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Label Polynomial Discriminant Galois group Class group Regulator
18.2.897...489.1 $x^{18} - x^{17} + 3 x^{15} - x^{14} + x^{13} + 7 x^{12} + 2 x^{11} + 3 x^{10} + 11 x^{9} + 3 x^{8} + 2 x^{7} + 7 x^{6} + x^{5} - x^{4} + 3 x^{3} - x + 1$ $7^{12}\cdot 41^{3}\cdot 97^{2}$ $D_6\wr C_3$ (as 18T472) trivial $95.2465332123$
18.2.212...913.1 $x^{18} - 3 x^{17} + 5 x^{16} - 6 x^{15} + 5 x^{14} + x^{13} - 9 x^{12} + 18 x^{11} - 26 x^{10} + 29 x^{9} - 26 x^{8} + 18 x^{7} - 9 x^{6} + x^{5} + 5 x^{4} - 6 x^{3} + 5 x^{2} - 3 x + 1$ $7^{12}\cdot 41^{2}\cdot 97^{3}$ $D_6\wr C_3$ (as 18T472) trivial $158.336114215$
18.8.307...727.1 $x^{18} - 5 x^{17} + 4 x^{16} + 18 x^{15} - 42 x^{14} + 40 x^{13} - 48 x^{12} + 70 x^{11} - 69 x^{10} + 89 x^{9} - 67 x^{8} - 96 x^{7} + 187 x^{6} - 65 x^{5} - 54 x^{4} + 47 x^{3} - 3 x^{2} - 7 x + 1$ $-\,7^{15}\cdot 41^{3}\cdot 97^{2}$ $D_6\wr C_3$ (as 18T472) trivial $6722.94980486$
18.4.710...744.1 $x^{18} - 4 x^{16} + 4 x^{14} + x^{12} - 5 x^{10} + 11 x^{8} - 8 x^{6} + 5 x^{4} - 5 x^{2} + 1$ $-\,2^{18}\cdot 7^{12}\cdot 1399^{2}$ $D_6\wr C_3$ (as 18T472) trivial $4470.74149556$
18.4.710...744.2 $x^{18} - x^{16} + 2 x^{14} + x^{12} - 3 x^{10} + 2 x^{8} - x^{6} - 4 x^{4} + x^{2} + 1$ $-\,2^{18}\cdot 7^{12}\cdot 1399^{2}$ $D_6\wr C_3$ (as 18T472) trivial $5513.9853122$
18.8.728...159.1 $x^{18} + x^{16} - 5 x^{15} - 13 x^{14} + 11 x^{13} - 2 x^{12} + 41 x^{11} + 6 x^{10} - 68 x^{9} + 53 x^{8} - 63 x^{7} + x^{6} + 50 x^{5} - 28 x^{4} + 24 x^{3} - 5 x^{2} - 4 x + 1$ $-\,7^{15}\cdot 41^{2}\cdot 97^{3}$ $D_6\wr C_3$ (as 18T472) trivial $11002.0590961$
18.6.150...009.1 $x^{18} - 3 x^{17} + x^{15} + 5 x^{14} + 17 x^{13} - 28 x^{12} - 12 x^{11} + 6 x^{10} + 17 x^{9} - 23 x^{8} + 13 x^{7} + 33 x^{6} - 15 x^{5} - 24 x^{4} + 3 x^{3} + 10 x^{2} - x - 1$ $7^{12}\cdot 41^{5}\cdot 97^{2}$ $D_6\wr C_3$ (as 18T472) trivial $10471.6837975$
18.2.247...873.1 $x^{18} - 2 x^{17} + 5 x^{16} - 12 x^{15} + 17 x^{14} - 27 x^{13} + 35 x^{12} - 23 x^{11} + 8 x^{10} + 21 x^{9} - 78 x^{8} + 130 x^{7} - 128 x^{6} + 164 x^{5} - 101 x^{4} + 86 x^{3} - 17 x^{2} + 5 x - 1$ $7^{12}\cdot 97^{3}\cdot 1399^{2}$ $D_6\wr C_3$ (as 18T472) trivial $6378.5311844$
18.2.247...873.2 $x^{18} - 2 x^{17} + 3 x^{16} - 12 x^{15} + 17 x^{14} - 11 x^{13} + 30 x^{12} - 31 x^{11} - 20 x^{10} - 14 x^{9} + 62 x^{8} - 30 x^{7} + 105 x^{6} - 209 x^{5} + 172 x^{4} - 33 x^{3} - 47 x^{2} - 9 x - 1$ $7^{12}\cdot 97^{3}\cdot 1399^{2}$ $D_6\wr C_3$ (as 18T472) trivial $6354.40327047$
