/* Cubic surfaces with a rational line 
   without galois-invariant trieder or double-six. */

gap_nr := 9;
gl := -4*x^2*y - 9*x^2*z + 56*x*y^2 - 57*x*y*z - 4*x*y*w + 34*x*z^2 - 6*x*z*w - 16*y^3 
      - 31*y^2*z - 12*y^2*w - 45*y*z^2 - y*z*w - y*w^2 - 30*z^3 + 11*z^2*w - z*w^2;
ch_pol_sm := t^9 + 3*t^8 - 864*t^7 - 10692*t^6;
h1_gal := 1; 
rk_pic := 3; 
ord_gal := 4;
Elt := [ 4 ];  
bp := [ 2, 3, 5, 11, 19, 1361 ];


gap_nr := 41;
gl := -x^3 - x^2*z + x*y*w + x*z^2 + x*z*w - y^3 + y^2*z + y^2*w + y*z^2 - y*w^2 - z^3 - w^3;
ch_pol_sm := tt^9 + 3*tt^8 - 1680*tt^7 - 21284*tt^6;
h1_gal := 1;
rk_pic := 3;
ord_gal := 8;
Elt := [ 2, 2, 2 ];
bp := [ 2, 3, 5, 7 ];


gap_nr := 54; 
gl := x^2*z - 2*x*w^2 + y^2*w - 2*y*z^2 - z^3 - 3*z^2*w - 3*z*w^2 - w^3;
ch_pol_sm := tt^8 + 3*tt^7 - 1408*tt^6 - 20484*tt^5;
h1_gal := 1;
rk_pic := 3;
ord_gal := 8;
Elt := [ 2, 2 ];
bp := [ 2, 5 ];

 
gap_nr := 66;
gl := -x^3 + x^2*z + 7*x*z^2 + y^2*z + y*z^2 - 10*z^3 + w^3;
ch_pol_sm := tt^6 - 31*tt^5 - 1220*tt^4;
h1_gal := 1;
rk_pic := 2;
ord_gal := 8;
Elt := [ 2, 2 ];
bp := [ 3, 11 ];

 
gap_nr := 99;
gl := x^2*z - 2*x*w^2 - 312*y^2*w + 624*y*z^2 + 50*z^3 - 219*z^2*w - 121*z*w^2 - 21*w^3;
ch_pol_sm := tt^7 - 63*tt^6 - 1364*tt^5;
h1_gal := 1;
rk_pic := 2;
ord_gal := 16;
Elt := [ 2, 2, 2, 2 ];
bp := [ 2, 3, 5, 7, 11, 13 ];

 
gap_nr := 57;
gl := -x^3 + x^2*z - x^2*w + x*y*z + x*y*w + x*z^2 + x*z*w - x*w^2 - y^3 
      + y^2*z - y^2*w + y*z^2 + y*z*w - y*w^2 - z^3 - z*w^2 - w^3;
ch_pol_sm := tt^8 + 3*tt^7 - 1944*tt^6 - 30260*tt^5;
h1_gal := 1;
rk_pic := 3;
ord_gal := 8;
Elt := [ 2, 4 ];
bp := [ 2, 5, 11, 19 ];


gap_nr := 63;
gl := -x^3 - x^2*z + x^2*w - x*y*z - x*y*w - x*z^2 - x*z*w - x*w^2 - y^3 - y^2*z 
      + y^2*w + y*z^2 - y*z*w + y*w^2 - z^3 - w^3;
ch_pol_sm := tt^8 + 3*tt^7 - 1944*tt^6 - 30260*tt^5;
h1_gal := 1;
rk_pic := 3;
ord_gal := 8;
Elt := [ 2, 2 ];
bp := [ 2, 3, 41 ];


gap_nr := 110;
gl := x^2*z - 2*x*w^2 - 8*y^2*w + 16*y*z^2 + 4*z^3 - 2*z^2*w + 3*z*w^2;
ch_pol_sm := tt^8 + 3*tt^7 - 1944*tt^6 - 30260*tt^5;
h1_gal := 1;
rk_pic := 3;
ord_gal := 16;
Elt := [ 2, 2, 2 ];
bp := [ 2, 3, 7 ];
 

gap_nr := 67;
gl := x^2*z - x*y^2 - x*y*z + x*y*w + x*z^2 - x*z*w + x*w^2 - y^3 
      + y^2*z + y*z*w + y*w^2 - z^2*w - z*w^2;
ch_pol_sm := tt^5 - 31*tt^4 - 2276*tt^3;
h1_gal := 1;
rk_pic := 2;
ord_gal := 8;
Elt := [ 8 ];
bp := [ 2, 17 ];


