Number field search results

Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)

Results (1-50 of 74637 matches)

 

Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
18.0.363...104.1	$x^{18} + 18 x^{16} + 125 x^{14} + 434 x^{12} + 818 x^{10} + 861 x^{8} + 509 x^{6} + 162 x^{4} + 24 x^{2} + 1$	$18$	[0,9]	$-\,2^{18}\cdot 11779563529^{2}$	$2$	$26.3053661419$		✓		✓	$C_2\times S_9$ (as 18T913)	$[15]$	$4$	$8$	$17984.8375825$
18.0.637...375.1	$x^{18} - 9 x^{17} + 66 x^{16} - 318 x^{15} + 1216 x^{14} - 3630 x^{13} + 8805 x^{12} - 17428 x^{11} + 28338 x^{10} - 37881 x^{9} + 41417 x^{8} - 36489 x^{7} + 25499 x^{6} - 13718 x^{5} + 5500 x^{4} - 1784 x^{3} + 688 x^{2} - 288 x + 64$	$18$	[0,9]	$-\,5^{9}\cdot 7^{12}\cdot 11^{9}$	$3$	$27.1381374705$	$27.138137470492882$		✓		$S_3 \times C_3$ (as 18T3)	$[12]$	$2$	$8$	$64768.63578$
18.0.740...000.1	$x^{18} + 18 x^{16} - 24 x^{15} + 147 x^{14} - 342 x^{13} + 996 x^{12} - 2514 x^{11} + 5586 x^{10} - 11958 x^{9} + 22581 x^{8} - 40962 x^{7} + 66838 x^{6} - 97902 x^{5} + 124314 x^{4} - 128200 x^{3} + 101529 x^{2} - 54078 x + 15931$	$18$	[0,9]	$-\,2^{27}\cdot 3^{24}\cdot 5^{9}$	$3$	$27.3647615794$	$27.364761579423373$			?	$S_3 \times C_6$ (as 18T6)	$[14]$	$2$	$8$	$17326.71661590147$
18.0.756...064.1	$x^{18} + 17 x^{16} + 120 x^{14} + 455 x^{12} + 1001 x^{10} + 1287 x^{8} + 924 x^{6} + 330 x^{4} + 45 x^{2} + 1$	$18$	[0,9]	$-\,2^{18}\cdot 19^{16}$	$2$	$27.3968015041$	$27.39680150407798$	✓	✓	✓	$C_{18}$ (as 18T1)	$[19]$	$4$	$8$	$22305.8950792$
18.0.104...456.1	$x^{18} + 17 x^{16} + 114 x^{14} + 389 x^{12} + 728 x^{10} + 758 x^{8} + 433 x^{6} + 131 x^{4} + 19 x^{2} + 1$	$18$	[0,9]	$-\,2^{18}\cdot 7^{12}\cdot 169457^{2}$	$3$	$27.889151509$		✓		✓	$S_4^3.C_6$ (as 18T768)	$[16]$	$2$	$8$	$12363.5982042$
18.0.110...583.1	$x^{18} - x^{17} + 5 x^{16} - 10 x^{15} + 31 x^{14} - 76 x^{13} + 210 x^{12} + 366 x^{11} + 550 x^{10} + 704 x^{9} + 1130 x^{8} + 1136 x^{7} + 2680 x^{6} + 734 x^{5} + 201 x^{4} + 55 x^{3} + 15 x^{2} + 4 x + 1$	$18$	[0,9]	$-\,7^{15}\cdot 13^{12}$	$2$	$27.9819043822$	$27.981904382200295$	✓	✓		$C_6 \times C_3$ (as 18T2)	$[13]$	$14$	$8$	$205236.825908$
18.0.134...848.1	$x^{18} - 35 x^{12} + 907 x^{6} + 27$	$18$	[0,9]	$-\,2^{12}\cdot 3^{21}\cdot 11^{12}$	$3$	$28.2871971762$	$28.28719717616423$		✓		$C_3^2 : C_2$ (as 18T4)	$[2, 6]$	$6$	$8$	$707198.261609$
