Cubic surfaces with galois-invariant six gap_nr := 1; gl := 12*x^2*w - 3*x*y^2 - x*y*w - 9*x*z*w - 3*x*w^2 + 6*y^2*z - 6*y^2*w + 2*y*z*w - 2*y*w^2 - z^3 - 9*z^2*w - 11*z*w^2 + 21*w^3; ch_pol_sm := tt^27 + 27*tt^26 + 216*tt^25 - 540*tt^24 - 19440*tt^23 - 128304*tt^22 - 373248*tt^21 - 419904*tt^20; h1_gal := 1; rk_pic := 7; ord_gal := 1; bp := [ 2, 3, 5, 7, 11 ]; gap_nr := 2; gl := 2*x^2*y + 6*x^2*z - 6*x^2*w - x*y^2 + 11*x*y*w + 9*x*z^2 + 5*x*w^2 - y^3 - 3*y^2*z + 7*y^2*w + y*z^2 - 7*y*w^2 + 3*z^3 + 6*z^2*w - 4*w^3; ch_pol_sm := tt^21 + 27*tt^20 + 120*tt^19 - 3200*tt^18 - 46080*tt^17 - 233472*tt^16 - 425984*tt^15; h1_gal := 1; rk_pic := 6; ord_gal := 2; bp := [ 2, 3, 5, 7, 11, 31, 59 ]; gap_nr := 4; gl := 4*x^2*z - 3*x^2*w - 8*x*y*z + 3*x*y*w + 5*x*z^2 - 2*x*z*w - 4*x*w^2 + 2*y^2*z - y^2*w + 2*y*z^2 - 2*y*z*w - 4*y*w^2 + z^3 - 3*z^2*w + 4*w^3; ch_pol_sm := tt^17 + 23*tt^16 - 44*tt^15 - 5120*tt^14 - 47200*tt^13 - 134000*tt^12; h1_gal := 1; rk_pic := 5; ord_gal := 2; bp := [ 2, 3, 5, 7, 11, 19 ]; gap_nr := 10; gl := x^3 + 3*x^2*z + 2*x^2*w + 3*x*y*w - 2*x*z^2 + x*w^2 - y^2*w - 2*y*z^2 + 3*y*z*w; ch_pol_sm := tt^16 + 23*tt^15 - 116*tt^14 - 7280*tt^13 - 68800*tt^12 - 206000*tt^11; h1_gal := 1; rk_pic := 5; ord_gal := 4; bp := [ 2, 3, 5, 7, 19 ]; gap_nr := 24; gl := x^2*y + x^2*z + x^2*w + 2*x*y*z + x*y*w - x*z^2 + x*w^2 - y^3 - y^2*z - 2*y*z*w - 2*y*w^2 - 3*z^3 - 2*z^2*w - z*w^2 - 2*w^3; ch_pol_sm := tt^15 + 27*tt^14 - 144*tt^13 - 11232*tt^12 - 124416*tt^11 - 435456*tt^10; h1_gal := 1; rk_pic := 5; ord_gal := 6; bp := [ 2, 3, 11, 29, 31 ]; gap_nr := 7; gl := -2*x^2*y - 2*x^2*w + 5*x*y*z - x*w^2 - 2*y^2*z + y^2*w + y*z^2 + 2*y*z*w - 2*y*w^2 + w^3; ch_pol_sm := tt^15 + 27*tt^14 - 144*tt^13 - 11232*tt^12 - 124416*tt^11 - 435456*tt^10; h1_gal := 1; rk_pic := 5; ord_gal := 3; bp := [ 2, 3, 7, 13, 29 ]; gap_nr := 5; gl := -x^2*y - 2*x*y*z + 2*x*y*w + x*z^2 + 2*x*z*w + x*w^2 - y^3 + y^2*z - y^2*w + 2*y*z^2 - y*z*w + 2*y*w^2 - z^3 - 2*z^2*w + 2*z*w^2 + w^3; ch_pol_sm := tt^15 + 15*tt^14 - 204*tt^13 - 4580*tt^12 - 20400*tt^11; h1_gal := 1; rk_pic := 4; ord_gal := 2; bp := [ 2, 5, 11, 19 ]; gap_nr := 22; gl := -x^2*y + x^2*z + 2*x*y^2 + x*y*z - x*z^2 + 4*x*z*w + 2*x*w^2 + 2*y^3 + 2*y^2*z + 3*y^2*w - 2*y*z^2 - 2*y*z*w + 2*y*w^2 + z^2*w - 5*z*w^2 - 2*w^3; ch_pol_sm := tt^13 + 15*tt^12 - 364*tt^11 - 8244*tt^10 - 41328*tt^9; h1_gal := 1; rk_pic := 4; ord_gal := 4; bp := [ 2, 3, 5, 7, 19, 29 ]; gap_nr := 11; gl := -2*x^2*w - 2*x*y^2 - 5*x*y*w + 19*x*z*w + 30*x*w^2 + 5*y^3 + y^2*z + 19*y^2*w - y*z^2 - 27*y*z*w + 30*y*w^2 + z^3 - 11*z^2*w; ch_pol_sm := tt^12 + 21*tt^11 - 504*tt^10 - 15228*tt^9 - 93312*tt^8; h1_gal := 1; rk_pic := 4; ord_gal := 4; bp := [ 2, 3, 5, 7, 11, 17, 23, 41, 313 ]; gap_nr := 46; gl := -3*x^3 - 4*x^2*y - 5*x^2*w - 7*x*y^2 - 9*x*y*z + x*y*w + 4*x*z^2 + 7*x*z*w + x*w^2 + 9*y^3 - 3*y^2*z + 6*y^2*w - 5*y*z^2 - 4*y*z*w + y*w^2 + 3*z^3 - 2*z^2*w - z*w^2; ch_pol_sm := tt^12 + 15*tt^11 - 468*tt^10 - 10948*tt^9 - 58800*tt^8; h1_gal := 1; rk_pic := 4; ord_gal := 8; bp := [ 2, 3, 5, 7, 11, 479 ]; gap_nr := 15; gl := 4*x^2*z + x^2*w + 4*x*y*z - 2*x*y*w - x*z^2 + x*z*w + y^2*z - 2*y^2*w - y*z^2 - 5*y*z*w - 6*y*w^2 - 4*z^3 + z^2*w - 4*w^3; ch_pol_sm := tt^12 + 15*tt^11 - 468*tt^10 - 10948*tt^9 - 58800*tt^8; h1_gal := 1; rk_pic := 4; ord_gal := 4; bp := [ 2, 3, 191 ]; gap_nr := 48; gl := -x^2*w + 3*x*y*w - x*z^2 - 11*x*z*w - 107*x*w^2 + y^3 + y^2*z + 44*y^2*w - 7*y*z^2 + 72*y*z*w - 44*y*w^2 - 11*z^3 - 80*z^2*w + 12*z*w^2 + 24*w^3; ch_pol_sm := tt^11 + 21*tt^10 - 640*tt^9 - 20124*tt^8 - 137376*tt^7; h1_gal := 1; rk_pic := 4; ord_gal := 8; bp := [ 2, 3, 5, 7, 79, 89, 211 ]; gap_nr := 18; gl := x^2*w - x*y^2 + x*z*w + y*z*w + y*w^2 - z^3 - w^3; ch_pol_sm := tt^11 + 21*tt^10 - 640*tt^9 - 20124*tt^8 - 137376*tt^7; h1_gal := 1; rk_pic := 4; ord_gal := 4; bp := [ 2, 5, 11 ]; gap_nr := 79; gl := 2*x^2*w + 2*x*y^2 + 3*x*y*w + x*z*w + 5*x*w^2 + 2*y^3 - y^2*w + 4*y*z*w - 3*y*w^2 + z^3 - 2*z^2*w - 7*z*w^2 + 2*w^3; ch_pol_sm := tt^11 + 15*tt^10 - 624*tt^9 - 15316*tt^8 - 89376*tt^7; h1_gal := 1; rk_pic := 4; ord_gal := 12; bp := [ 2, 3, 11, 31, 251 ]; gap_nr := 33; gl := 9*x^3 + 30*x^2*y - 28*x^2*z - 66*x^2*w + 33*x*y^2 - 62*x*y*z + 212*x*y*w + 29*x*z^2 + 113*x*z*w + 164*x*w^2 + 11*y^3 - 34*y^2*z + 310*y^2*w + 32*y*z^2 - 265*y*z*w - 32*y*w^2 - 10*z^3 - 46*z^2*w + 236*z*w^2 - 