18.6.365...433.1 $x^{18} - 6 x^{16} - x^{15} + 9 x^{14} + 18 x^{13} - x^{12} - 60 x^{11} + 33 x^{10} + 28 x^{9} - 66 x^{8} + 81 x^{7} - 44 x^{6} + 3 x^{5} + 15 x^{4} - 19 x^{3} + 6 x^{2} + 3 x - 1$ $3^{24}\cdot 73^{3}\cdot 577^{2}$ $D_6\wr C_3$ (as 18T472) trivial $16259.2607836$
18.4.573...376.1 $x^{18} + 4 x^{16} + 10 x^{14} + 4 x^{12} - 24 x^{10} - 23 x^{8} + 6 x^{6} + 15 x^{4} + 7 x^{2} + 1$ $-\,2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2}$ $D_6\wr C_3$ (as 18T472) trivial $12064.8420969$
18.8.573...376.6 $x^{18} - 3 x^{16} - 4 x^{14} + 25 x^{12} - 38 x^{10} + 26 x^{8} - 15 x^{6} + 15 x^{4} - 7 x^{2} + 1$ $-\,2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2}$ $D_6\wr C_3$ (as 18T472) trivial $31797.506877630192$
18.4.124...176.1 $x^{18} + 3 x^{16} - 7 x^{12} - 30 x^{10} - 72 x^{8} - 47 x^{6} + 30 x^{4} + 12 x^{2} + 1$ $-\,2^{18}\cdot 3^{24}\cdot 1297^{2}$ $D_6\wr C_3$ (as 18T472) trivial $19131.524628$
18.8.124...176.1 $x^{18} + 3 x^{14} - 6 x^{12} - 9 x^{10} - 12 x^{8} + 29 x^{6} + 9 x^{4} - 15 x^{2} + 1$ $-\,2^{18}\cdot 3^{24}\cdot 1297^{2}$ $D_6\wr C_3$ (as 18T472) trivial $51430.002503910466$
18.6.199...417.1 $x^{18} - x^{17} - 3 x^{16} + 7 x^{15} - 15 x^{14} - 39 x^{13} + 38 x^{12} + 19 x^{11} - 121 x^{10} - 27 x^{9} + 104 x^{8} + 12 x^{7} - 62 x^{6} - 26 x^{5} + 57 x^{4} + 74 x^{3} + 15 x^{2} - 5 x - 1$ $7^{12}\cdot 41^{2}\cdot 97^{5}$ $D_6\wr C_3$ (as 18T472) trivial $37759.6260558$
18.6.289...217.1 $x^{18} - 3 x^{17} - 3 x^{16} + 24 x^{15} - 51 x^{14} + 69 x^{13} - 67 x^{12} + 48 x^{11} - 24 x^{10} + 13 x^{9} - 24 x^{8} + 48 x^{7} - 67 x^{6} + 69 x^{5} - 51 x^{4} + 24 x^{3} - 3 x^{2} - 3 x + 1$ $3^{24}\cdot 73^{2}\cdot 577^{3}$ $D_6\wr C_3$ (as 18T472) trivial $55706.1333097$
18.12.987...691.1 $x^{18} - 3 x^{17} - 12 x^{16} + 46 x^{15} + 15 x^{14} - 165 x^{13} + 11 x^{12} + 321 x^{11} - 9 x^{10} - 405 x^{9} - 60 x^{8} + 297 x^{7} + 126 x^{6} - 90 x^{5} - 93 x^{4} - 10 x^{3} + 21 x^{2} + 9 x + 1$ $-\,3^{27}\cdot 73^{3}\cdot 577^{2}$ $D_6\wr C_3$ (as 18T472) trivial $318063.575479$
18.0.235...416.1 $x^{18} + 6 x^{16} - 3 x^{14} - 64 x^{12} - 75 x^{10} + 124 x^{8} + 366 x^{6} + 377 x^{4} + 194 x^{2} + 41$ $-\,2^{18}\cdot 7^{12}\cdot 41^{3}\cdot 97^{2}$ $D_6\wr C_3$ (as 18T472) $[4]$ $9031.17095004$