18.0.161...272.1	$x^{18} + 12 x^{16} + 54 x^{14} + 173 x^{12} + 681 x^{10} + 2232 x^{8} + 4894 x^{6} + 7221 x^{4} + 5484 x^{2} + 1297$	$18$	[0,9]	$-\,2^{18}\cdot 3^{24}\cdot 1297^{3}$	$3$	$28.5768922941$				?	$D_6\wr C_3$ (as 18T472)	$[20]$	$2$	$8$	$19338.0324864$
18.0.208...000.1	$x^{18} - 6 x^{17} + 6 x^{16} + 21 x^{15} - 18 x^{14} - 84 x^{13} + 41 x^{12} + 270 x^{11} - 184 x^{10} - 305 x^{9} + 96 x^{8} + 240 x^{7} + 316 x^{6} - 396 x^{5} + 32 x^{4} - 116 x^{3} + 136 x^{2} + 16 x + 16$	$18$	[0,9]	$-\,2^{12}\cdot 3^{9}\cdot 5^{12}\cdot 13^{9}$	$4$	$28.9867129753$	$28.98671297530016$				$S_3^2$ (as 18T9)	$[12]$	$2$	$8$	$369880.27456028434$
18.0.220...679.1	$x^{18} - 4 x^{17} + 7 x^{16} - 13 x^{15} + 73 x^{14} - 196 x^{13} + 456 x^{12} - 1442 x^{11} + 5024 x^{10} - 11878 x^{9} + 20482 x^{8} - 24026 x^{7} + 20896 x^{6} - 9772 x^{5} + 3997 x^{4} + 1484 x^{3} + 1519 x^{2} + 343 x + 49$	$18$	[0,9]	$-\,3^{9}\cdot 7^{15}\cdot 11^{9}$	$3$	$29.0740368545$	$29.074036854473896$		✓		$S_3 \times C_3$ (as 18T3)	$[2, 6]$	$2$	$8$	$81487.9586443$
18.0.225...616.2	$x^{18} - x^{17} + 13 x^{16} + 14 x^{15} + 56 x^{14} + 169 x^{13} + 406 x^{12} + 308 x^{11} + 2504 x^{10} - 1429 x^{9} + 9291 x^{8} - 10863 x^{7} + 21735 x^{6} - 23733 x^{5} + 43497 x^{4} - 20412 x^{3} + 48114 x^{2} - 13122 x + 19683$	$18$	[0,9]	$-\,2^{12}\cdot 11^{9}\cdot 13^{12}$	$3$	$29.1079692793$	$36.67374321467981$			?	$S_3 \times C_6$ (as 18T6)	$[14]$	$2$	$8$	$25638.894138274067$
18.0.232...000.1	$x^{18} + 14 x^{16} + 77 x^{14} + 310 x^{12} + 994 x^{10} + 1876 x^{8} + 3289 x^{6} + 3290 x^{4} + 1400 x^{2} + 1000$	$18$	[0,9]	$-\,2^{33}\cdot 5^{9}\cdot 7^{12}$	$3$	$29.15895938$	$32.72982527225799$			?	$S_3 \times C_6$ (as 18T6)	$[3, 6]$	$2$	$8$	$34883.98422806271$
18.0.242...064.1	$x^{18} - 2 x^{17} - 4 x^{16} + 22 x^{15} + 44 x^{14} - 74 x^{13} + 223 x^{12} + 312 x^{11} - 1620 x^{10} - 576 x^{9} + 5508 x^{8} - 2916 x^{7} - 3861 x^{6} + 7614 x^{5} + 2916 x^{4} - 486 x^{3} + 2916 x^{2} + 1458 x + 729$	$18$	[0,9]	$-\,2^{12}\cdot 3^{9}\cdot 113^{9}$	$3$	$29.2271529888$	$29.22715298876584$		✓		$C_3^2 : C_2$ (as 18T4)	$[3, 6]$	$2$	$8$	$1281109.48365$
18.0.258...864.7	$x^{18} + 18 x^{16} + 135 x^{14} + 546 x^{12} + 1287 x^{10} + 1782 x^{8} + 1386 x^{6} + 540 x^{4} + 81 x^{2} + 1$	$18$	[0,9]	$-\,2^{18}\cdot 3^{44}$	$2$	$29.3309679999$	$29.330967999939233$	✓	✓	✓	$C_{18}$ (as 18T1)	$[19]$	$4$	$8$	$40934.0329443$
