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Label Polynomial pp ee ff cc Galois group uu tt Visible slopes Slope content Unram. Ext. Eisen. Poly. Ind. of Insep. Assoc. Inertia
2.18.24.10 x18+6x17+8x162x15+14x14+24x13+18x12+120x11+64x10+24x9+232x816x7+228x6+264x548x4+216x3+72x2+216x^{18} + 6 x^{17} + 8 x^{16} - 2 x^{15} + 14 x^{14} + 24 x^{13} + 18 x^{12} + 120 x^{11} + 64 x^{10} + 24 x^{9} + 232 x^{8} - 16 x^{7} + 228 x^{6} + 264 x^{5} - 48 x^{4} + 216 x^{3} + 72 x^{2} + 216 22 66 33 2424 S3×C6S_3 \times C_6 (as 18T6) 66 33 [2][2] [2]36[2]_{3}^{6} t3+t+1t^{3} + t + 1 x6+2x5+2t2x4+2x3+(2t2+2t+2)x2+6x^{6} + 2 x^{5} + 2 t^{2} x^{4} + 2 x^{3} + \left(2 t^{2} + 2 t + 2\right) x^{2} + 6 [3,0][3, 0] [1,2][1, 2]
2.18.24.30 x18+6x16+18x15+2x14+36x13+94x12+128x11+112x10+32x9+256x8+184x7+292x616x5+248x4+120x3+216x2+72x^{18} + 6 x^{16} + 18 x^{15} + 2 x^{14} + 36 x^{13} + 94 x^{12} + 128 x^{11} + 112 x^{10} + 32 x^{9} + 256 x^{8} + 184 x^{7} + 292 x^{6} - 16 x^{5} + 248 x^{4} + 120 x^{3} + 216 x^{2} + 72 22 66 33 2424 S3×C6S_3 \times C_6 (as 18T6) 66 33 [2][2] [2]36[2]_{3}^{6} t3+t+1t^{3} + t + 1 x6+2tx5+(2t2+2t+2)x4+2x3+(2t2+2)x2+4t2+4t+2x^{6} + 2 t x^{5} + \left(2 t^{2} + 2 t + 2\right) x^{4} + 2 x^{3} + \left(2 t^{2} + 2\right) x^{2} + 4 t^{2} + 4 t + 2 [3,0][3, 0] [1,2][1, 2]
2.18.33.58 x188x17+22x16+92x1558x14+172x13+374x12+272x11+444x10+816x9+712x8+1024x7+980x6+784x5+560x4+272x3+136x2+48x+8x^{18} - 8 x^{17} + 22 x^{16} + 92 x^{15} - 58 x^{14} + 172 x^{13} + 374 x^{12} + 272 x^{11} + 444 x^{10} + 816 x^{9} + 712 x^{8} + 1024 x^{7} + 980 x^{6} + 784 x^{5} + 560 x^{4} + 272 x^{3} + 136 x^{2} + 48 x + 8 22 66 33 3333 S3×C6S_3 \times C_6 (as 18T6) 66 33 [3][3] [3]36[3]_{3}^{6} t3+t+1t^{3} + t + 1 x6+4t2x5+(4t+2)x4+4x3+(4t2+4t+6)x2+4x+2x^{6} + 4 t^{2} x^{5} + \left(4 t + 2\right) x^{4} + 4 x^{3} + \left(4 t^{2} + 4 t + 6\right) x^{2} + 4 x + 2 [6,0][6, 0] [1,2][1, 2]
2.18.33.159 x188x17+80x16+48x15182x14492x13746x12176x11+152x10376x9+464x8+560x7+3204x6+4224x5+3360x4+3824x3+2536x2+4080x+3624x^{18} - 8 x^{17} + 80 x^{16} + 48 x^{15} - 182 x^{14} - 492 x^{13} - 746 x^{12} - 176 x^{11} + 152 x^{10} - 376 x^{9} + 464 x^{8} + 560 x^{7} + 3204 x^{6} + 4224 x^{5} + 3360 x^{4} + 3824 x^{3} + 2536 x^{2} + 4080 x + 3624 22 66 33 3333 S3×C6S_3 \times C_6 (as 18T6) 66 33 [3][3] [3]36[3]_{3}^{6} t3+t+1t^{3} + t + 1 x6+(4t2+4t)x5+6tx4+(4t2+4t)x3+(2t+2)x2+(4t2+4t+4)x+12t2+8t+10x^{6} + \left(4 t^{2} + 4 t\right) x^{5} + 6 t x^{4} + \left(4 t^{2} + 4 t\right) x^{3} + \left(2 t + 2\right) x^{2} + \left(4 t^{2} + 4 t + 4\right) x + 12 t^{2} + 8 t + 10 [6,0][6, 0] [1,2][1, 2]
2.18.33.308 x18+8x168x15+28x14176x13182x12128x11684x10536x924x8+544x7+404x6+1904x5+3768x4+3152x3+1072x2+3424x+6392x^{18} + 8 x^{16} - 8 x^{15} + 28 x^{14} - 176 x^{13} - 182 x^{12} - 128 x^{11} - 684 x^{10} - 536 x^{9} - 24 x^{8} + 544 x^{7} + 404 x^{6} + 1904 x^{5} + 3768 x^{4} + 3152 x^{3} + 1072 x^{2} + 3424 x + 6392 22 66 33 3333 S3×C6S_3 \times C_6 (as 18T6) 66 33 [3][3] [3]36[3]_{3}^{6} t3+t+1t^{3} + t + 1 x6+4tx5+(4t2+2t)x4+(4t2+4t)x3+2tx2+(4t2+4t)x+12t2+12t+14x^{6} + 4 t x^{5} + \left(4 t^{2} + 2 t\right) x^{4} + \left(4 t^{2} + 4 t\right) x^{3} + 2 t x^{2} + \left(4 t^{2} + 4 t\right) x + 12 t^{2} + 12 t + 14 [6,0][6, 0] [1,2][1, 2]