18.10.235...416.1 $x^{18} - 6 x^{16} - 3 x^{14} + 64 x^{12} - 75 x^{10} - 124 x^{8} + 366 x^{6} - 377 x^{4} + 194 x^{2} - 41$ $2^{18}\cdot 7^{12}\cdot 41^{3}\cdot 97^{2}$ $D_6\wr C_3$ (as 18T472) trivial $331347.433899$
18.6.235...416.4 $x^{18} - 3 x^{16} - 6 x^{14} + 8 x^{12} + 29 x^{10} - 3 x^{8} - 82 x^{6} + 18 x^{4} + 80 x^{2} - 41$ $2^{18}\cdot 7^{12}\cdot 41^{3}\cdot 97^{2}$ $D_6\wr C_3$ (as 18T472) trivial $136678.81618157946$
18.10.556...472.1 $x^{18} - 5 x^{16} + 31 x^{12} - 54 x^{10} - 100 x^{8} + 603 x^{6} - 886 x^{4} + 506 x^{2} - 97$ $2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{3}$ $D_6\wr C_3$ (as 18T472) trivial $553431.752643$
18.2.649...193.1 $x^{18} + 7 x^{16} - x^{15} + 21 x^{14} + 42 x^{13} - 99 x^{12} + 364 x^{11} - 581 x^{10} + 1146 x^{9} - 1225 x^{8} + 1330 x^{7} - 754 x^{6} + 371 x^{5} - 84 x^{4} + 10 x^{3} - 1$ $7^{12}\cdot 97^{3}\cdot 22679^{2}$ $D_6\wr C_3$ (as 18T472) trivial $88562.6720172$
18.6.649...193.1 $x^{18} + 7 x^{16} - 8 x^{15} - 7 x^{14} - 28 x^{13} - 253 x^{12} - 168 x^{11} - 364 x^{10} - 639 x^{9} - 448 x^{8} - 350 x^{7} - 348 x^{6} - 112 x^{5} - 7 x^{4} - 32 x^{3} + 7 x^{2} + 7 x - 1$ $7^{12}\cdot 97^{3}\cdot 22679^{2}$ $D_6\wr C_3$ (as 18T472) trivial $212857.267748$
18.6.649...193.2 $x^{18} + 7 x^{16} - 13 x^{15} + 21 x^{14} - 49 x^{13} - 8 x^{12} - 49 x^{11} - 231 x^{10} + 310 x^{9} - 490 x^{8} + 364 x^{7} - 607 x^{6} + 98 x^{5} - 56 x^{4} - 164 x^{3} + 14 x^{2} + 14 x - 1$ $7^{12}\cdot 97^{3}\cdot 22679^{2}$ $D_6\wr C_3$ (as 18T472) trivial $238937.486343$
18.12.780...859.1 $x^{18} - 15 x^{16} - x^{15} + 60 x^{14} + 48 x^{13} - 40 x^{12} - 375 x^{11} + 87 x^{10} + 729 x^{9} - 756 x^{8} + 336 x^{7} + 108 x^{6} - 279 x^{5} + 108 x^{4} + 28 x^{3} - 21 x^{2} + 1$ $-\,3^{27}\cdot 73^{2}\cdot 577^{3}$ $D_6\wr C_3$ (as 18T472) trivial $987631.658974$
18.12.101...104.1 $x^{18} - 3 x^{16} - 4 x^{14} - 23 x^{12} + 79 x^{10} + 139 x^{8} - 303 x^{6} + 135 x^{4} - 21 x^{2} + 1$ $-\,2^{18}\cdot 7^{12}\cdot 52879^{2}$ $D_6\wr C_3$ (as 18T472) trivial $973728.615269$
18.8.101...104.1 $x^{18} + x^{16} - 30 x^{14} + 75 x^{12} - 87 x^{10} + 31 x^{8} + 40 x^{6} - 24 x^{4} - 7 x^{2} + 1$ $-\,2^{18}\cdot 7^{12}\cdot 52879^{2}$ $D_6\wr C_3$ (as 18T472) trivial $368972.618742$
18.8.101...104.2 $x^{18} + 2 x^{16} - 22 x^{14} + 19 x^{12} + 36 x^{10} - 170 x^{8} + 173 x^{6} - 20 x^{4} - 7 x^{2} + 1$ $-\,2^{18}\cdot 7^{12}\cdot 52879^{2}$ $D_6\wr C_3$ (as 18T472) trivial $474885.391467$
