[ 9, 9, 9 ] #H^1 = 1 Rg(Pic) = 1 x_1^3-81*x_1^2 73 |U| = 9 Exp = 9 ElT = [ 9 ] gerade x^2*z - x*y^2 + 3*x*y*w + x*z^2 - x*z*w - x*w^2 + y^2*w + y*z^2 - 3*y*z*w - y*w^2 - z*w^2 144 |U| = 18 Exp = 18 ElT = [ 2 ] ungerade -x^3 - x^2*z - x^2*w + x*y^2 + x*y*z + x*w^2 - y^3 - y^2*z - y*z^2 - y*w^2 - z^3 - z^2*w - z*w^2 - w^3 [ 3, 12, 12 ] #H^1 = 1 Rg(Pic) = 1 x_1^3-99*x_1^2 90 |U| = 12 Exp = 12 ElT = [ 3, 4 ] gerade x^3 + 6*x^2*z - 2*x^2*w - 3*x*y^2 + 3*x*y*z + 9*x*z^2 - x*z*w - 2*x*w^2 - y^3 + 3*y*z^2 - y*w^2 + z^3 + z^2*w - z*w^2 172 |U| = 24 Exp = 12 ElT = [ 2, 2 ] ungerade -x^3 + x^2*z + 7*x*z^2 + y^2*z + y*z^2 - 10*z^3 + 2*w^3 [ 3, 24 ] #H^1 = 1 Rg(Pic) = 1 x_1^2-195*x_1 149 |U| = 24 Exp = 12 ElT = [ 3 ] gerade 7*x^3 + 45*x^2*y + 53*x^2*z - 21*x^2*w + 6*x*y^2 + 38*x*y*z - 3*x*y*w + 5*x*z^2 - 18*x*z*w - y^2*z - 12*y^2*w - 17*y*z^2 - 84*y*w^2 - 41*z^3 + 3*z^2*w + 31*w^3 153 |U| = 24 Exp = 12 ElT = [ 2, 2, 3 ] gerade -2*x^2*y - x^2*z - x^2*w - x*y^2 - 2*x*y*z + 2*x*y*w + 2*x*z^2 - x*z*w - 2*x*w^2 + y^3 + 2*y^2*z - 6*y^2*w - y*z^2 - y*z*w + 5*y*w^2 - z^3 + 2*z^2*w + z*w^2 - w^3 155 |U| = 24 Exp = 12 ElT = [ 3 ] gerade -x^3 - 5*x^2*y - x^2*z - 3*x^2*w + 6*x*y^2 + 7*x*y*z - 9*x*y*w - 12*x*z^2 + 11*x*z*w - 14*x*w^2 - 3*y^3 + 3*y^2*z- 2*y^2*w - 10*y*z^2- 17*y*z*w - 15*y*w^2 + z^3 + 23*z^2*w - 24*z*w^2 + 19*w^3 169 |U| = 24 Exp = 24 ElT = [ 8 ] ungerade x^3 - 3*x^2*y - x^2*w + 2*x*y^2 - x*y*z - 2*x*y*w - x*z^2 - 3*x*z*w - 4*x*w^2 + y^2*z - 4*y^2*w - 9*y*z*w + z^3 + 8*z^2*w + 5*z*w^2 + 3*w^3 216 |U| = 48 Exp = 12 ElT = [ 2, 3 ] gerade x^2*w - 2*x*w^2 - 5*y^3 - 9*y^2*z + 24*y*z^2 + y*w^2 - 5*z^3 + 2*z*w^2 + w^3 232 |U| = 48 Exp = 24 ElT = [ 2 ] ungerade x^2*z + x^2*w + y^3 + y^2*z + y^2*w + y*z^2 + y*w^2 + z^3 + z*w^2 + w^3 235 |U| = 48 Exp = 24 ElT = [ 2, 2 ] ungerade x^3 + x*z^2 - 11*y^2*z + 2*w^3 236 |U| = 48 Exp = 24 ElT = [ 2 ] ungerade x^2*w + x*z^2 + y^3 + z^2*w + w^3 260 |U| = 72 Exp = 12 ElT = [ 3, 3 ] gerade x^3 + 6*x^2*z - x^2*w - 3*x*y^2 + 3*x*y*z - x*y*w + 9*x*z^2 - x*z*w - x*w^2 - y^3 + y^2*w + 3*y*z^2 - y*z*w + y*w^2 + z^3 - z^2*w - z*w^2 