18.0.267...616.1	$x^{18} - 6 x^{17} + 13 x^{16} + 10 x^{15} - 136 x^{14} + 370 x^{13} - 397 x^{12} - 442 x^{11} + 2502 x^{10} - 4778 x^{9} + 5325 x^{8} - 3574 x^{7} + 2237 x^{6} - 5348 x^{5} + 11786 x^{4} - 13880 x^{3} + 9112 x^{2} - 2592 x + 526$	$18$	[0,9]	$-\,2^{33}\cdot 3^{8}\cdot 7^{15}$	$3$	$29.3893907449$	$31.239014120786564$				$S_3\times D_6$ (as 18T29)	$[12]$	$2$	$8$	$1040005.4350050329$
18.0.294...144.1	$x^{18} - 3 x^{17} + 11 x^{16} - 11 x^{15} + 24 x^{14} - 12 x^{13} + 121 x^{12} - 95 x^{11} + 727 x^{10} + 25 x^{9} + 1172 x^{8} + 1386 x^{7} + 3079 x^{6} + 893 x^{5} + 4781 x^{4} + 825 x^{3} + 1247 x^{2} - 1319 x + 982$	$18$	[0,9]	$-\,2^{12}\cdot 3^{9}\cdot 7^{9}\cdot 67^{6}$	$4$	$29.5452665237$	$172.57049793444716$				$C_2\times C_6^2:D_6$ (as 18T228)	$[2, 8]$	$2$	$8$	$189663.911394$
18.0.303...000.1	$x^{18} - 2 x^{17} + 8 x^{16} - x^{15} + 58 x^{14} - 55 x^{13} + 123 x^{12} + 9 x^{11} + 70 x^{10} - 12 x^{9} + 49 x^{8} + 204 x^{7} + 37 x^{6} + 175 x^{5} + 118 x^{4} + 90 x^{3} + 264 x^{2} + 208 x + 64$	$18$	[0,9]	$-\,2^{18}\cdot 5^{12}\cdot 7^{15}$	$3$	$29.5977273519$	$41.857507436411844$				$C_3\times S_3^2$ (as 18T46)	$[18]$	$2$	$8$	$1994143.01875251$
18.0.309...000.1	$x^{18} + 8 x^{16} + 35 x^{14} + 139 x^{12} + 433 x^{10} + 823 x^{8} + 857 x^{6} + 450 x^{4} + 108 x^{2} + 9$	$18$	[0,9]	$-\,2^{18}\cdot 3^{8}\cdot 5^{4}\cdot 257^{6}$	$4$	$29.6293139253$				?	$C_6^3:S_4$ (as 18T487)	$[12]$	$2$	$8$	$185412.405856$
18.0.316...927.1	$x^{18} - 6 x^{17} + 6 x^{16} + 20 x^{15} - 48 x^{14} - 96 x^{13} + 459 x^{12} + 66 x^{11} - 435 x^{10} + 664 x^{9} + 4833 x^{8} + 900 x^{7} + 287 x^{6} + 3024 x^{5} + 13032 x^{4} + 5976 x^{3} + 12069 x^{2} + 7938 x + 20331$	$18$	[0,9]	$-\,3^{24}\cdot 47^{9}$	$2$	$29.6626947048$	$29.66269470481324$		✓		$S_3 \times C_3$ (as 18T3)	$[15]$	$2$	$8$	$483473.437416$
18.0.352...591.1	$x^{18} + 9 x^{16} - 9 x^{15} + 162 x^{14} - 99 x^{13} + 1473 x^{12} - 1404 x^{11} + 6264 x^{10} - 5939 x^{9} + 12636 x^{8} - 11961 x^{7} + 14742 x^{6} - 10530 x^{5} + 7452 x^{4} - 3267 x^{3} + 1215 x^{2} - 243 x + 27$	$18$	[0,9]	$-\,3^{44}\cdot 71^{3}$	$2$	$29.8427924526$	$123.5735646798655$	✓		?	$C_2^2:C_{18}$ (as 18T26)	$[21]$	$2$	$8$	$40934.0329443$
18.0.411...416.1	$x^{18} - 3 x^{17} - 9 x^{16} + 6 x^{15} + 129 x^{14} - 123 x^{13} - 90 x^{12} - 909 x^{11} + 1545 x^{10} + 446 x^{9} - 519 x^{8} - 1077 x^{7} + 3981 x^{6} - 3468 x^{5} + 2646 x^{4} - 816 x^{3} + 1608 x^{2} + 792 x + 484$	$18$	[0,9]	$-\,2^{12}\cdot 3^{25}\cdot 17^{9}$	$3$	$30.100903663$	$30.100903662957226$				$S_3^2$ (as 18T11)	$[3, 6]$	$2$	$8$	$163929.43344817942$