2.18.33.309 x18+4x17+6x16+84x15+24x14+304x13+190x12+480x11+1096x10+640x9+1912x8+1312x7+1340x6+3408x5+1016x4+2480x3+1488x2+2728x^{18} + 4 x^{17} + 6 x^{16} + 84 x^{15} + 24 x^{14} + 304 x^{13} + 190 x^{12} + 480 x^{11} + 1096 x^{10} + 640 x^{9} + 1912 x^{8} + 1312 x^{7} + 1340 x^{6} + 3408 x^{5} + 1016 x^{4} + 2480 x^{3} + 1488 x^{2} + 2728 22 66 33 3333 S3×C6S_3 \times C_6 (as 18T6) 66 33 [3][3] [3]36[3]_{3}^{6} t3+t+1t^{3} + t + 1 x6+(4t2+4)x5+2x4+(4t2+4)x3+(4t+4)x2+12t2+4t+10x^{6} + \left(4 t^{2} + 4\right) x^{5} + 2 x^{4} + \left(4 t^{2} + 4\right) x^{3} + \left(4 t + 4\right) x^{2} + 12 t^{2} + 4 t + 10 [6,0][6, 0] [1,2][1, 2]
5.18.15.1 x18+18x16+18x15+135x14+270x13+690x12+1620x11+2475x10+3150x9+10773x8+16200x7+38064x6+9234x5+34200x411862x3+43200x219386x+12329x^{18} + 18 x^{16} + 18 x^{15} + 135 x^{14} + 270 x^{13} + 690 x^{12} + 1620 x^{11} + 2475 x^{10} + 3150 x^{9} + 10773 x^{8} + 16200 x^{7} + 38064 x^{6} + 9234 x^{5} + 34200 x^{4} - 11862 x^{3} + 43200 x^{2} - 19386 x + 12329 55 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+3t+3t^{3} + 3 t + 3 x6+5x^{6} + 5 [0][0] [2][2]
5.18.15.2 x18+75x6375x^{18} + 75 x^{6} - 375 55 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+3t+3t^{3} + 3 t + 3 x6+5tx^{6} + 5 t [0][0] [2][2]
11.18.15.1 x18+242x611979x^{18} + 242 x^{6} - 11979 1111 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+2t+9t^{3} + 2 t + 9 x6+11tx^{6} + 11 t [0][0] [2][2]
11.18.15.2 x18+12x16+54x15+60x14+540x13+1408x12+2160x11+9432x10+4050x9+31332x8+109620x7+516199x6+148176x5+568860x4690336x3+570672x2+248832x+820224x^{18} + 12 x^{16} + 54 x^{15} + 60 x^{14} + 540 x^{13} + 1408 x^{12} + 2160 x^{11} + 9432 x^{10} + 4050 x^{9} + 31332 x^{8} + 109620 x^{7} + 516199 x^{6} + 148176 x^{5} + 568860 x^{4} - 690336 x^{3} + 570672 x^{2} + 248832 x + 820224 1111 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+2t+9t^{3} + 2 t + 9 x6+11x^{6} + 11 [0][0] [2][2]
17.18.15.1 x18+6x16+84x15+15x14+420x13+3011x12+840x11+11367x10+20020x9+18411x8+186480x7+1998610x6+147588x5+1446885x43479756x3+734952x2+1984584x+9683028x^{18} + 6 x^{16} + 84 x^{15} + 15 x^{14} + 420 x^{13} + 3011 x^{12} + 840 x^{11} + 11367 x^{10} + 20020 x^{9} + 18411 x^{8} + 186480 x^{7} + 1998610 x^{6} + 147588 x^{5} + 1446885 x^{4} - 3479756 x^{3} + 734952 x^{2} + 1984584 x + 9683028 1717 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+t+14t^{3} + t + 14 x6+17x^{6} + 17 [0][0] [2][2]
17.18.15.2 x18+289x668782x^{18} + 289 x^{6} - 68782 1717 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+t+14t^{3} + t + 14 x6+17tx^{6} + 17 t [0][0] [2][2]