gap_nr := 127;
gl := -x^3 - x^2*z + x*y*z + x*y*w + x*z^2 - x*z*w - y^3 - y^2*w - y*z*w - z^3 - z*w^2 - w^3;
ch_pol_sm := tt^5 - 31*tt^4 - 2276*tt^3;
h1_gal := 1;
rk_pic := 2;
ord_gal := 16;
Elt := [ 2, 2 ];
bp := [ 2, 3, 13, 37 ];


gap_nr := 101;
gl := -x^2*y - x^2*z + x^2*w - x*y^2 + x*z^2 - y^3 + y^2*z - y^2*w - y*z^2 - y*z*w 
      + y*w^2 - z^3 - z^2*w - z*w^2 + w^3;
ch_pol_sm := tt^6 - 63*tt^5 - 1884*tt^4;
h1_gal := 1;
rk_pic := 2;
ord_gal := 16;
Elt := [ 2, 2, 4 ];
bp := [ 2, 3, 5, 11, 61 ];


gap_nr := 117;
gl := -x^3 + x^2*z + x*y*z - x*y*w + x*z^2 - x*z*w - x*w^2 - y^3 
      + y^2*w - y*z*w + y*w^2 - z^3 - z*w^2 - w^3;
ch_pol_sm := tt^6 - 63*tt^5 - 1884*tt^4;
h1_gal := 1;
rk_pic := 2;
ord_gal := 16;
Elt := [ 2, 2, 2 ];
bp := [ 2, 7, 23 ];


gap_nr := 120;
gl := -x^3 - x^2*z + x^2*w - x*y*z - x*y*w - x*z^2 - x*z*w - y^3 
      + y^2*w + y*z^2 - y*z*w + y*w^2 - z^3 - w^3;
ch_pol_sm := tt^6 - 63*tt^5 - 1884*tt^4;
h1_gal := 1;
rk_pic := 2;
ord_gal := 16;
Elt := [ 2, 2, 2 ];
bp := [ 2, 3, 41 ];


gap_nr := 181;
gl := x^2*z - 2*x*w^2 - 266*y^2*w + 532*y*z^2 - 480*z^3 - 1033*z^2*w - 319*z*w^2 - 33*w^3;
ch_pol_sm := tt^6 - 63*tt^5 - 1884*tt^4;
h1_gal := 1;
rk_pic := 2;
ord_gal := 32;
Elt := [ 2, 2, 2, 2 ];
bp := [ 2, 3, 5, 7, 11, 19 ];


gap_nr := 45; 
gl := 3*x^3 + 2*x^2*y + 4*x^2*z - 8*x^2*w + x*y^2 + 8*x*y*z + 2*x*z^2 + 2*x*z*w 
      - x*w^2 + y^3 - y^2*z - y^2*w + 2*y*z^2 + 2*y*z*w - 4*z^2*w;
ch_pol_sm := tt^7 + 3*tt^6 - 2208*tt^5 - 39236*tt^4;
h1_gal := 1;
rk_pic := 3;
ord_gal := 8;
Elt := [2, 4];
bp := [ 2, 5, 11, 31, 41, 281 ];


gap_nr := 104;
gl := x^2*z - 2*x*w^2 + 2*y^2*w - 4*y*z^2 - z^3 - 10*z^2*w - 5*z*w^2 - 2*w^3;
ch_pol_sm := tt^7 + 3*tt^6 - 2208*tt^5 - 39236*tt^4;
h1_gal := 1;
rk_pic := 3;
ord_gal := 16;
Elt := [ 2, 2, 2 ];
bp := [ 2, 3, 7, 37 ];


gap_nr := 106;
gl := -x^2*y - x^2*z + x^2*w - x*y^2 - x*y*z - x*z^2 + x*z*w + x*w^2 - y^3 
      + y^2*z + y*z*w - z^3 - z^2*w + z*w^2 + w^3; 
ch_pol_sm := tt^7 + 3*tt^6 - 2208*tt^5 - 39236*tt^4;
h1_gal := 1;
rk_pic := 3;
ord_gal := 16;
Elt := [ 2, 4 ];
bp := [ 2, 3, 5 ];


gap_nr := 121;
gl := -x^3 - x^2*z + x^2*w + x*y^2 - x*y*z - x*y*w - x*z*w - x*w^2 - y^3 
      + y^2*z - y^2*w + y*z^2 - z^3 - z^2*w + z*w^2 + w^3;
ch_pol_sm := tt^7 + 3*tt^6 - 2208*tt^5 - 39236*tt^4;
h1_gal := 1;
rk_pic := 3;
ord_gal := 16;
Elt := [ 2, 4 ];
bp := [ 2, 5, 41 ];