267 |U| = 96 Exp = 12 ElT = [ 3 ] gerade x^2*z + x^2*w - x*y^2 - x*z^2 - x*z*w + x*w^2 - y^2*z - y^2*w - z^3 - z*w^2 - w^3 269 |U| = 96 Exp = 12 ElT = [ 2, 2, 3 ] gerade -x^2*y - x^2*z - x*y*z - x*y*w - x*z^2 - x*z*w - y^3 + y^2*z + y*z^2 + y*z*w + y*w^2 - z^2*w + w^3 272 |U| = 96 Exp = 24 ElT = [ 4 ] ungerade -x^2*y - x^2*z - x*y^2 - x*y*w + x*z^2 - x*z*w + y^2*z - y*z^2 + y*z*w + y*w^2 - z^2*w - z*w^2 + w^3 273 |U| = 96 Exp = 24 ElT = [ 2, 2 ] ungerade x^2*w + x*z*w + y^3 + y^2*w + y*z^2 + y*z*w + y*w^2 + z^3 + z*w^2 299 |U| = 144 Exp = 24 ElT = [ 2 ] ungerade x^2*w + x*z^2 + x*w^2 + y^3 + z^3 + z*w^2 305 |U| = 192 Exp = 12 ElT = [ 2 ] gerade -x^3 + x^2*z + x*y*z + x*y*w + x*z^2 - x*w^2 - y^3 - y^2*w + y*z*w - y*w^2 - z^3 - z*w^2 - w^3 307 |U| = 192 Exp = 24 ElT = [ 2 ] ungerade -x^3 + x^2*z - x^2*w + x*y*z + x*z^2 - x*z*w - x*w^2 - y^3 + y^2*w + y*z^2 - y*w^2 - z^3 - z*w^2 - w^3 309 |U| = 192 Exp = 12 ElT = [ 2, 3 ] ungerade -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*z*w + y*w^2 - z^3 + z*w^2 - w^3 310 |U| = 192 Exp = 24 ElT = [ 2, 2 ] ungerade x^2*w + y^3 + y*z^2 + z^3 + z*w^2 324 |U| = 288 Exp = 12 ElT = [ 3, 3 ] gerade x^3 - x^2*y + 9*x^2*z + x^2*w - 4*x*y^2 + 7*x*y*z - x*y*w + 14*x*z^2 - 2*x*z*w - y^3 + y^2*z + y^2*w + 4*y*z^2 + y*z*w + y*w^2 + z^3 - z^2*w + z*w^2 329 |U| = 384 Exp = 24 ElT = [ 2, 2 ] ungerade x^2*w + y^3 + y*z^2 + y*z*w + z^3 + z^2*w + w^3 333 |U| = 576 Exp = 24 ElT = [ 2 ] ungerade x^3 + x^2*w + x*y*z + x*z^2 + x*w^2 + y^3 + y^2*w + y*z^2 + y*w^2 + z^3 + w^3 334 |U| = 576 Exp = 12 ElT = [ 2, 3 ] gerade x^2*w + x*y*z + x*w^2 + y^3 + y^2*w + y*z*w + z^3 + z^2*w 335 |U| = 576 Exp = 12 ElT = [ 2, 3 ] ungerade x^3 - 6*x^2*z - 3*x*y^2 - 3*x*y*z + 9*x*z^2 + x*w^2 + y^3 + 3*y^2*z + y^2*w - 3*z^3 + z*w^2 + w^3 344 |U| = 1152 Exp = 24 ElT = [ 2, 2 ] ungerade (x-y+z)^2*w + x*y*z + (x+y+z)*(x+y+z)*(x+y+z) + w^3 Transitiv: 177 |U| = 27 Exp = 3 ElT = [ 3, 3 ] gerade 2*x^2*z + 2*x^2*w - 4*x*y*z - x*y*w + 3*x*z^2 + 3*x*z*w + 3*x*w^2 - y^3 - 4*y^2*z + 8*y^2*w + 3*y*z^2 - 9*y*z*w - 6*y*w^2 + 9*z^2*w - 3*z*w^2 - 38*w^3 