23.18.15.1 x18+1058x6219006x^{18} + 1058 x^{6} - 219006 2323 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+2t+18t^{3} + 2 t + 18 x6+23tx^{6} + 23 t [0][0] [2][2]
23.18.15.2 x18+12x16+108x15+60x14+1080x13+5089x12+4320x11+38016x10+63180x9+120972x8+783000x7+4887319x6+1283904x5+7691460x47377912x3+7707816x2+15625224x+42132627x^{18} + 12 x^{16} + 108 x^{15} + 60 x^{14} + 1080 x^{13} + 5089 x^{12} + 4320 x^{11} + 38016 x^{10} + 63180 x^{9} + 120972 x^{8} + 783000 x^{7} + 4887319 x^{6} + 1283904 x^{5} + 7691460 x^{4} - 7377912 x^{3} + 7707816 x^{2} + 15625224 x + 42132627 2323 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+2t+18t^{3} + 2 t + 18 x6+23x^{6} + 23 [0][0] [2][2]
29.18.15.1 x18+12x16+162x15+60x14+1620x13+11182x12+6480x11+86328x10+289170x9+267852x8+2515860x7+17270941x6+4503600x5+35823300x4+4796172x3+35798328x2+143350560x+436522680x^{18} + 12 x^{16} + 162 x^{15} + 60 x^{14} + 1620 x^{13} + 11182 x^{12} + 6480 x^{11} + 86328 x^{10} + 289170 x^{9} + 267852 x^{8} + 2515860 x^{7} + 17270941 x^{6} + 4503600 x^{5} + 35823300 x^{4} + 4796172 x^{3} + 35798328 x^{2} + 143350560 x + 436522680 2929 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+2t+27t^{3} + 2 t + 27 x6+29x^{6} + 29 [0][0] [2][2]
29.18.15.2 x18+1682x6658503x^{18} + 1682 x^{6} - 658503 2929 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+2t+27t^{3} + 2 t + 27 x6+29tx^{6} + 29 t [0][0] [2][2]
41.18.15.1 x18+6x16+210x15+15x14+1050x13+18518x12+2100x11+72531x10+644350x9+112101x8+2702700x7+43833832x6+2469390x5+49507560x4+55794550x3+24820176x2+271168590x+2029387125x^{18} + 6 x^{16} + 210 x^{15} + 15 x^{14} + 1050 x^{13} + 18518 x^{12} + 2100 x^{11} + 72531 x^{10} + 644350 x^{9} + 112101 x^{8} + 2702700 x^{7} + 43833832 x^{6} + 2469390 x^{5} + 49507560 x^{4} + 55794550 x^{3} + 24820176 x^{2} + 271168590 x + 2029387125 4141 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+t+35t^{3} + t + 35 x6+41x^{6} + 41 [0][0] [2][2]
41.18.15.2 x18+1681x62412235x^{18} + 1681 x^{6} - 2412235 4141 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+t+35t^{3} + t + 35 x6+41tx^{6} + 41 t [0][0] [2][2]
47.18.15.1 x18+6627x64360566x^{18} + 6627 x^{6} - 4360566 4747 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+3t+42t^{3} + 3 t + 42 x6+47tx^{6} + 47 t [0][0] [2][2]
47.18.15.2 x18+18x16+252x15+135x14+3780x13+27141x12+22680x11+315351x10+1253700x9+1449333x8+13970880x7+84633402x6+38789604x5+304439355x4+305802252x3+454321656x2+2092419000x+5952920804x^{18} + 18 x^{16} + 252 x^{15} + 135 x^{14} + 3780 x^{13} + 27141 x^{12} + 22680 x^{11} + 315351 x^{10} + 1253700 x^{9} + 1449333 x^{8} + 13970880 x^{7} + 84633402 x^{6} + 38789604 x^{5} + 304439355 x^{4} + 305802252 x^{3} + 454321656 x^{2} + 2092419000 x + 5952920804 4747 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+3t+42t^{3} + 3 t + 42 x6+47x^{6} + 47 [0][0] [2][2]