gap_nr := 187;
gl := -x^3 - x^2*z - x^2*w - x*y*z - x*z^2 - x*z*w - x*w^2 - y^3 + y^2*z 
      + y*z^2 + y*z*w + y*w^2 - z^3 - z*w^2 - w^3;
ch_pol_sm := tt^7 + 3*tt^6 - 2208*tt^5 - 39236*tt^4;
h1_gal := 1;
rk_pic := 3;
ord_gal := 32;
Elt := [ 2, 2, 2 ];
bp := [ 2, 3, 5, 73 ];


gap_nr := 160;
gl := -x^3 - x^2*z - x^2*w + x*y*z - x*y*w - x*z^2 - x*z*w - y^3 + y^2*w - y*z^2 - z^3 - z*w^2 - w^3;
ch_pol_sm := tt^7 + 3*tt^6 - 2472*tt^5 - 48212*tt^4;
h1_gal := 1;
rk_pic := 3;
ord_gal := 24;
Elt := [ 2 ];
bp := [ 2, 5, 37 ];


gap_nr := 166;
gl := -x^3 + x^2*z - x^2*w - x*y*z + x*y*w + x*z^2 - x*w^2 - y^3 + y^2*z - y^2*w 
      + y*z^2 - y*w^2 - z^3 - z*w^2 - w^3;
ch_pol_sm := tt^7 + 3*tt^6 - 2472*tt^5 - 48212*tt^4;
h1_gal := 1;
rk_pic := 3;
ord_gal := 24;
Elt := [ 6 ];
bp := [ 2, 3, 7, 13 ];


gap_nr := 225;
gl := x*y*z + w *(x^2 + y^2 + z^2)+w^2*(x+y)+w^3;
ch_pol_sm := tt^7 + 3*tt^6 - 2472*tt^5 - 48212*tt^4;
h1_gal := 1;
rk_pic := 3;
ord_gal := 48;
Elt := [ 2, 2 ];
bp := [ 19, 23 ];
 
 
gap_nr := 105;
gl := -x^3 - x^2*z - x^2*w + x*y^2 - x*y*w - x*z*w + x*w^2 - y^3 - y^2*z 
      + y^2*w - y*z^2 + y*z*w - z^3 - z^2*w + z*w^2 + w^3;
ch_pol_sm := tt^5 - 63*tt^4 - 2404*tt^3;
h1_gal := 1;
rk_pic := 2;
ord_gal := 16;
Elt := [ 2, 4 ];
bp := [ 2, 3, 5, 11 ];


gap_nr := 107;
gl := -8*x^2*y + 6*x^2*z + 8*x*y^2 + 2*x*y*z - 2*x*z^2 + 4*x*z*w + 7*x*w^2 
      + 2*y^3 - 6*y^2*z - 20*y^2*w - y*z^2 + 6*y*z*w + y*w^2 - 3*z^3 
      + 6*z^2*w - 14*z*w^2 - 5*w^3;
ch_pol_sm := tt^5 - 63*tt^4 - 2404*tt^3;
h1_gal := 1; 
rk_pic := 2;
ord_gal := 16;
Elt := [ 2, 2, 2 ];
bp := [ 2, 3, 5, 23, 37, 2017, 6073 ];


gap_nr := 108;
gl := 3*x^2*w - 4*x*y^2 - 4*x*y*z + 5*x*y*w - 3*x*z^2 - 10*x*z*w - 11*x*w^2 
      - 3*y^2*w - 3*y*z^2 + 14*y*z*w - 2*y*w^2 + 2*z^3 - 7*z^2*w - 2*z*w^2 + w^3;
ch_pol_sm := tt^5 - 63*tt^4 - 2404*tt^3;
h1_gal := 1; 
rk_pic := 2; 
ord_gal := 16;
Elt := [ 4, 4 ];
bp := [ 2, 3, 5, 13, 17, 23, 61, 131, 911 ];


gap_nr := 111;
gl := -x^2*y + x^2*z - x^2*w - x*y^2 + x*z^2 + y^3 - y^2*z - y^2*w + y*z^2 
      + y*z*w - y*w^2 - z^3 - z^2*w + z*w^2 + w^3;
ch_pol_sm := tt^5 - 63*tt^4 - 2404*tt^3;
h1_gal := 1;
rk_pic := 2;
ord_gal := 16;
Elt := [ 2, 4 ];
bp := [ 2, 13, 17 ];


gap_nr := 113;
gl := -x^2*y - x^2*z - x*y^2 + x*y*z + x*z^2 - x*w^2 - y^2*z + y*z^2 - y*w^2 - z^2*w - z*w^2;
ch_pol_sm := tt^5 - 63*tt^4 - 2404*tt^3;
h1_gal := 1;
rk_pic := 2;
ord_gal := 16;
Elt := [ 2, 4 ];
bp := [ 2, 5, 19 ];