16*w^3; ch_pol_sm := tt^11 + 15*tt^10 - 624*tt^9 - 15316*tt^8 - 89376*tt^7; h1_gal := 1; rk_pic := 4; ord_gal := 6; bp := [ 2, 3, 11, 31, 67, 607, 4597, 27901 ]; gap_nr := 28; gl := x^2*w + 5*x*y*w + x*z^2 - 3*x*z*w + 3*x*w^2 + y^3 + 2*y^2*z - 4*y^2*w - y*z^2 + y*z*w + 3*y*w^2 - 2*z^3 + 3*z^2*w + 9*z*w^2; ch_pol_sm := tt^11 + 15*tt^10 - 624*tt^9 - 15316*tt^8 - 89376*tt^7; h1_gal := 1; rk_pic := 4; ord_gal := 6; bp := [ 2, 3, 5, 7, 29, 41, 71 ]; gap_nr := 152; gl := -x^3 + x^2*z + x*z^2 + x*w^2 - y^2*w - y*z^2 + y*z*w - 2*y*w^2 - z^3 + z^2*w + 3*w^3; ch_pol_sm := tt^10 + 21*tt^9 - 912*tt^8 - 29916*tt^7 - 225504*tt^6; h1_gal := 1; rk_pic := 4; ord_gal := 24; bp := [ 2, 3, 5, 19, 47, 229 ]; gap_nr := 77; gl := x^2*w - x*y^2 - 2*x*y*z - y^2*w + 2*y*z*w - 3*z^2*w - 2*z*w^2 - w^3; ch_pol_sm := tt^10 + 21*tt^9 - 912*tt^8 - 29916*tt^7 - 225504*tt^6; h1_gal := 1; rk_pic := 4; ord_gal := 12; bp := [ 2, 3, 11 ]; gap_nr := 19; gl := x^3 + 2*x^2*z - x^2*w + 7*x*y^2 - 4*x*y*z + 2*x*y*w + x*z^2 - 2*x*z*w + 2*y^3 - 6*y^2*z - 6*y^2*w - 3*y*z^2 - 2*y*z*w + 7*y*w^2 - z^2*w + w^3; ch_pol_sm := tt^10 + 5*tt^9 - 656*tt^8 - 7120*tt^7; h1_gal := 1; rk_pic := 3; ord_gal := 4; bp := [ 2, 5, 17 ]; gap_nr := 8; gl := 2*x^3 + x^2*y + 3*x^2*z + 3*x*y*w - x*z^2 - x*z*w - x*w^2 + y^2*w - 5*y*z*w + 2*y*w^2 - z^3 - 5*z^2*w - 3*z*w^2; ch_pol_sm := tt^9 + 9*tt^8 - 648*tt^7 - 8748*tt^6; h1_gal := 1; rk_pic := 3; ord_gal := 3; bp := [ 2, 3, 5, 7, 13 ]; gap_nr := 61; gl := -x^2*w + x*y^2 + 2*x*y*z + 4*x*y*w + x*z^2 - 5*x*w^2 - y^2*z - 2*y*z^2 - 4*y*z*w + 3*z^3 + z^2*w + w^3; ch_pol_sm := tt^9 + 5*tt^8 - 792*tt^7 - 9840*tt^6; h1_gal := 1; rk_pic := 3; ord_gal := 8; bp := [ 2, 7, 73 ]; gap_nr := 20; gl := x^2*w - 4*x*y*w + x*z^2 - 2*x*z*w + 7*x*w^2 - y^3 + y^2*z + 11*y^2*w + y*z^2 - y*z*w + 8*y*w^2 - 3*z^3 - 6*z^2*w - 3*z*w^2; ch_pol_sm := tt^9 + 5*tt^8 - 792*tt^7 - 9840*tt^6; h1_gal := 1; rk_pic := 3; ord_gal := 4; bp := [ 2, 3, 5, 11, 41, 71 ]; gap_nr := 47; gl := x^2*w + 9*x*y^2 + 6*x*y*z - 7*x*y*w + x*z^2 - 8*x*z*w + 14*x*w^2 + 10*y^3 - 3*y^2*z - 8*y^2*w - 5*y*z^2 - 11*y*z*w - 6*y*w^2 - z^3 + 5*z^2*w - 2*z*w^2 + 8*w^3; ch_pol_sm := tt^9 - 3*tt^8 - 984*tt^7 - 