53.18.15.1 x18+18x16+306x15+135x14+4590x13+39714x12+27540x11+465579x10+2330190x9+2129733x8+24730920x7+164038368x6+69954354x5+649060200x4+1093613706x3+969968304x2+5690051334x+18716241401x^{18} + 18 x^{16} + 306 x^{15} + 135 x^{14} + 4590 x^{13} + 39714 x^{12} + 27540 x^{11} + 465579 x^{10} + 2330190 x^{9} + 2129733 x^{8} + 24730920 x^{7} + 164038368 x^{6} + 69954354 x^{5} + 649060200 x^{4} + 1093613706 x^{3} + 969968304 x^{2} + 5690051334 x + 18716241401 5353 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+3t+51t^{3} + 3 t + 51 x6+53x^{6} + 53 [0][0] [2][2]
53.18.15.2 x18+8427x67592727x^{18} + 8427 x^{6} - 7592727 5353 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+3t+51t^{3} + 3 t + 51 x6+53tx^{6} + 53 t [0][0] [2][2]
59.18.15.1 x18+17405x611706603x^{18} + 17405 x^{6} - 11706603 5959 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+5t+57t^{3} + 5 t + 57 x6+59tx^{6} + 59 t [0][0] [2][2]
59.18.15.2 x18+30x16+342x15+375x14+8550x13+51412x12+85500x11+976995x10+3626910x9+7395375x8+58140000x7+263951626x6+272804850x5+1700151450x4+2433470562x3+4177869750x2+16697221470x+36342813987x^{18} + 30 x^{16} + 342 x^{15} + 375 x^{14} + 8550 x^{13} + 51412 x^{12} + 85500 x^{11} + 976995 x^{10} + 3626910 x^{9} + 7395375 x^{8} + 58140000 x^{7} + 263951626 x^{6} + 272804850 x^{5} + 1700151450 x^{4} + 2433470562 x^{3} + 4177869750 x^{2} + 16697221470 x + 36342813987 5959 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+5t+57t^{3} + 5 t + 57 x6+59x^{6} + 59 [0][0] [2][2]
71.18.15.1 x18+20164x622906304x^{18} + 20164 x^{6} - 22906304 7171 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+4t+64t^{3} + 4 t + 64 x6+71tx^{6} + 71 t [0][0] [2][2]
71.18.15.2 x18+24x16+384x15+240x14+7680x13+62933x12+61440x11+980064x10+4807040x9+5955504x8+65041920x7+390503059x6+246816768x5+2133356040x4+3996794624x3+4238775264x2+23937335808x+72466644375x^{18} + 24 x^{16} + 384 x^{15} + 240 x^{14} + 7680 x^{13} + 62933 x^{12} + 61440 x^{11} + 980064 x^{10} + 4807040 x^{9} + 5955504 x^{8} + 65041920 x^{7} + 390503059 x^{6} + 246816768 x^{5} + 2133356040 x^{4} + 3996794624 x^{3} + 4238775264 x^{2} + 23937335808 x + 72466644375 7171 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+4t+64t^{3} + 4 t + 64 x6+71x^{6} + 71 [0][0] [2][2]
83.18.15.1 x18+20667x646314747x^{18} + 20667 x^{6} - 46314747 8383 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+3t+81t^{3} + 3 t + 81 x6+83tx^{6} + 83 t [0][0] [2][2]
83.18.15.2 x18+18x16+486x15+135x14+7290x13+99204x12+43740x11+1176219x10+9751590x9+5349483x8+97671420x7+886741518x6+282739734x5+4028689350x4+14619279006x3+6033836394x2+59532739614x+293372245691x^{18} + 18 x^{16} + 486 x^{15} + 135 x^{14} + 7290 x^{13} + 99204 x^{12} + 43740 x^{11} + 1176219 x^{10} + 9751590 x^{9} + 5349483 x^{8} + 97671420 x^{7} + 886741518 x^{6} + 282739734 x^{5} + 4028689350 x^{4} + 14619279006 x^{3} + 6033836394 x^{2} + 59532739614 x + 293372245691 8383 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+3t+81t^{3} + 3 t + 81 x6+83x^{6} + 83 [0][0] [2][2]