gap_nr := 115;
gl := -x^3 - x^2*z + x^2*w - x*y*z + x*y*w - x*z^2 - x*z*w - y^3 + y^2*w 
      + y*z^2 + y*z*w + y*w^2 - z^3 - w^3;
ch_pol_sm := tt^5 - 63*tt^4 - 2404*tt^3;
h1_gal := 1;
rk_pic := 2;
ord_gal := 16;
Elt := [ 2, 4 ];
bp := [ 2, 3, 17 ];


gap_nr := 183;
gl := -x^3 + x^2*z - x^2*w + x*y^2 + x*y*z - y^3 - y^2*z 
      + y^2*w - y*z^2 - y*z*w - y*w^2 - z^3 + z*w^2 - w^3;
ch_pol_sm := tt^5 - 63*tt^4 - 2404*tt^3;
h1_gal := 1;
rk_pic := 2;
ord_gal := 32;
Elt := [ 2, 2, 2 ];
bp := [ 2, 3, 5, 7, 13, 337 ];


gap_nr := 185;
gl := x^2*z - 2*x*w^2 + 14*y^2*w - 28*y*z^2 - 7*z^3 - 2*z^2*w - 8*z*w^2;
ch_pol_sm := tt^5 - 63*tt^4 - 2404*tt^3;
h1_gal := 1;
rk_pic := 2;
ord_gal := 32;
Elt := [ 2, 2, 2 ];
bp := [ 2, 7 ];


gap_nr := 188;
gl := -x^2*y - x^2*z + x^2*w - x*y^2 - x*z^2 - x*w^2 - y^3 + y^2*z + y^2*w 
      + y*z^2 - y*w^2 - z^3 - z^2*w + z*w^2 + w^3;
ch_pol_sm := tt^5 - 63*tt^4 - 2404*tt^3;
h1_gal := 1;
rk_pic := 2;
ord_gal := 32;
Elt := [ 2, 2, 2 ];
bp := [ 2, 3, 7 ];


gap_nr := 189;
gl := x^2*y + 2*x*y*z - 10*x*y*w + 8*x*z^2 + 4*x*z*w - 12*x*w^2 + 3*y^3 + 10*y^2*w 
      + 8*y*z^2 + 14*y*z*w - 2*y*w^2 + 10*z^3 + 7*z^2*w - 12*z*w^2;
ch_pol_sm := tt^5 - 63*tt^4 - 2404*tt^3;
h1_gal := 1;
rk_pic := 2;
ord_gal := 32;
Elt := [ 2, 2, 2 ];
bp := [ 2, 7, 401, 421, 761, 39119 ];


gap_nr := 192;
gl := -x^3 - x^2*z - x^2*w - x*y*z + x*y*w + x*z*w - x*w^2 - y^3 
      + y^2*z + y*z^2 - y*z*w - y*w^2 - z^3 - w^3;
ch_pol_sm := tt^5 - 63*tt^4 - 2404*tt^3;
h1_gal := 1;
rk_pic := 2;
ord_gal := 32;
Elt := [ 2, 2, 2 ];
bp := [ 2, 3, 11, 433 ];


gap_nr := 194;
gl := -x^3 + x^2*z - x^2*w + x*y*z + x*y*w - x*z^2 - x*z*w - x*w^2 - y^3 
      + y^2*z - y^2*w - y*z^2 - y*z*w - y*w^2 - z^3  - z*w^2 - w^3;
ch_pol_sm := tt^5 - 63*tt^4 - 2404*tt^3;
h1_gal := 1;
rk_pic := 2;
ord_gal := 32;
Elt := [ 2, 2, 4 ];
bp := [ 2, 5, 7, 29 ];


gap_nr := 251;
gl := x^2*z - 2*x*w^2 - 42*y^2*w + 84*y*z^2 + 4*z^3 - 21*z^2*w - 18*z*w^2 - 6*w^3;
ch_pol_sm := tt^5 - 63*tt^4 - 2404*tt^3;
h1_gal := 1;
rk_pic := 2;
ord_gal := 64;
Elt := [ 2, 2, 2, 2 ];
bp := [ 2, 3, 7, 11, 19 ];


gap_nr := 215;
gl := -x^3 - x^2*z + x^2*w + x*y*z - x*y*w + x*w^2 - y^3 + y^2*w + y*z^2 - y*z*w - z^3 - w^3;
ch_pol_sm := tt^5 - 63*tt^4 - 2924*tt^3;
h1_gal := 1;
rk_pic := 2;
ord_gal := 48;
Elt := [ 2, 2 ];
bp := [ 2, 3, 37, 53 ];