18.12.101...584.1 $x^{18} - 10 x^{16} + 36 x^{14} - 48 x^{12} - 27 x^{10} + 158 x^{8} - 180 x^{6} + 88 x^{4} - 18 x^{2} + 1$ $-\,2^{18}\cdot 7^{12}\cdot 52919^{2}$ $D_6\wr C_3$ (as 18T472) trivial $1197133.31669$
18.0.161...272.1 $x^{18} + 12 x^{16} + 54 x^{14} + 173 x^{12} + 681 x^{10} + 2232 x^{8} + 4894 x^{6} + 7221 x^{4} + 5484 x^{2} + 1297$ $-\,2^{18}\cdot 3^{24}\cdot 1297^{3}$ $D_6\wr C_3$ (as 18T472) $[20]$ $19338.0324864$
18.0.250...467.1 $x^{18} - 4 x^{17} + 27 x^{16} - 60 x^{15} + 184 x^{14} - 362 x^{13} + 1149 x^{12} - 2823 x^{11} + 6431 x^{10} - 8311 x^{9} + 12191 x^{8} - 16179 x^{7} + 72116 x^{6} - 64228 x^{5} - 9158 x^{4} + 235477 x^{3} + 50634 x^{2} - 611585 x + 912673$ $-\,7^{12}\cdot 1399^{2}\cdot 4523^{3}$ $D_6\wr C_3$ (as 18T472) $[3]$ $471320.757853$
18.0.250...467.2 $x^{18} - 3 x^{17} + 13 x^{16} - 38 x^{15} + 58 x^{14} - 100 x^{13} - 41 x^{12} + 1255 x^{11} - 2627 x^{10} + 6918 x^{9} - 10699 x^{8} - 9658 x^{7} + 36052 x^{6} - 83059 x^{5} + 215570 x^{4} - 28704 x^{3} - 43068 x^{2} - 639812 x + 912673$ $-\,7^{12}\cdot 1399^{2}\cdot 4523^{3}$ $D_6\wr C_3$ (as 18T472) $[6]$ $216238.286744$
18.0.250...467.3 $x^{18} - 3 x^{17} + 2 x^{16} - 11 x^{15} + 4 x^{14} + 5 x^{13} - 9 x^{12} + 431 x^{11} + 320 x^{10} - 327 x^{9} - 3 x^{8} - 5172 x^{7} - 7827 x^{6} - 39344 x^{5} + 127973 x^{4} - 331152 x^{3} + 805779 x^{2} - 837401 x + 912673$ $-\,7^{12}\cdot 1399^{2}\cdot 4523^{3}$ $D_6\wr C_3$ (as 18T472) $[3]$ $575924.9149668515$
18.2.347...672.1 $x^{18} + 7 x^{16} - 28 x^{14} - 182 x^{12} + 147 x^{10} - 2009 x^{8} - 14847 x^{6} - 13034 x^{4} - 3773 x^{2} - 343$ $2^{18}\cdot 7^{15}\cdot 52879^{2}$ $D_6\wr C_3$ (as 18T472) trivial $2800923.07754$
18.0.958...352.1 $x^{18} + 24 x^{16} + 222 x^{14} + 1049 x^{12} + 2799 x^{10} + 4389 x^{8} + 4075 x^{6} + 2187 x^{4} + 624 x^{2} + 73$ $-\,2^{18}\cdot 3^{24}\cdot 73^{3}\cdot 577^{2}$ $D_6\wr C_3$ (as 18T472) $[84]$ $26510.9946997$
18.18.958...352.1 $x^{18} - 24 x^{16} + 222 x^{14} - 1049 x^{12} + 2799 x^{10} - 4389 x^{8} + 4075 x^{6} - 2187 x^{4} + 624 x^{2} - 73$ $2^{18}\cdot 3^{24}\cdot 73^{3}\cdot 577^{2}$ $D_6\wr C_3$ (as 18T472) trivial $128886114.001$
18.0.757...248.1 $x^{18} + 30 x^{16} + 357 x^{14} + 2216 x^{12} + 7917 x^{10} + 16836 x^{8} + 21078 x^{6} + 14613 x^{4} + 4866 x^{2} + 577$ $-\,2^{18}\cdot 3^{24}\cdot 73^{2}\cdot 577^{3}$ $D_6\wr C_3$ (as 18T472) $[3, 84]$ $26510.9946997$
18.18.757...248.1 $x^{18} - 30 x^{16} + 357 x^{14} - 2216 x^{12} + 7917 x^{10} - 16836 x^{8} + 21078 x^{6} - 14613 x^{4} + 4866 x^{2} - 577$ $2^{18}\cdot 3^{24}\cdot 73^{2}\cdot 577^{3}$ $D_6\wr C_3$ (as 18T472) trivial $377837069.192$