10480*tt^6; h1_gal := 1; rk_pic := 3; ord_gal := 8; bp := [ 2, 5, 13, 17, 31, 41 ]; gap_nr := 34; gl := -23*x^3 + 67*x^2*y + 45*x^2*z + 49*x^2*w + 20*x*y^2 - 9*x*y*z - 22*x*y*w - x*z^2 + 64*x*z*w - 2*x*w^2 + y^3 + 20*y^2*w - 9*y*z*w - 90*y*w^2 - z^2*w + 20*z*w^2 - 60*w^3; ch_pol_sm := tt^8 + 3*tt^7 - 864*tt^6 - 10692*tt^5; h1_gal := 1; rk_pic := 3; ord_gal := 6; bp := [ 2, 3, 5, 7, 31, 47, 1327, 5807 ]; gap_nr := 125; gl := -x^3 + 2*x^2*y - 8*x^2*w + 4*x*y*z - 3*x*y*w + 2*x*z*w - x*w^2 - 2*y^2*w + 2*y*z^2 - 12*y*z*w - 2*y*w^2 + z^2*w - 6*z*w^2 + 4*w^3; ch_pol_sm := tt^8 - 3*tt^7 - 1184*tt^6 - 14480*tt^5; h1_gal := 1; rk_pic := 3; ord_gal := 16; bp := [ 2, 5, 7, 19, 23, 139 ]; gap_nr := 59; gl := x^3 - 5*x^2*w - 2*x*y^2 + x*z*w - 6*x*w^2 + 2*y^2*z + y^2*w - 2*z^2*w + z*w^2 + w^3; ch_pol_sm := tt^8 - 3*tt^7 - 1184*tt^6 - 14480*tt^5; h1_gal := 1; rk_pic := 3; ord_gal := 8; bp := [ 2, 5, 7, 577 ]; gap_nr := 58; gl := -x^2*z + x^2*w - x*y^2 - 3*x*z^2 + 4*x*z*w - x*w^2 - 7*z^2*w - 6*z*w^2 + 9*w^3; ch_pol_sm := tt^8 - 3*tt^7 - 1184*tt^6 - 14480*tt^5; h1_gal := 1; rk_pic := 3; ord_gal := 8; bp := [ 2, 3, 7, 19 ]; gap_nr := 68; gl := x^3 + 14*x^2*y + x^2*z - 3*x*y^2 + 5*x*y*z - 4*x*z^2 + 2*y^2*z - y^2*w - 8*y*z^2 - 10*y*z*w + y*w^2 - 8*z^3 + z^2*w; ch_pol_sm := tt^8 - 3*tt^7 - 1184*tt^6 - 14480*tt^5; h1_gal := 1; rk_pic := 3; ord_gal := 8; bp := [ 2, 3, 5, 7, 11, 1801, 2801 ]; gap_nr := 76; gl := x^2*y - x^2*z + 2*x*y^2 - 3*x*y*z - x*y*w + x*z^2 + x*z*w + 2*x*w^2 + 2*y^2*z + y*w^2 + 2*z^3 - 2*z*w^2 + w^3; ch_pol_sm := tt^7 + 7*tt^6 - 1464*tt^5 - 25220*tt^4; h1_gal := 1; rk_pic := 3; ord_gal := 10; bp := [ 2, 3, 5, 17 ]; gap_nr := 23; gl := -x^2*w + x*y^2 - 2*x*y*z - x*y*w + x*z^2 - x*z*w + x*w^2 - y^3 + 2*y^2*z + y^2*w + y*z^2 + 2*y*w^2 - z^3 + 2*z^2*w + z*w^2 - 2*w^3; ch_pol_sm := tt^7 + 7*tt^6 - 1464*tt^5 - 25220*tt^4; h1_gal := 1; rk_pic := 3; ord_gal := 5; bp := [ 3, 11, 23 ]; gap_nr := 224; gl := x^2*w - 16*x*y^2 - 8*x*y*z - 5*x*y*w - x*z^2 + x*z*w + 2*x*w^2 + y^3 + 3*y^2*w - 7*y*z*w - 5*y*w^2 - z^2*w + 20*z*w^2 + w^3; ch_pol_sm := tt^7 - 3*tt^6 - 1584*tt^5 - 22480*tt^4; h1_gal := 1; rk_pic := 3; ord_gal := 48; bp := [ 2, 3, 5, 11, 19, 