gap_nr := 219;
gl := -x^3 + x^2*w + x*y*z - x*y*w + x*z^2 + x*w^2 - y^3 + y^2*w + y*z^2 + y*w^2 - z^3 - z*w^2 - w^3;
ch_pol_sm := tt^5 - 63*tt^4 - 2924*tt^3;
h1_gal := 1;
rk_pic := 2;
ord_gal := 48;
Elt := [ 2, 6 ];
bp := [ 3, 7, 53 ];


gap_nr := 230;
gl := -x^3 - x^2*z + x^2*w + x*y*w - x*z^2 + x*w^2 - y^3 - y*z^2 - z^3 - w^3;
ch_pol_sm := tt^5 - 63*tt^4 - 2924*tt^3;
h1_gal := 1;
rk_pic := 2;
ord_gal := 48;
Elt := [ 2, 2 ];
bp := [ 2, 3, 29, 139 ];


gap_nr := 271;
gl := x^2*z - 2*x*w^2 - 3*y^2*w + 6*y*z^2 + 7*z^3 - 7*z^2*w - 2*w^3;
ch_pol_sm := tt^5 - 63*tt^4 - 2924*tt^3;
h1_gal := 1;
rk_pic := 2;
ord_gal := 96;
Elt := [ 2, 2, 2 ];
bp := [ 2, 3, 5, 7 ];


gap_nr := 40;
gl := -x^3 - x^2*z - 2*x^2*w + x*y^2 + 2*x*y*w + x*z^2 + x*w^2 
      - y^2*z + y*z^2 - 2*y*z*w - 2*y*w^2 + z^3 + z*w^2 + 2*w^3;
ch_pol_sm := tt^6 + 3*tt^5 - 3264*tt^4 - 75140*tt^3;
h1_gal := 1;  
rk_pic := 3;  
ord_gal := 8;
Elt := [ 2, 2 ];
bp := [ 2, 3, 23 ];


gap_nr := 102;
gl := -x^3 - x^2*z - x^2*w + x*y^2 + x*y*z - x*z^2 + x*z*w + x*w^2 - y^3 
      + y^2*z - z^3 - z^2*w + z*w^2 + w^3;
ch_pol_sm := tt^6 + 3*tt^5 - 3264*tt^4 - 75140*tt^3;
h1_gal := 1;
rk_pic := 3;
ord_gal := 16;
Elt := [ 2, 2, 2 ];
bp := [ 2, 3, 5 ];


gap_nr := 154;
gl := -x^3 - x^2*z - x^2*w + x*y*z + x*y*w + x*z^2 - x*w^2 - y^3 + y^2*z 
      + y*z^2 - y*w^2 - z^3 - z*w^2 - w^3;
ch_pol_sm := tt^6 + 3*tt^5 - 3264*tt^4 - 75140*tt^3;
h1_gal := 1;
rk_pic := 3;
ord_gal := 24;
Elt := [ 3 ];
bp := [ 2, 3, 5, 547 ];


gap_nr := 180;
gl := -x^2*y + x^2*z - x*y^2 + x*z^2 - y^3 + y^2*z 
      + y*z^2 - y*z*w - z^3 - z^2*w + z*w^2 + w^3;
ch_pol_sm := tt^6 + 3*tt^5 - 3264*tt^4 - 75140*tt^3;
h1_gal := 1;
rk_pic := 3;
ord_gal := 32;
Elt := [ 2, 2, 2, 2 ];
bp := [ 2, 3, 5, 7 ];


gap_nr := 182;
gl := x^2*z - 2*x*w^2 - y^2*w + 2*y*z^2 - 2*z^3 - 5*z^2*w + 7*z*w^2;
ch_pol_sm := tt^6 + 3*tt^5 - 3264*tt^4 - 75140*tt^3;
h1_gal := 1;
rk_pic := 3;
ord_gal := 32;
Elt := [ 2, 4 ];
bp := [ 2, 17 ];


gap_nr := 249;
gl := -x^3 - x^2*z - x*y*w - x*z^2 - y^3 + y^2*z + y^2*w - y*z*w 
      + y*w^2 - z^3 - z*w^2 - w^3;
ch_pol_sm := tt^6 + 3*tt^5 - 3264*tt^4 - 75140*tt^3;
h1_gal := 1;
rk_pic := 3;
ord_gal := 64;
Elt := [ 2, 2, 2 ];
bp := [ 2, 7, 103 ];


gap_nr := 268;
gl := -x^2*y - x^2*z + x^2*w - x*y^2 - x*y*w - x*z^2 + x*z*w - x*w^2 
      + y^2*z - y*z^2 - y*w^2 - z^2*w - z*w^2 - w^3;
ch_pol_sm := tt^6 + 3*tt^5 - 3264*tt^4 - 75140*tt^3;
h1_gal := 1;
rk_pic := 3;
ord_gal := 96;
Elt := [ 3 ];
bp := [ 2, 3, 7, 67 ];