89.18.15.1 x18+18x16+516x15+135x14+7740x13+111747x12+46440x11+1326087x10+11712340x9+6028263x8+116765640x7+1110998718x6+338635836x5+5109180705x4+20112416316x3+7653467412x2+80535987936x+419455081800x^{18} + 18 x^{16} + 516 x^{15} + 135 x^{14} + 7740 x^{13} + 111747 x^{12} + 46440 x^{11} + 1326087 x^{10} + 11712340 x^{9} + 6028263 x^{8} + 116765640 x^{7} + 1110998718 x^{6} + 338635836 x^{5} + 5109180705 x^{4} + 20112416316 x^{3} + 7653467412 x^{2} + 80535987936 x + 419455081800 8989 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+3t+86t^{3} + 3 t + 86 x6+89x^{6} + 89 [0][0] [2][2]
89.18.15.2 x18+23763x660627334x^{18} + 23763 x^{6} - 60627334 8989 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+3t+86t^{3} + 3 t + 86 x6+89tx^{6} + 89 t [0][0] [2][2]
101.18.15.1 x18+18x16+594x15+135x14+8910x13+147858x12+53460x11+1758123x10+18066510x9+7981173x8+177594120x7+1875580176x6+517626450x5+8923750200x4+42935829354x3+13371857568x2+164026444230x+971047065545x^{18} + 18 x^{16} + 594 x^{15} + 135 x^{14} + 8910 x^{13} + 147858 x^{12} + 53460 x^{11} + 1758123 x^{10} + 18066510 x^{9} + 7981173 x^{8} + 177594120 x^{7} + 1875580176 x^{6} + 517626450 x^{5} + 8923750200 x^{4} + 42935829354 x^{3} + 13371857568 x^{2} + 164026444230 x + 971047065545 101101 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+3t+99t^{3} + 3 t + 99 x6+101x^{6} + 101 [0][0] [2][2]
101.18.15.2 x18+30603x6101999799x^{18} + 30603 x^{6} - 101999799 101101 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+3t+99t^{3} + 3 t + 99 x6+101tx^{6} + 101 t [0][0] [2][2]
107.18.15.1 x18+57245x6128629515x^{18} + 57245 x^{6} - 128629515 107107 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+5t+105t^{3} + 5 t + 105 x6+107tx^{6} + 107 t [0][0] [2][2]
107.18.15.2 x18+30x16+630x15+375x14+15750x13+168196x12+157500x11+3304035x10+22254750x9+24945375x8+354312000x7+2405240122x6+1718183250x5+18866092650x4+60921072450x3+46919211750x2+367798110750x+1380376857843x^{18} + 30 x^{16} + 630 x^{15} + 375 x^{14} + 15750 x^{13} + 168196 x^{12} + 157500 x^{11} + 3304035 x^{10} + 22254750 x^{9} + 24945375 x^{8} + 354312000 x^{7} + 2405240122 x^{6} + 1718183250 x^{5} + 18866092650 x^{4} + 60921072450 x^{3} + 46919211750 x^{2} + 367798110750 x + 1380376857843 107107 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+5t+105t^{3} + 5 t + 105 x6+107x^{6} + 107 [0][0] [2][2]
113.18.15.1 x18+48x16+660x15+960x14+26400x13+192079x12+422400x11+5847744x10+28134700x9+70218048x8+661346400x7+3147571759x6+5075389440x5+36870158160x4+87592940600x3+144538157184x2+743524842720x+1825875840013x^{18} + 48 x^{16} + 660 x^{15} + 960 x^{14} + 26400 x^{13} + 192079 x^{12} + 422400 x^{11} + 5847744 x^{10} + 28134700 x^{9} + 70218048 x^{8} + 661346400 x^{7} + 3147571759 x^{6} + 5075389440 x^{5} + 36870158160 x^{4} + 87592940600 x^{3} + 144538157184 x^{2} + 743524842720 x + 1825875840013 113113 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+8t+110t^{3} + 8 t + 110 x6+113x^{6} + 113 [0][0] [2][2]
