*x^4), _a=RootOf(_Z^2-3));

# BranchPattern (3^2), (1^2,2^2), (2,4)  (in parametric Heun table)
Belyi_inf24_22 := -(x^2-4)^3/(27*x^4);

# BranchPattern (6), (2^3), (1^3,3)  (in parametric Heun table)
Belyi_inf24_23 := x^6/(4*x^3-4);

# BranchPattern (6), (2^3), (1^2,2^2)  (in parametric Heun table)
Belyi_inf24_24 := 1/((x^2+1)*(4*x^2+1)^2);

# BranchPattern (1,5), (2^3), (1,2,3)  (in parametric Heun table)
Belyi_inf24_25 := (x+6)^5*x/((3*x+50)*(5*x-2)^3);

# BranchPattern (2,4), (2^3), (1,2,3)  (in parametric Heun table)
Belyi_inf24_26 := (2*x+3)^4*x^2/((2*x-1)^3*(6*x+1)^2);

# BranchPattern (3^2), (2^3), (2^3)
Belyi_inf24_27 := -4*x^3/(x^3-1)^2;

# BranchPattern (1^2,4), (2^3), (1,5)  (in parametric Heun table)
Belyi_inf24_28 := (x^2+2*x+5)*x^4/(8*x-4);

# BranchPattern (1^2,4), (2^3), (3^2)  (in parametric Heun table)
Belyi_inf24_29 := (3*x^2+1)/(4*x^2+1)^3;

# BranchPattern (1,2,3), (2^3), (1,5)  (in parametric Heun table)
Belyi_inf24_30 := (3*x+50)*(5*x-2)^3/((x+6)^5*x);

# BranchPattern (2^3), (2^3), (3^2)
Belyi_inf24_31 := -(x^3-1)^2/(4*x^3);

# BranchPattern (1^3,3), (2^3), (6)  (in parametric Heun table)
Belyi_inf24_32 := 4*x^3-4*x^6;

# BranchPattern (1^2,2^2), (2^3), (6)  (in parametric Heun table)
Belyi_inf24_33 := (4-x^2)*(x^2-1)^2/4;

# BranchPattern (7), (1,2^3), (1^3,4)  (in non-parametric Heun table)
Belyi_inf24_34 := 4/((50*x^3+35*x^2+28*x+35)*x^4);

# BranchPattern (1,6), (1,2^3), (1,2,4)  (in non-parametric Heun table)
Belyi_inf24_35 := eval((2*_a^3-6*_a^2+8*_a-9*x-5)^6*(x-1)/((2*_a^3-2*_a^2+9*x-11)^4*(8*_a^3-50*_a^2+102*_a+9*x-71)^2*x), _a=RootOf(_Z^4-2*_Z^3+3));

# BranchPattern (2,5), (1,2^3), (1,2,4)  (in non-parametric Heun table)
Belyi_inf24_36 := eval(16*(10*_a^2+8*_a-49*x+39)^2/(2401*(71*_a^2+52*_a+191)*(_a^2+x)*(x-1)^4*x^2), _a=RootOf(_Z^3+2*_Z-2));

# BranchPattern (3,4), (1,2^3), (1,2,4)
Belyi_inf24_37 := eval(40353607*(x-1)^3*x^4/((7+2*_a)*(-147*x+35+16*_a)^2*(49*x-21+12*_a)), _a=RootOf(_Z^2-7));

# BranchPattern (1^2,5), (1,2^3), (3,4)  (in non-parametric Heun table)
Belyi_inf24_38 := eval(-7203*(x^2+_a-x-1)*(15*x-26+5*_a)^5/(4*(115+1322*_a)*(35*x-66+13*_a)^4), _a=RootOf(_Z^2+5));

# BranchPattern (1,2,4), (1,2^3), (3,4)
Belyi_inf24_39 := eval(-3*(-147*x+35+16*_a)^2*(49*x-21+12*_a)/(5764801*(-7+2*_a)*(x-1)^3*x^4), _a=RootOf(_Z^2-7));