61, 109, 229 ]; gap_nr := 165; gl := x^2*y - 4*x^2*z + 3*x^2*w + 2*x*y^2 - 10*x*y*z + 8*x*z^2 + 14*x*z*w - 2*x*w^2 + y^3 - 6*y^2*z - 2*y^2*w + 9*y*z^2 + 3*y*z*w + 27*y*w^2 - 8*z^3 + 19*z^2*w + 4*z*w^2 + 10*w^3; ch_pol_sm := tt^7 - 3*tt^6 - 1584*tt^5 - 22480*tt^4; h1_gal := 1; rk_pic := 3; ord_gal := 24; bp := [ 2, 3, 5, 11, 19, 1049, 17029 ]; gap_nr := 156; gl := x^2*w + x*y^2 + 2*x*y*z - 16*x*y*w + x*z^2 - 12*x*z*w - 94*x*w^2 - 12*y^3 - 38*y^2*z + 43*y^2*w - 37*y*z^2 - 32*y*z*w + 23*y*w^2 - 12*z^3 - 54*z^2*w - 12*w^3; ch_pol_sm := tt^7 - 3*tt^6 - 1584*tt^5 - 22480*tt^4; h1_gal := 1; rk_pic := 3; ord_gal := 24; bp := [ 2, 3, 5, 7, 79, 337 ]; gap_nr := 197; gl := -3*x^2*y - 2*x^2*z + 7*x^2*w - 3*x*y^2 - 2*x*y*w + 3*x*z*w - 2*x*w^2 - y^3 - 7*y^2*w - 3*y*z*w + 3*y*w^2 - 2*z^2*w - 5*z*w^2 + 3*w^3; ch_pol_sm := tt^7 - 9*tt^6 - 1296*tt^5 - 14580*tt^4; h1_gal := 1; rk_pic := 3; ord_gal := 36; bp := [ 2, 3, 5, 13, 17, 29, 31, 587 ]; gap_nr := 128; gl := 2*x^2*z - 2*x*y^2 - 5*x*y*z - 4*x*y*w - 10*x*z^2 + 3*x*z*w - 2*x*w^2 - 2*y^3 + 2*y^2*z + 2*y*z^2 - 9*y*z*w - 2*z^3 + 11*z^2*w + z*w^2 - w^3; ch_pol_sm := tt^7 - 9*tt^6 - 1296*tt^5 - 14580*tt^4; h1_gal := 1; rk_pic := 3; ord_gal := 18; bp := [ 2, 3, 5, 457, 3491 ]; gap_nr := 130; gl := x^2*y - 5*x*y^2 - 2*x*y*z + 3*x*y*w - x*z^2 - 3*y^3 + y^2*z + 3*y^2*w + 3*y*z^2 + y*z*w + y*w^2 - z^3 - z^2*w + 2*z*w^2 - w^3; ch_pol_sm := tt^7 - 9*tt^6 - 1296*tt^5 - 14580*tt^4; h1_gal := 1; rk_pic := 3; ord_gal := 18; bp := [ 2, 3, 7, 13, 31, 293 ]; gap_nr := 70; gl := -x^3 + x^2*y + 2*x^2*z + x^2*w + x*y^2 - x*y*z + x*y*w + x*w^2 + y^2*z + 2*y^2*w + y*z^2 + y*z*w - z^3 - z^2*w - w^3; ch_pol_sm := tt^7 - 9*tt^6 - 1296*tt^5 - 14580*tt^4; h1_gal := 1; rk_pic := 3; ord_gal := 9; bp := [ 2, 3, 7, 13 ]; gap_nr := 292; gl := -x^2*w - 2*x*y*w + x*z^2 + 2*x*z*w + 9*x*w^2 + y^3 + y^2*w - y*z^2 - y*z*w + y*w^2 - 6*z^2*w + 3*z*w^2 + w^3; ch_pol_sm := tt^6 - 3*tt^5 - 2484*tt^4 - 44980*tt^3; h1_gal := 1; rk_pic := 3; ord_gal := 120; bp := [ 2, 19, 151, 839, 1559 ]; gap_nr := 247; gl := -x^2*y - x^2*w - x*y^2 + 2*x*y*w - x*w^2 + y^3 - y^2*z - y^2*w - y*z^2 + y*z*w + z^3 - z^2*w + 2*w^3; ch_pol_sm := tt^6 - 3*tt^5 - 