18.0.147...047.1 $x^{18} + 28 x^{16} - 31 x^{15} + 343 x^{14} - 560 x^{13} + 2535 x^{12} - 4606 x^{11} + 14791 x^{10} - 17924 x^{9} + 29428 x^{8} + 15897 x^{7} - 50004 x^{6} + 185423 x^{5} - 114961 x^{4} + 122123 x^{3} + 237580 x^{2} - 217679 x + 451879$ $-\,7^{12}\cdot 97^{3}\cdot 22679^{3}$ $D_6\wr C_3$ (as 18T472) $[104]$ $99994.2543337$
18.6.331...952.1 $x^{18} - 6 x^{16} + 15 x^{14} - 28 x^{12} + 47 x^{10} - 54 x^{8} + 52 x^{6} - 46 x^{4} + 19 x^{2} - 13$ $2^{18}\cdot 7^{12}\cdot 13^{3}\cdot 239^{2}\cdot 853^{2}$ $D_6\wr C_3$ (as 18T472) trivial $84186702.5914$
18.14.536...416.1 $x^{18} - 12 x^{16} - 38 x^{14} + 642 x^{12} + 1195 x^{10} - 28537 x^{8} + 111638 x^{6} - 195808 x^{4} + 163791 x^{2} - 52879$ $2^{18}\cdot 7^{12}\cdot 52879^{3}$ $D_6\wr C_3$ (as 18T472) trivial $646900087.476$
18.14.537...696.1 $x^{18} - 26 x^{16} + 277 x^{14} - 1739 x^{12} + 8504 x^{10} - 34994 x^{8} + 100505 x^{6} - 170701 x^{4} + 150743 x^{2} - 52919$ $2^{18}\cdot 7^{12}\cdot 52919^{3}$ $D_6\wr C_3$ (as 18T472) trivial $402701722.218$
18.6.222...216.1 $x^{18} - 28 x^{16} + 210 x^{14} + 56 x^{12} - 27440 x^{10} + 350105 x^{8} + 1255282 x^{6} - 17267649 x^{4} - 48409305 x^{2} - 313046839$ $2^{18}\cdot 7^{15}\cdot 97^{3}\cdot 1399^{2}$ $D_6\wr C_3$ (as 18T472) trivial $193202004.379$
18.6.222...216.2 $x^{18} - 35 x^{16} + 301 x^{14} - 2296 x^{12} + 19061 x^{10} + 47285 x^{8} + 453005 x^{6} + 5123734 x^{4} - 58091166 x^{2} - 313046839$ $2^{18}\cdot 7^{15}\cdot 97^{3}\cdot 1399^{2}$ $D_6\wr C_3$ (as 18T472) trivial $153539667.1016583$
18.0.299...247.1 $x^{18} + 34 x^{16} - 13 x^{15} + 567 x^{14} - 279 x^{13} + 7100 x^{12} - 380 x^{11} + 71045 x^{10} + 25446 x^{9} + 522337 x^{8} + 265934 x^{7} + 2635061 x^{6} + 1204439 x^{5} + 8662708 x^{4} + 2593860 x^{3} + 16839843 x^{2} + 2010611 x + 14591569$ $-\,7^{12}\cdot 71^{3}\cdot 113^{3}\cdot 64679^{2}$ $D_6\wr C_3$ (as 18T472) $[6]$ $26315478.7454$
18.0.299...247.2 $x^{18} + 42 x^{16} - 13 x^{15} + 819 x^{14} - 333 x^{13} + 10315 x^{12} - 3234 x^{11} + 91408 x^{10} - 7235 x^{9} + 580513 x^{8} + 111247 x^{7} + 2542751 x^{6} + 992153 x^{5} + 6949849 x^{4} + 3610528 x^{3} + 9340260 x^{2} + 5226611 x + 1604947$ $-\,7^{12}\cdot 71^{3}\cdot 113^{3}\cdot 64679^{2}$ $D_6\wr C_3$ (as 18T472) $[6]$ $35754468.73275179$
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