# BranchPattern (1,3^2), (1,2^3), (3,4)  (in parametric Heun table)
Belyi_inf24_40 := (7*x^2-56*x+108)^3/((2*x-7)^3*x^4);

# BranchPattern (2^2,3), (1,2^3), (3,4)
Belyi_inf24_41 := (112*x^2-35*x+4)^2/((16*x-7)^4*x^3);

# BranchPattern (1^2,6), (1^2,2^3), (4^2)  (in non-parametric Heun table)
Belyi_inf24_42 := (7168*x^2+2048*x+7168)/(3*(9*x^2+7)^4);
Belyi_inf24_43 := eval((-4*_a*x^2-20*x^2+27)/(27*(x-1)^4*(x+1)^4), _a=RootOf(_Z^2+2));

# BranchPattern (1,2,5), (1^2,2^3), (4^2)  (in non-parametric Heun table)
Belyi_inf24_44 := eval(-(13*_a^2-18*_a-14*x+13)^5*(5*_a^2-6*_a-10*x-3)/(25*(863*_a^2-2680*_a+2753)*(_a^2*x-2*_a*x-x^2-_a+2*x+1)^4), _a=RootOf(_Z^3-_Z^2+2*_Z+2));

# BranchPattern (1,3,4), (1^2,2^3), (4^2)
Belyi_inf24_45 := eval(3373232128*(x-1)*x^3/((35123+24844*_a)*(32*_a*x-16*x^2-54*_a-40*x+81)^4), _a=RootOf(_Z^2-2));

# BranchPattern (2^2,4), (1^2,2^3), (4^2)
Belyi_inf24_46 := eval(-(2*x^2+1)^2/((-17+12*_a)*(-x^2+_a+1)^4), _a=RootOf(_Z^2-2));

# BranchPattern (2,3^2), (1^2,2^3), (4^2)
Belyi_inf24_47 := eval((-4*x^2+_a-1)^3/((x^2-1)^4*(5+_a)), _a=RootOf(_Z^2+2));

# BranchPattern (8), (2^4), (1^4,4)  (in non-parametric Heun table)
Belyi_inf24_48 := 1/(4*x^4-4*x^8);

# BranchPattern (1,7), (2^4), (1^2,2,4)  (in non-parametric Heun table)
Belyi_inf24_49 := eval(-524288*(16*x+3+5*_a)^7/((4411+4049*_a)*(-2*x^2+_a+1)*(-4*x-13+11*_a)^4*(512*x+635+111*_a)^2), _a=RootOf(_Z^2+7));

# BranchPattern (2,6), (2^4), (1^2,2,4)  (in non-parametric Heun table)
Belyi_inf24_50 := -64*(2*x+3)^2/((x^2-4*x+12)*(x+2)^2*x^4);

# BranchPattern (3,5), (2^4), (1^2,2,4)  (in non-parametric Heun table)
Belyi_inf24_51 := 64*(4*x-1)^5/((x^2+88*x-8)*(x+6)^4*x^2);

# BranchPattern (4^2), (2^4), (1^2,2,4)  (in parametric Heun table)
Belyi_inf24_52 := -(x^2-1)^4/(4*x^4*(2*x^2-1));

# BranchPattern (1^2,6), (2^4), (1,3,4)  (in non-parametric Heun table)
Belyi_inf24_53 := eval(21609*(-2*x^2+_a+3)*(-6*x+7+_a)^6/(16*(71+39*_a)*(-21*x+27+4*_a)^4*(-12*x+15+2*_a)), _a=RootOf(_Z^2+3));

# BranchPattern (1,2,5), (2^4), (1,3,4)  (in non-parametric Heun table)
Belyi_inf24_54 := 64*(5*x+7)^2*(5*x+3)*x^5/((8*x-5)*(7*x+5)^4);

# BranchPattern (1,3,4), (2^4), (1,3,4)
Belyi_inf24_55 := eval(3294172*(x-1)^3*(-x-11+8*_a)/((835+872*_a)*(-x-8+9*_a)^3*(-x+8+5*_a)*x^4), _a=RootOf(_Z^2-2));