2484*tt^4 - 44980*tt^3; h1_gal := 1; rk_pic := 3; ord_gal := 60; bp := [ 2, 5, 7 ]; gap_nr := 148; gl := -4*x^3 - 3*x^2*z + x*y^2 - x*y*z - 2*x*z*w + y^2*w - 4*y*z^2 - z^3 + z*w^2; ch_pol_sm := tt^6 - 3*tt^5 - 2484*tt^4 - 44980*tt^3; h1_gal := 1; rk_pic := 3; ord_gal := 20; bp := [ 2, 5, 79, 431 ]; gap_nr := 29; gl := x^2*y - x^2*z - 3*x^2*w - x*y^2 + 2*x*y*z + x*y*w - x*z^2 - x*z*w + 6*x*w^2 + 2*y^3 - 2*y^2*w + y*z*w + 4*y*w^2 + 2*z^3 - 5*z^2*w - z*w^2 + 3*w^3; ch_pol_sm := tt^6 - 9*tt^5 - 1620*tt^4; h1_gal := 1; rk_pic := 2; ord_gal := 6; bp := [ 2, 3, 43, 109 ]; gap_nr := 98; gl := 2*x^3 + 2*x^2*z - 2*x*y^2 - 2*x*z*w - x*w^2 + 8*y^2*w + z^3; ch_pol_sm := tt^5 - 15*tt^4 - 1836*tt^3; h1_gal := 1; rk_pic := 2; ord_gal := 12; bp := [ 2, 3, 11 ]; gap_nr := 39; gl := -x^2*w + x*y*w - x*z^2 + 5*x*w^2 + y^3 + 2*y^2*z + y*z^2 - 2*y*z*w + 4*y*w^2 + 2*z^2*w + 2*z*w^2 + w^3; ch_pol_sm := tt^5 - 15*tt^4 - 1836*tt^3; h1_gal := 1; rk_pic := 2; ord_gal := 6; bp := [ 2, 3, 7, 29, 43 ]; gap_nr := 259; gl := x^3 - 3*x^2*y + 3*x^2*z + 2*x^2*w + 3*x*y^2 - 6*x*y*z - 2*x*y*w + x*z^2 - 4*x*z*w - 13*x*w^2 - y^3 + 3*y^2*z + y^2*w - 2*y*z^2 + 6*y*z*w - 15*y*w^2 + 2*z^2*w + 3*z*w^2 - 5*w^3; ch_pol_sm := tt^4 - 27*tt^3 - 2268*tt^2; h1_gal := 1; rk_pic := 2; ord_gal := 72; bp := [ 2, 113, 281, 733 ]; gap_nr := 202; gl := -x^3 + 3*x^2*z + 2*x*y*z - 2*x*y*w - 2*x*z*w - x*w^2 + y^2*z - y^2*w - 2*y*z^2 - 6*y*w^2 - 4*z^2*w + 5*z*w^2; ch_pol_sm := tt^4 - 27*tt^3 - 2268*tt^2; h1_gal := 1; rk_pic := 2; ord_gal := 36; bp := [ 2, 3, 11, 47 ]; gap_nr := 201; gl := -x^2*w + 2*x*z^2 - x*z*w + 4*x*w^2 + y^3 - 5*y^2*w + y*z^2 + 3*y*z*w - 2*y*w^2 + 3*z^2*w - z*w^2 + w^3; ch_pol_sm := tt^4 - 27*tt^3 - 2268*tt^2; h1_gal := 1; rk_pic := 2; ord_gal := 36; bp := [ 2, 3, 5, 109469 ]; gap_nr := 141; gl := x^3 + 2*x^2*y - x^2*z - x^2*w + x*y^2 - x*y*w - 4*x*z^2 - x*z*w + 8*x*w^2 + y^2*z - y^2*w - 5*y*z^2 + 4*y*z*w - 8*y*w^2 + 3*z^3 - 12*z^2*w - 3*z*w^2 + 6*w^3; ch_pol_sm := tt^4 - 27*tt^3 - 2268*tt^2; h1_gal := 1; rk_pic := 2; ord_gal := 18; bp := [ 2, 3, 1290907 ]; gap_nr := 229; gl := 2*x^2*y + 8*x*y^2 - 4*x*y*w + 2*x*z^2 + y*z^2 + y*w^2 - 4*z^2*w + w^3; ch_pol_sm := tt^4 - 