18.0.430...168.1	$x^{18} - 2 x^{17} - 11 x^{16} + 2 x^{15} + 95 x^{14} - 26 x^{13} - 85 x^{12} - 154 x^{11} + 1159 x^{10} - 2970 x^{9} - 4843 x^{8} - 4982 x^{7} + 12797 x^{6} + 18420 x^{5} + 54332 x^{4} + 85532 x^{3} + 82964 x^{2} + 37800 x + 46984$	$18$	[0,9]	$-\,2^{18}\cdot 7^{12}\cdot 17^{9}$	$3$	$30.1754079177$	$30.175407917701083$		✓		$S_3 \times C_3$ (as 18T3)	$[12]$	$2$	$8$	$117049.901978$
18.0.439...144.1	$x^{18} + 26 x^{14} + 52 x^{12} + 169 x^{10} + 7436 x^{8} + 25181 x^{6} + 43940 x^{4} + 43940 x^{2} + 17576$	$18$	[0,9]	$-\,2^{33}\cdot 13^{15}$	$2$	$30.2116505235$	$33.911431129417196$			?	$S_3 \times C_6$ (as 18T6)	$[18]$	$2$	$8$	$45895.39455567389$
18.0.530...608.1	$x^{18} - 2 x^{17} + 10 x^{16} + 10 x^{15} + 7 x^{14} + 97 x^{13} + 127 x^{12} - 201 x^{11} + 915 x^{10} - 653 x^{9} + 656 x^{8} + 76 x^{7} - 34 x^{6} + 161 x^{5} + 28 x^{4} - 8 x^{3} + 27 x^{2} - 5 x + 1$	$18$	[0,9]	$-\,2^{12}\cdot 3^{9}\cdot 37^{12}$	$3$	$30.529177728$	$38.464353655440554$			?	$S_3 \times C_6$ (as 18T6)	$[12]$	$6$	$8$	$174504.17013875535$
18.0.530...608.2	$x^{18} - 3 x^{17} + 5 x^{16} + 6 x^{15} - 12 x^{14} - 28 x^{13} + 63 x^{12} + 17 x^{11} - 17 x^{10} - 126 x^{9} + 130 x^{8} - 112 x^{7} + 216 x^{6} - 144 x^{5} + 200 x^{4} - 112 x^{3} + 112 x^{2} - 32 x + 64$	$18$	[0,9]	$-\,2^{12}\cdot 3^{9}\cdot 37^{12}$	$3$	$30.529177728$	$38.464353655440554$				$S_3^2$ (as 18T11)	$[12]$	$6$	$8$	$3307615.5705449595$
18.0.535...671.2	$x^{18} - 17 x^{15} + 193 x^{12} - 1057 x^{9} + 3187 x^{6} - 4125 x^{3} + 15625$	$18$	[0,9]	$-\,3^{21}\cdot 13^{15}$	$2$	$30.5441181347$	$30.544118134667247$				$S_3 \times C_6$ (as 18T6)	$[12]$	$2$	$8$	$305948.58795593923$
18.0.569...707.1	$x^{18} + 6 x^{16} - 18 x^{15} + 60 x^{14} - 75 x^{13} + 256 x^{12} - 459 x^{11} + 966 x^{10} - 871 x^{9} + 1740 x^{8} - 1116 x^{7} + 2869 x^{6} - 2424 x^{5} + 6450 x^{4} - 2606 x^{3} + 3006 x^{2} - 513 x + 361$	$18$	[0,9]	$-\,3^{27}\cdot 73^{3}\cdot 577^{3}$	$3$	$30.6500834262$	$1066.4272127060524$	✓		?	$S_3^3:C_6$ (as 18T285)	$[2, 12]$	$2$	$8$	$26510.9946997$
18.0.592...000.1	$x^{18} - 6 x^{17} + 18 x^{16} - 36 x^{15} + 57 x^{14} + 54 x^{13} - 262 x^{12} - 408 x^{11} + 4434 x^{10} - 14948 x^{9} + 43596 x^{8} - 97524 x^{7} + 191241 x^{6} - 297918 x^{5} + 389286 x^{4} - 440316 x^{3} + 419904 x^{2} - 314928 x + 157464$	$18$	[0,9]	$-\,2^{30}\cdot 3^{24}\cdot 5^{9}$	$3$	$30.7159063339$	$38.69961695672673$			?	$S_3 \times C_6$ (as 18T6)	$[2, 6]$	$2$	$8$	$55865.67541359784$