# BranchPattern (1,3,4), (2^4), (2^2,4)
Belyi_inf24_56 := -4*(x+4)*(x+1)^4*x^3/(6*x^2+4*x+1)^2;

# BranchPattern (2^2,4), (2^4), (1,3,4)
Belyi_inf24_57 := (x+1)^4*(x^2-2*x+3)^2/(4*(4*x+3)*x^4);

# BranchPattern (2^2,4), (2^4), (2^2,4)
Belyi_inf24_58 := -4*(x^2-1)^2/(x^4*(x^2-2)^2);

# BranchPattern (1^2,7), (1,2^4), (1,4^2)  (in non-parametric Heun table)
Belyi_inf24_59 := eval(-(645*_a^3*x+71*_a^3-382*_a^2*x-830*_a^2-74*_a*x+784*x^2+458*_a-216*x+190)*(x-1+_a)^7/((7391*_a^3-7850*_a^2-14234*_a+14720)*(_a^3*x-_a^2*x-_a^2+x^2+_a)^4), _a=RootOf(_Z^4-2*_Z^3+2*_Z^2+2));

# BranchPattern (1,2,6), (1,2^4), (1,4^2)  (in non-parametric Heun table)
Belyi_inf24_60 := eval(343*(_a^3+3*_a^2-12*x+10)^6*(3*_a^3+10*_a-9*x+10)/(216*(249*_a^3-432*_a^2+1310*_a-607)*(335*_a^3+2448*_a^2-1302*_a-9261*x+5506)*(_a^2*x-x^2+_a+2*x-1)^4), _a=RootOf(_Z^4-2*_Z^3+6*_Z^2-4*_Z+2));

# BranchPattern (1,3,5), (1,2^4), (1,4^2)  (in non-parametric Heun table)
Belyi_inf24_61 := eval((_a^4-10*_a^3+8*_a^2+20*_a+24*x+16)^5*(17*_a^4-14*_a^3-14*_a^2-116*_a-60*x-58)/(2916*(395*_a^4-1466*_a^3+1668*_a^2-1988*_a+2296)*(8*_a^4+34*_a^3-36*_a^2-149*_a+5*x-97)*(_a^2-x^2-1)^4), _a=RootOf(_Z^5-2*_Z^3-4*_Z^2-6*_Z-4));

# BranchPattern (1,4^2), (1,2^4), (1,4^2)
Belyi_inf24_62 := (3*x^2-6*x-1)^4/((x^2+6*x-3)^4*x);

# BranchPattern (2^2,5), (1,2^4), (1,4^2)  (in non-parametric Heun table)
Belyi_inf24_63 := (5376*x^2-7152*x+2401)^2/((256*x^2-336*x+105)^4*x);

# BranchPattern (2,3,4), (1,2^4), (1,4^2)
Belyi_inf24_64 := eval(-69620547427158196224*(x-1)^2*x^3/((47751405489*_a^2+104908025556*_a+86984289661)*(45*_a^2-66*_a-16*x-72)*(45*_a^2*x+9*_a^2-57*_a*x-128*x^2+27*_a+36*x-108)^4), _a=RootOf(_Z^3-3*_Z-4));

# BranchPattern (1^2,8), (2^5), (1^2,4^2)  (in non-parametric Heun table)
Belyi_inf24_65 := (192*x^2-512*x+1024)/((x^2+8)*(x^2-2*x+4)^4);
Belyi_inf24_66 := eval((-_a*x^2-3*x^2+4)/((_a*x^2-x^2+4)*(x+1)^4*(x-1)^4), _a=RootOf(_Z^2+1));

# BranchPattern (1,2,7), (2^5), (1^2,4^2)  (in non-parametric Heun table)
Belyi_inf24_67 := (20*x-19)*(60*x-41)^2/((5*x^2+1)*(40*x^2-50*x+13)^4);