gap_nr := 304;
gl := x*y*z + w *(x^2 + 7*y^2 + 2*z^2)+w^2*(x+y)+w^3;
ch_pol_sm := tt^6 + 3*tt^5 - 3264*tt^4 - 75140*tt^3;
h1_gal := 1;
rk_pic := 3;
ord_gal := 192;
Elt := [ 2 ];
bp := [ 2, 7, 53, 227, 134867 ];
 

gap_nr := 217;
gl := -x^2*y - x^2*z + x^2*w - x*y^2 - x*y*z - x*z^2 + x*z*w - y^3 - y^2*z - y^2*w 
      + y*z^2 - y*z*w + y*w^2 - z^3 - z^2*w + z*w^2 +  w^3;
ch_pol_sm := tt^4 - 63*tt^3 - 3444*tt^2;
h1_gal := 1;
rk_pic := 2;
ord_gal := 48;
Elt := [ 4 ];
bp := [ 2, 3, 5 ];


gap_nr := 220;
gl := -x^3 - x^2*z + x^2*w + x*y*z + x*y*w + x*z^2 + x*z*w - y^3 
      + y^2*w + y*z^2 - z^3 + z*w^2 - w^3;
ch_pol_sm := tt^4 - 63*tt^3 - 3444*tt^2;
h1_gal := 1;
rk_pic := 2;
ord_gal := 48;
Elt := [ 12 ];
bp := [ 2, 5, 11, 13 ];


gap_nr := 274;
gl := x^2*z - 2*x*w^2 + 7*y^2*w - 14*y*z^2 + 21*z^3 - z^2*w - 4*z*w^2;
ch_pol_sm := tt^4 - 63*tt^3 - 3444*tt^2;
h1_gal := 1;
rk_pic := 2;
ord_gal := 96;
Elt := [ 2, 6 ];
bp := [ 2, 3, 7, 701 ];


gap_nr := 275;
gl := -x^3 + x^2*z + x^2*w + x*z*w - x*w^2 - y^3 + y^2*w - y*z^2 - z^3 - z*w^2 - w^3;
ch_pol_sm := tt^4 - 63*tt^3 - 3444*tt^2;
h1_gal := 1;
rk_pic := 2;
ord_gal := 96;
Elt := [ 2, 2 ];
bp := [ 2, 3, 7, 11, 43 ];


gap_nr := 276;
gl := -x^3 - x^2*z - x^2*w + x*y*z + x*y*w 
      + x*z^2 - x*z*w - x*w^2 - y^3 - y^2*w - y*w^2 - z^3 - z*w^2 - w^3;
ch_pol_sm := tt^4 - 63*tt^3 - 3444*tt^2;
h1_gal := 1;
rk_pic := 2;
ord_gal := 96;
Elt := [ 2, 4 ];
bp := [ 3, 5, 19, 1181 ];


gap_nr := 277;
gl := -x^3 + x^2*z - x^2*w + x*y^2 + x*y*z + x*z^2 + x*z*w - x*w^2 - y^3 - y^2*z 
      - y^2*w - y*z^2 - y*w^2 - z^3 - z^2*w - z*w^2 - w^3;
ch_pol_sm := tt^4 - 63*tt^3 - 3444*tt^2;
h1_gal := 1;
rk_pic := 2;
ord_gal := 96;
Elt := [ 2, 2 ];
bp := [ 2, 3, 11 ];

 
gap_nr := 278;
gl := x^2*z - 2*x*w^2 + 15*y^2*w - 30*y*z^2 - 45*z^3 - z^2*w - 18*z*w^2;
ch_pol_sm := tt^4 - 63*tt^3 - 3444*tt^2;
h1_gal := 1;
rk_pic := 2;
ord_gal := 96;
Elt := [ 2, 2 ];
bp := [ 2, 3, 5, 2161 ];


gap_nr := 311;
gl := 2*x^3 + 2*x^2*y + 90*x*y^2 + 42*x*z^2 + 28*x*z*w + 630*x*w^2 - 504*y^3 
      + 14*y*z^2 + 1260*y*z*w - 1512*y*w^2;
ch_pol_sm := tt^4 - 63*tt^3 - 3444*tt^2;
h1_gal := 1;
rk_pic := 2;
ord_gal := 192;
Elt := [ 2, 2, 2 ];
bp := [ 2, 3, 5, 7, 53, 373, 24517, 47387, 50671 ];