39*tt^3 - 2700*tt^2; h1_gal := 1; rk_pic := 2; ord_gal := 48; bp := [ 2, 3, 5, 7, 37 ]; gap_nr := 159; gl := 2*x^2*y + x^2*z - x^2*w - 4*x*y^2 + 2*x*y*z - 6*x*y*w + 2*x*z^2 - 6*x*z*w + 4*x*w^2 + y^3 - 3*y^2*z + 6*y^2*w - 2*y*z*w + 4*y*w^2 + z^3 - 4*z^2*w - 12*z*w^2 - 4*w^3; ch_pol_sm := tt^4 - 39*tt^3 - 2700*tt^2; h1_gal := 1; rk_pic := 2; ord_gal := 24; bp := [ 2, 3, 5, 13, 53 ]; gap_nr := 157; gl := x^2*y + x*y*z + 2*x*z^2 + 2*y^2*w + 2*y*z^2 + y*w^2 + z^3 + 2*z^2*w - w^3; ch_pol_sm := tt^4 - 39*tt^3 - 2700*tt^2; h1_gal := 1; rk_pic := 2; ord_gal := 24; bp := [ 2, 3, 47, 229 ]; gap_nr := 163; gl := -x^2*w + 4*x*y^2 - 4*x*y*z + 6*x*y*w + x*z^2 + 7*x*z*w + 117*x*w^2 - 21*y^3 + 20*y^2*z - 18*y^2*w - 5*y*z^2 - 39*y*z*w + 35*y*w^2 + z^2*w + 7*z*w^2 - 30*w^3; ch_pol_sm := tt^4 - 39*tt^3 - 2700*tt^2; h1_gal := 1; rk_pic := 2; ord_gal := 24; bp := [ 2, 3, 5, 7, 11, 67, 229 ]; gap_nr := 78; gl := -2*x^3 + 3*x^2*z + 8*x^2*w + 5*x*y^2 + 9*x*z^2 - 2*x*z*w + x*w^2 + y^2*z + y^2*w - z^3; ch_pol_sm := tt^4 - 39*tt^3 - 2700*tt^2; h1_gal := 1; rk_pic := 2; ord_gal := 12; bp := [ 2, 3, 11, 17 ]; gap_nr := 340; gl := x^3 - 3*x^2*y + 3*x*y^2 - 2*x*y*w - x*z^2 + 3*x*z*w - 5*x*w^2 - y^3 + y^2*w + 2*y*z^2 - 5*y*z*w - 8*y*w^2 + 8*z^2*w - z*w^2 - w^3; ch_pol_sm := tt^3 - 63*tt^2 - 3564*tt; h1_gal := 1; rk_pic := 2; ord_gal := 720; bp := [ 2, 3, 5, 101, 431, 135887 ]; gap_nr := 328; gl := -x^2*z + 2*x*y^2 - x*y*z + 2*x*z^2 - 2*x*z*w + y^3 - y^2*z + 4*y*z^2 + 2*y*z*w - 3*z^2*w + 4*w^3; ch_pol_sm := tt^3 - 63*tt^2 - 3564*tt; h1_gal := 1; rk_pic := 2; ord_gal := 360; bp := [ 2, 3, 5, 229 ]; gap_nr := 293; gl := 7*x^3 - 4*x^2*y - x^2*z + 8*x^2*w + 8*x*y*w + 4*x*z^2 + 4*x*z*w - 5*x*w^2 - 8*y^2*w + 2*y*z*w - 5*y*w^2 - 5*z^3 + 13*z^2*w + z*w^2; ch_pol_sm := tt^3 - 63*tt^2 - 3564*tt; h1_gal := 1; rk_pic := 2; ord_gal := 120; bp := [ 2, 3, 17, 19, 151, 151883 ]; gap_nr := 248; gl := 39*x^3 + 16*x^2*y - 22*x^2*z - 3*x^2*w - 8*x*y*z - 55*x*y*w + 3*x*z^2 - 56*x*z*w + 8*x*w^2 - 4*y^2*w + y*z^2 + 4*y*z*w - 55*y*w^2 + 10*z^2*w + 100*z*w^2 - 35*w^3; ch_pol_sm := tt^3 - 63*tt^2 - 3564*tt; h1_gal := 1; rk_pic := 2; ord_gal := 60; bp := [ 2, 3, 5, 23, 43, 199, 257, 22877 ];