113.18.15.2 x18+102152x6158718670x^{18} + 102152 x^{6} - 158718670 113113 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+8t+110t^{3} + 8 t + 110 x6+113tx^{6} + 113 t [0][0] [2][2]
131.18.15.1 x18+51483x6290003739x^{18} + 51483 x^{6} - 290003739 131131 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+3t+129t^{3} + 3 t + 129 x6+131tx^{6} + 131 t [0][0] [2][2]
131.18.15.2 x18+18x16+774x15+135x14+11610x13+250548x12+69660x11+2987163x10+40607910x9+13533723x8+391280220x7+5103045246x6+1148449590x5+25530484950x4+173434221054x3+38272301658x2+622559906910x+4718315655755x^{18} + 18 x^{16} + 774 x^{15} + 135 x^{14} + 11610 x^{13} + 250548 x^{12} + 69660 x^{11} + 2987163 x^{10} + 40607910 x^{9} + 13533723 x^{8} + 391280220 x^{7} + 5103045246 x^{6} + 1148449590 x^{5} + 25530484950 x^{4} + 173434221054 x^{3} + 38272301658 x^{2} + 622559906910 x + 4718315655755 131131 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+3t+129t^{3} + 3 t + 129 x6+131x^{6} + 131 [0][0] [2][2]
137.18.15.1 x18+36x16+804x15+540x14+24120x13+274071x12+289440x11+6463872x10+47105020x9+58446036x8+881320680x7+6110182575x6+5155852608x5+59711962860x4+220204895544x3+178117502472x2+1507281043464x+5926050257733x^{18} + 36 x^{16} + 804 x^{15} + 540 x^{14} + 24120 x^{13} + 274071 x^{12} + 289440 x^{11} + 6463872 x^{10} + 47105020 x^{9} + 58446036 x^{8} + 881320680 x^{7} + 6110182575 x^{6} + 5155852608 x^{5} + 59711962860 x^{4} + 220204895544 x^{3} + 178117502472 x^{2} + 1507281043464 x + 5926050257733 137137 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+6t+134t^{3} + 6 t + 134 x6+137x^{6} + 137 [0][0] [2][2]
137.18.15.2 x18+112614x6344561302x^{18} + 112614 x^{6} - 344561302 137137 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+6t+134t^{3} + 6 t + 134 x6+137tx^{6} + 137 t [0][0] [2][2]
149.18.15.1 x18+18x16+882x15+135x14+13230x13+325122x12+79380x11+3880107x10+60483150x9+17565093x8+578045160x7+8401329984x6+1701343602x5+42919167240x4+342747017802x3+64348305552x2+1201164636294x+10300987559321x^{18} + 18 x^{16} + 882 x^{15} + 135 x^{14} + 13230 x^{13} + 325122 x^{12} + 79380 x^{11} + 3880107 x^{10} + 60483150 x^{9} + 17565093 x^{8} + 578045160 x^{7} + 8401329984 x^{6} + 1701343602 x^{5} + 42919167240 x^{4} + 342747017802 x^{3} + 64348305552 x^{2} + 1201164636294 x + 10300987559321 149149 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+3t+147t^{3} + 3 t + 147 x6+149x^{6} + 149 [0][0] [2][2]
149.18.15.2 x18+66603x6486268503x^{18} + 66603 x^{6} - 486268503 149149 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+3t+147t^{3} + 3 t + 147 x6+149tx^{6} + 149 t [0][0] [2][2]
167.18.15.1 x18+195223x6754509006x^{18} + 195223 x^{6} - 754509006 167167 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+7t+162t^{3} + 7 t + 162 x6+167tx^{6} + 167 t [0][0] [2][2]