179 |U| = 27 Exp = 9 ElT = [ 3, 3 ] gerade x^3 - 2*x^2*y + 2*x^2*z - 6*x^2*w - 6*x*y^2 + x*y*z + 3*x*y*w + x*z^2 - 8*x*z*w - 15*x*w^2 - 4*y^3 + 3*y^2*w + 3*y*z^2 + y*z*w + 9*y*w^2 - z^3 + 11*z^2*w + 3*z*w^2 - 4*w^3 239 |U| = 54 Exp = 6 ElT = [ 2 ] gerade 3*x^3 - 6*x^2*y - 12*x^2*z + 24*x*y^2 - 24*x*y*z + 12*x*y*w - 9*x*z^2 - 24*x*z*w + x*w^2 - 2*y^3 - 12*y^2*z + 7*y^2*w + 6*y*z^2 - 20*y*z*w + 14*y*w^2 - 16*z^3 - 8*z^2*w + 8*z*w^2 + 19*w^3 245 |U| = 54 Exp = 6 ElT = [ 2, 3 ] ungerade 2*x^3 + 2*x^2*y - x^2*z - 3*x^2*w - 2*x*y^2 + 2*x*y*z - 4*x*y*w - 4*x*z^2 + 2*x*z*w + 9*x*w^2 + 3*y^3 - y^2*z + 2*y^2*w - 3*y*z^2 - 2*y*z*w + 2*y*w^2 + 4*z^3 + 4*z^2*w - z*w^2 + w^3 246 |U| = 54 Exp = 18 ElT = [ 2, 3 ] ungerade -2*x^2*z + x*w^2 + 3*y^3 + z^2*w 266 |U| = 81 Exp = 9 ElT = [ 3, 3 ] gerade 8*x^3 - 22*x^2*y + 5*x^2*z - 35*x^2*w + 72*x*y^2 - 148*x*y*z - 42*x*y*w - 9*x*z^2 - 35*x*z*w - 63*x*w^2 + y^3 - 23*y^2*z + 68*y*z^2 + 7*y*z*w - 105*y*w^2 + z^3 - 35*z^2*w - 56*z*w^2 + 182*w^3 286 |U| = 108 Exp = 12 ElT = [ 4 ] gerade x^3 + x^2*y - 5*x^2*z - x^2*w - x*y^2 + 8*x*y*z + 4*x*y*w + 3*x*z^2 + 6*x*z*w + y^3 - 5*y^2*z + 2*y^2*w - 6*y*z^2 - 3*y*z*w - 3*y*w^2 - 3*z^3 + 9*z*w^2 + 8*w^3 289 |U| = 108 Exp = 6 ElT = [ 2, 2 ] ungerade 4*x^3 + 7*x^2*z + 2*x^2*w + 6*x*y^2 + 2*x*y*z + 4*x*y*w - 2*x*z^2 + 3*x*w^2 + y^3 + 4*y^2*z + 2*y^2*w - 5*y*z^2 + 3*y*w^2 + 3*z^3 + 3*z^2*w - 4*z*w^2 301 |U| = 162 Exp = 18 ElT = [ 2, 3 ] ungerade 13*x^3 + x^2*y - 12*x^2*z - 7*x^2*w + 9*x*y^2 - 4*x*y*z - 10*x*y*w - 2*x*z^2 + 4*x*z*w - 5*x*w^2 - 3*y^3 - 2*y^2*z - 2*y*w^2 - 2*z^3 + 4*z^2*w - 4*z*w^2 302 |U| = 162 Exp = 18 ElT = [ 2, 3 ] gerade -5*x^3 + x^2*y + 22*x^2*z - 41*x^2*w + 2*x*y^2 - 4*x*y*z + 9*x*y*w + 12*x*z^2 + 61*x*z*w - 26*x*w^2 + 11*y^3 - 5*y^2*z + 15*y^2*w + 6*y*z^2 + 36*y*z*w - 8*y*w^2 + 12*z^3 - 56*z^2*w + 3*z*w^2 - 23*w^3 303 |U| = 162 Exp = 18 ElT = [ 2 ] ungerade 2*x^2*y - x^2*z - 2*x*y^2 - x*z^2 - 2*y^2*z + y*z^2 - w^3 313 |U| = 216 Exp = 12 ElT = [ 2, 2 ] gerade 2*x^2*y - x^2*z + x^2*w - 6*x*y*w + 2*x*z^2 + y^3 - 2*y^2*z + 2*y*z*w - z^3 + 3*z^2*w + z*w^2 + w^3 317 |U| = 216 Exp = 12 ElT = [ 2, 2 ] ungerade -x^3 + 3*x^2*w - 3*x*z^2 + 3*x*w^2 - y^3 - z^3 - w^3 319 |U| = 216 Exp = 24 ElT = [ 8 ] ungerade 11*x^3 + 6*x^2*y + 6*x^2*z - 12*x^2*w - 27*x*y^2 - 54*x*y*z + 12*x*y*w - 27*x*z^2 + 12*x*z*w - 94*x*w^2 + 12*y^3 + 48*y^2*z - 68*y^2*w - 12*y*z^2 - 120*y*z*w + 6*y*w^2 - 150*z^2*w - 66*z*w^2 - 67*w^3 326 |U| = 324 Exp = 18 ElT = [ 3 ] gerade x^3 - 10*x^2*y - 25*x^2*z + 20*x^2*w + 20*x*y^2 + 70*x*y*z - 92*x*y*w + 80*x*z^2 - 206*x*z*w + 104*x*w^2 - 2*y^3 - 31*y^2*z - 6*y^2*w - 226*y*z^2 - 140*y*z*w - 24*y*w^2 + 86*z^3 - 22*z^2*w + 35*z*w^2 + 64*w^3 327 |U| = 324 Exp = 18 ElT = [ 2, 2 ] ungerade x^3 + 9*x^2*y + 6*x^2*z + 3*x^2*w - 2*x*y^2 + 27*x*z^2 + 9*x*w^2 - 9*y^2*z + 3*y*z^2 - z^3 + 9*w^3 332 |U| = 432 Exp = 24 ElT = [ 2, 2 ] ungerade -x^3 - y^3 + y^2*z - y^2*w + y*z^2 + y*w^2 - z^3 - z*w^2 - w^3 336 |U| = 648 Exp = 36 ElT = [ 2 ] gerade 6*x^3 + 2*x^2*y + x^2*z - 12*x^2*w - 7*x*y^2 + 8*x*y*z + 12*x*y*w - 19*x*z^2 + 12*x*z*w - 9*x*w^2 + y^3 - y^2*z - 2*y^2*w + 8*y*z^2 + 16*y*z*w + 21*y*w^2 - z^3 + 7*z^2*w - 21*z*w^2 + 8*w^3 337 |U| = 648 Exp = 36 ElT = [ 2 ] ungerade x^3 - 6*x^2*z - 3*x^2*w - 3*x*y^2 - 6*x*y*z - 6*x*z^2 - 6*x*z*w - 6*x*w^2 - 3*y^3 - 4*y^2*z + y^2*w - 6*y*z^2 + 6*y*z*w - 9*y*w^2 + 4*z^3 + 6*z^2*w + 12*z*w^2 - 4*w^3 338 |U| = 648 Exp = 18 ElT = [ 2, 3 ] ungerade x^3 + 15*x^2*y - 5*x^2*z + 5*x^2*w + 5*x*y^2 + 6*x*y*z - 6*x*y*w - 10*x*z^2 - 4*x*z*w + 5*x*w^2 - y^3 + y^2*z - y^2*w - y*z^2 + 8*y*z*w + 11*y*w^2 - 2*z^3 + 3*z^2*w + 9*z*w^2 - w^3 339 |U| = 648 Exp = 36 ElT = [ 3 ] gerade x^2*w + x*y^2 + x*y*z + x*y*w + x*z^2 + x*z*w + y^2*w + y*z^2 + y*z*w + z^2*w + z*w^2 345 |U| = 1296 Exp = 72 ElT = [ 2 ] ungerade x^3 + y^3 + z^3 + w^3 + (x+y+z)^3 - x*y^2 346 |U| = 1296 Exp = 36 ElT = [ 2, 2 ] ungerade -9*x^2*z - 24*x^2*w - 9*x*y^2 - 48*x*y*z + 18*x*z*w + 42*x*w^2 - 8*y^3 + 9*y^2*w + 9*y*z^2 + 84*y*z*w + 48*y*w^2 + 14*z^3 + 48*z^2*w - 9*z*w^2 - 20*w^3 349 |U| = 25920 Exp = 180 ElT = [ ] gerade 2*x^2*y + 37*x*z^2 - 3*x*w^2 - 37*y^2*z - 2*w^3 350 |U| = 51840 Exp = 360 ElT = [ 2 ] ungerade generisch