 
gap_nr := 118;
gl := x^2*z + x^2*w - x*y^2 - x*y*z - x*y*w - x*z*w - x*w^2 - y^3 + y^2*z 
      + y*z^2 + y*z*w - y*w^2 - z*w^2 - w^3;
ch_pol_sm := tt^4 - 63*tt^3 - 4484*tt^2;
h1_gal := 1;
rk_pic := 2;
ord_gal := 16;
Elt := [ 2, 4 ];
bp := [ 3, 5 ];


gap_nr := 122;
gl := x^3 + x*z^2 - 11*y^2*z + w^3;
ch_pol_sm := tt^4 - 63*tt^3 - 4484*tt^2;
h1_gal := 1;
rk_pic := 2;
ord_gal := 16;
Elt := [ 2, 2 ];
bp := [ 2, 3, 11 ];


gap_nr := 184;
gl := -x^3 + x^2*z - x*y*z + x*z^2 + x*z*w - y^3 + y^2*z + y*z^2 + y*z*w - z^3 + z*w^2 - w^3;
ch_pol_sm := tt^4 - 63*tt^3 - 4484*tt^2;
h1_gal := 1;
rk_pic := 2;
ord_gal := 32;
Elt := [ 2, 4 ];
bp := [ 3, 5, 11 ];


gap_nr := 186;
gl := -x^2*y + x^2*z - x^2*w - x*y^2 - x*y*z - x*z^2 + x*z*w + x*w^2 + y^2*z 
      + y^2*w + y*z^2 - y*z*w - z^3 - z*w^2 - w^3;
ch_pol_sm := tt^4 - 63*tt^3 - 4484*tt^2;
h1_gal := 1;
rk_pic := 2;
ord_gal := 32;
Elt := [ 2, 4 ];
bp := [ 2, 3, 5 ];


gap_nr := 190;
gl := -x^2*y - x^2*z - x*y^2 + x*y*z + x*z^2 + x*z*w 
      + x*w^2 - y^3 - y^2*w - y*z*w - z^3 - z^2*w + z*w^2 + w^3;
ch_pol_sm := tt^4 - 63*tt^3 - 4484*tt^2;
h1_gal := 1;
rk_pic := 2;
ord_gal := 32;
Elt := [ 2, 4 ];
bp := [ 5, 7, 11, 29 ];


gap_nr := 191;
gl := -x^3 - x^2*w - x*w^2 - y^3 - y*w^2 - z^3 - z*w^2 - w^3;
ch_pol_sm := tt^4 - 63*tt^3 - 4484*tt^2;
h1_gal := 1;
rk_pic := 2;
ord_gal := 32;
Elt := [ 2, 2, 2 ];
bp := [ 2, 3, 5 ];


gap_nr := 237;
gl := -x^3 - 4*x*z^2 + 3*y^2*z - 2*z^3 + w^3;
ch_pol_sm := tt^4 - 63*tt^3 - 4484*tt^2;
h1_gal := 1;
rk_pic := 2;
ord_gal := 48;
Elt := [ 2 ];
bp := [ 2, 3, 7, 13 ];


gap_nr := 250;
gl := x^2*z - 2*x*w^2 + 37*y^2*w - 74*y*z^2 - 89*z^3 - 81*z^2*w - 37*z*w^2 - 9*w^3;
ch_pol_sm := tt^4 - 63*tt^3 - 4484*tt^2;
h1_gal := 1;
rk_pic := 2;
ord_gal := 64;
Elt := [ 2, 2, 2 ];
bp := [ 2, 3, 7, 37 ];


gap_nr := 252;
gl := -x^3 - x^2*z - x^2*w + x*y*z + x*y*w + x*z*w - x*w^2 - y^3 - y^2*z - y^2*w 
      + y*z*w - y*w^2 - z^3 + z*w^2 - w^3;
ch_pol_sm := tt^4 - 63*tt^3 - 4484*tt^2;
h1_gal := 1;
rk_pic := 2;
ord_gal := 64;
Elt := [ 2, 4 ];
bp := [ 3, 5, 7, 19 ];


gap_nr := 253;
gl := -x^2*y + x^2*z + x^2*w - x*y^2 + x*y*z - x*z^2 - x*z*w - x*w^2 - y^3 
      + y^2*z + y*z^2 + y*z*w - z^3 - z*w^2 - w^3;
ch_pol_sm := tt^4 - 63*tt^3 - 4484*tt^2;
h1_gal := 1;
rk_pic := 2;
ord_gal := 64;
Elt := [ 2, 4 ];
bp := [ 2, 5, 17 ];