167.18.15.2 x18+42x16+972x15+735x14+34020x13+401021x12+476280x11+11030439x10+84306420x9+116205117x8+1814354640x7+12726449338x6+12420382212x5+148343449275x4+592120006092x3+515951235744x2+4565618841672x+18431773475444x^{18} + 42 x^{16} + 972 x^{15} + 735 x^{14} + 34020 x^{13} + 401021 x^{12} + 476280 x^{11} + 11030439 x^{10} + 84306420 x^{9} + 116205117 x^{8} + 1814354640 x^{7} + 12726449338 x^{6} + 12420382212 x^{5} + 148343449275 x^{4} + 592120006092 x^{3} + 515951235744 x^{2} + 4565618841672 x + 18431773475444 167167 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+7t+162t^{3} + 7 t + 162 x6+167x^{6} + 167 [0][0] [2][2]
173.18.15.1 x18+12x16+1026x15+60x14+10260x13+439294x12+41040x11+3500856x10+95648850x9+10558092x8+605432340x7+14979518797x6+1191563568x5+52217993220x4+748611549036x3+52216354296x2+1712702374560x+25448746759416x^{18} + 12 x^{16} + 1026 x^{15} + 60 x^{14} + 10260 x^{13} + 439294 x^{12} + 41040 x^{11} + 3500856 x^{10} + 95648850 x^{9} + 10558092 x^{8} + 605432340 x^{7} + 14979518797 x^{6} + 1191563568 x^{5} + 52217993220 x^{4} + 748611549036 x^{3} + 52216354296 x^{2} + 1712702374560 x + 25448746759416 173173 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+2t+171t^{3} + 2 t + 171 x6+173x^{6} + 173 [0][0] [2][2]
173.18.15.2 x18+59858x6885389607x^{18} + 59858 x^{6} - 885389607 173173 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+2t+171t^{3} + 2 t + 171 x6+173tx^{6} + 173 t [0][0] [2][2]
179.18.15.1 x18+128164x61015155003x^{18} + 128164 x^{6} - 1015155003 179179 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+4t+177t^{3} + 4 t + 177 x6+179tx^{6} + 179 t [0][0] [2][2]
179.18.15.2 x18+24x16+1062x15+240x14+21240x13+471752x12+169920x11+7505616x10+106831890x9+45248784x8+1343621160x7+17215341295x6+5288012352x5+119916735480x4+900847464192x3+239615658816x2+4073420011968x+31281845110592x^{18} + 24 x^{16} + 1062 x^{15} + 240 x^{14} + 21240 x^{13} + 471752 x^{12} + 169920 x^{11} + 7505616 x^{10} + 106831890 x^{9} + 45248784 x^{8} + 1343621160 x^{7} + 17215341295 x^{6} + 5288012352 x^{5} + 119916735480 x^{4} + 900847464192 x^{3} + 239615658816 x^{2} + 4073420011968 x + 31281845110592 179179 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+4t+177t^{3} + 4 t + 177 x6+179x^{6} + 179 [0][0] [2][2]
191.18.15.1 x18+145924x61198473812x^{18} + 145924 x^{6} - 1198473812 191191 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+4t+172t^{3} + 4 t + 172 x6+191tx^{6} + 191 t [0][0] [2][2]
191.18.15.2 x18+24x16+1032x15+240x14+20640x13+445613x12+165120x11+7085664x10+97501640x9+42744624x8+1234375200x7+15632312083x6+4848121344x5+107169720840x4+764262460112x3+214138209504x2+3518774284128x+26399210781039x^{18} + 24 x^{16} + 1032 x^{15} + 240 x^{14} + 20640 x^{13} + 445613 x^{12} + 165120 x^{11} + 7085664 x^{10} + 97501640 x^{9} + 42744624 x^{8} + 1234375200 x^{7} + 15632312083 x^{6} + 4848121344 x^{5} + 107169720840 x^{4} + 764262460112 x^{3} + 214138209504 x^{2} + 3518774284128 x + 26399210781039 191191 66 33 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ]66[\ ]_{6}^{6} t3+4t+172t^{3} + 4 t + 172 x6+191x^{6} + 191 [0][0] [2][2]
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