# BranchPattern (1,3,6), (2^5), (1^2,4^2)  (in non-parametric Heun table)
Belyi_inf24_68 := eval(-25000*(2*_a^2-3*x-1)^6*(7*_a^2+4*_a-6*x+3)/(729*(1572*_a^2+1941*_a+2498)*(22*_a^2*x+13*_a^2-26*_a*x+3*x^2-40*_a-6*x+31)*(_a^2*x+_a*x-x^2-1)^4), _a=RootOf(_Z^3-2));

# BranchPattern (1,4,5), (2^5), (1^2,4^2)  (in non-parametric Heun table)
Belyi_inf24_69 := (x+4)*(x+12)^5*x^4/((2*x-1)*(3*x^2-32)^4);

# BranchPattern (2^2,6), (2^5), (1^2,4^2)  (in non-parametric Heun table)
Belyi_inf24_70 := (80*x^2-1)^2/((x^2+1)*(16*x^2+1)^4);

# BranchPattern (2,4^2), (2^5), (1^2,4^2)
Belyi_inf24_71 := eval(3125*(x^2-1)^4/((38+41*_a)*(2*x^2-_a-2)*(x^2-2*_a+1)^4), _a=RootOf(_Z^2+1));

# BranchPattern (3^2,4), (2^5), (1^2,4^2)
Belyi_inf24_72 := 8*(10*x^2-1)^3/((81*x^2-8)*(12*x^2-1)^4);

# BranchPattern (1^2,3,5), (2^5), (2,4^2)  (in non-parametric Heun table)
Belyi_inf24_73 := 256*(9*x^2-15*x+40)*x^3/((x+1)^2*(3*x^2-4*x+8)^4);

# BranchPattern (1^2,4^2), (2^5), (2,4^2)
Belyi_inf24_74 := eval((-2*x^2+_a+2)*(x^2-2*_a+1)^4/((x^2-1)^4*(41*_a-38)), _a=RootOf(_Z^2+1));

# BranchPattern (1,2^2,5), (2^5), (2,4^2)  (in non-parametric Heun table)
Belyi_inf24_75 := (20*x^2+20*x+1)^2*(2*x-1)^5/((4*x^2+20*x+5)^4*x^2);

# BranchPattern (1,2,3,4), (2^5), (2,4^2)
Belyi_inf24_76 := (30*x+1)^4*(2*x-1)^3*(162*x-1)^2/((324*x^2+380*x-15)^4*x^2);

# BranchPattern (2^2,3^2), (2^5), (2,4^2)
Belyi_inf24_77 := (x^2+1)^3*(81*x^2+1)^2/(15*x^2-1)^4;

# BranchPattern (1^3,3,6), (2^6), (4^3)  (in non-parametric Heun table)
Belyi_inf24_78 := 4*(x^3+2)*x^3/(x^3+1)^4;

# BranchPattern (1^3,4,5), (2^6), (4^3)  (in non-parametric Heun table)
Belyi_inf24_79 := 16*(2*x^3-3*x^2+8*x+5)*x^4/(x^3-x^2+2*x+2)^4;

# BranchPattern (1^2,2^2,6), (2^6), (4^3)  (in non-parametric Heun table)
Belyi_inf24_80 := (2*x^2-1)*(8*x^2-1)^2/((8*x^2-3)^4*x^4);

# BranchPattern (1^2,2,3,5), (2^6), (4^3)  (in non-parametric Heun table)
Belyi_inf24_81 := 16*(4*x^2-23*x-6)*(5*x+2)^2*x^5/(2*x^3-6*x^2-9*x-2)^4;

# BranchPattern (1^2,3^2,4), (2^6), (4^3)
Belyi_inf24_82 := -4*(3*x^2+1)*(4*x^2+1)^3/(x^4*(8*x^2+3)^4);

# BranchPattern (1,2^2,3,4), (2^6), (4^3)
Belyi_inf24_83 := 16*(x+4)*(3*x^2-10*x+8)^2*x^3/(x^3-6*x+8)^4;

# BranchPattern (2^3,3^2), (2^6), (4^3)
Belyi_inf24_84 := 16*(x^3-1)^2*x^3/(x^3+1)^4;