gap_nr := 254;
gl := -x^3 - x^2*z + x^2*w + x*y*z - x*y*w - x*z^2 - x*z*w 
      - y^3 - y^2*w + y*z^2 - z^3 - z*w^2 - w^3;
ch_pol_sm := tt^4 - 63*tt^3 - 4484*tt^2;
h1_gal := 1;
rk_pic := 2;
ord_gal := 64;
Elt := [ 2, 2, 2 ];
bp := [ 2, 5, 13 ];


gap_nr := 255;
gl := -x^3 + x^2*z - x^2*w + x*y*w + x*z^2 - x*w^2 - y^3 
      + y^2*z - y^2*w + y*z^2 - y*w^2 - z^3 - z*w^2 - w^3;
ch_pol_sm := tt^4 - 63*tt^3 - 4484*tt^2;
h1_gal := 1;
rk_pic := 2;
ord_gal := 64;
Elt := [ 2, 4 ];
bp := [ 2, 17, 89 ];


gap_nr := 297;
gl := x^2*z - 2*x*w^2 + 11*y^2*w - 22*y*z^2 - 35*z^3 - 46*z^2*w - 30*z*w^2 - 9*w^3;
ch_pol_sm := tt^4 - 63*tt^3 - 4484*tt^2;
h1_gal := 1;
rk_pic := 2;
ord_gal := 128;
Elt := [ 2, 2, 2 ];
bp := [ 2, 3, 11 ];


gap_nr := 306;
gl := -x^3 - x^2*w - x*y*z - x*z^2 - x*w^2 - y^3 - y^2*w - y*z*w - y*w^2 - z^3 - z*w^2 - w^3;
ch_pol_sm := tt^4 - 63*tt^3 - 4484*tt^2;
h1_gal := 1;
rk_pic := 2;
ord_gal := 192;
Elt := [ 2 ];
bp := [ 2, 3, 5, 109 ];


gap_nr := 308;
gl := x^2*z - 2*x*w^2 - 24*y^2*w + 48*y*z^2 - 28*z^3 + 8*z^2*w + 2*w^3;
ch_pol_sm := tt^4 - 63*tt^3 - 4484*tt^2;
h1_gal := 1;
rk_pic := 2;
ord_gal := 192;
Elt := [ 6 ];
bp := [ 2, 3 ];


gap_nr := 330;
gl := x^3 - x^2*y + 7*x*y^2 + x*y*z + x*y*w - 7*y^3 
      + z^3 + z^2*w + 7*z*w^2 + 7*w^3;
ch_pol_sm := tt^4 - 63*tt^3 - 4484*tt^2;
h1_gal := 1;
rk_pic := 2;
ord_gal := 384;
Elt := [ 2, 2 ];
bp := [ 2, 3, 7, 251, 1231 ];

 
gap_nr := 265;
gl := x^2*z - 2*x*w^2 - 131*y^2*w + 262*y*z^2 - 949*z^3  + 14*z^2*w + 70*z*w^2 - w^3;
ch_pol_sm := tt^3 - 63*tt^2 - 6564*tt;
h1_gal := 1;
rk_pic := 2;
ord_gal := 80;
Elt := [ 5 ];
bp := [ 2, 11, 131 ];


gap_nr := 300;
gl := x^2*z - 2*x*w^2 + 4*y^2*w - 8*y*z^2 + 8*z^3 - 7*z^2*w - 4*z*w^2 - 4*w^3;
ch_pol_sm := tt^3 - 63*tt^2 - 6564*tt;
h1_gal := 1;
rk_pic := 2;
ord_gal := 160;
Elt := [ 2 ];
bp := [ 2, 3, 233 ];


gap_nr := 325;
gl := x^2*w + 2*x*y*w - 2*x*z^2 - 2*x*w^2 - 3*y^2*z - 2*y^2*w - 2*y*z^2 
      + 4*y*w^2 + z^3 + z^2*w + z*w^2;
ch_pol_sm := tt^3 - 63*tt^2 - 6564*tt;
h1_gal := 1;
rk_pic := 2;
ord_gal := 320;
Elt := [ 4 ];
bp := [ 2, 3, 5 ];


gap_nr := 343;
gl := x^2*z - 2*x*w^2 - 16*y^2*w + 32*y*z^2 - 20*z^3;
ch_pol_sm := tt^3 - 63*tt^2 - 6564*tt;
h1_gal := 1;
rk_pic := 2;
ord_gal := 960;
Elt := [];
bp := [ 2, 5 ];


gap_nr := 348;
gl := x^3 + x*y^2 + x*y*z + x*z^2 + x*w^2 + y^2*w - y*z^2;
ch_pol_sm := tt^3 - 63*tt^2 - 6564*tt;
h1_gal := 1;
rk_pic := 2;
ord_gal := 1920;
Elt := [ 2 ];
bp := [ 2, 13, 12703 ];