18.0.615...751.1	$x^{18} + 22 x^{16} - 8 x^{15} + 193 x^{14} - 138 x^{13} + 1085 x^{12} - 921 x^{11} + 4781 x^{10} - 3596 x^{9} + 13950 x^{8} - 12017 x^{7} + 36528 x^{6} - 25667 x^{5} + 61742 x^{4} - 59237 x^{3} + 44674 x^{2} - 56832 x + 39944$	$18$	[0,9]	$-\,13^{12}\cdot 31^{9}$	$2$	$30.7829153777$	$30.78291537771342$		✓		$S_3 \times C_3$ (as 18T3)	$[2, 6]$	$2$	$8$	$138932.419034$
18.0.663...928.1	$x^{18} + 28 x^{16} + 252 x^{14} + 1157 x^{12} + 2772 x^{10} + 3556 x^{8} + 2575 x^{6} + 1092 x^{4} + 252 x^{2} + 27$	$18$	[0,9]	$-\,2^{12}\cdot 3^{9}\cdot 7^{12}\cdot 29^{6}$	$4$	$30.9109237467$	$54.18074637512324$				$S_3^2$ (as 18T11)	$[3, 6]$	$6$	$8$	$892484.3013079121$
18.0.684...103.1	$x^{18} + 4 x^{16} - x^{15} + 16 x^{14} - 8 x^{13} + 65 x^{12} + 64 x^{11} + 268 x^{10} + 191 x^{9} + 1008 x^{8} + 496 x^{7} + 3841 x^{6} + 976 x^{5} + 248 x^{4} + 63 x^{3} + 16 x^{2} + 4 x + 1$	$18$	[0,9]	$-\,7^{15}\cdot 229^{6}$	$2$	$30.964223541948527$	$76.58894863599332$	✓		?	$S_3 \times C_6$ (as 18T6)	$[18]$	$14$	$8$	$329652.9714188469$
18.0.737...136.1	$x^{18} + 17 x^{16} + 115 x^{14} + 400 x^{12} + 776 x^{10} + 851 x^{8} + 511 x^{6} + 157 x^{4} + 22 x^{2} + 1$	$18$	[0,9]	$-\,2^{30}\cdot 37^{6}\cdot 16361^{2}$	$3$	$31.0922149397$		✓		✓	$S_4^3.D_6$ (as 18T836)	$[28]$	$2$	$8$	$22681.8418286$
18.0.802...848.1	$x^{18} + 28 x^{16} + 336 x^{14} + 2226 x^{12} + 9212 x^{10} + 27440 x^{8} + 65464 x^{6} + 123480 x^{4} + 148176 x^{2} + 74088$	$18$	[0,9]	$-\,2^{33}\cdot 3^{9}\cdot 7^{15}$	$3$	$31.2390141208$	$31.239014120786564$			?	$S_3 \times C_6$ (as 18T6)	$[2, 14]$	$2$	$8$	$31684.521927615173$
18.0.802...848.2	$x^{18} - 8 x^{17} + 50 x^{16} - 214 x^{15} + 777 x^{14} - 2306 x^{13} + 5951 x^{12} - 13076 x^{11} + 25573 x^{10} - 42600 x^{9} + 65630 x^{8} - 85698 x^{7} + 110878 x^{6} - 123990 x^{5} + 146017 x^{4} - 124430 x^{3} + 112877 x^{2} - 54474 x + 17851$	$18$	[0,9]	$-\,2^{33}\cdot 3^{9}\cdot 7^{15}$	$3$	$31.2390141208$	$35.06460777718351$			?	$S_3 \times C_6$ (as 18T6)	$[2, 14]$	$2$	$8$	$53687.93588131197$
18.0.823...051.1	$x^{18} + 17 x^{16} - 7 x^{15} + 174 x^{14} - 142 x^{13} + 1276 x^{12} - 1068 x^{11} + 6618 x^{10} - 6859 x^{9} + 25026 x^{8} - 25559 x^{7} + 58530 x^{6} - 44688 x^{5} + 47915 x^{4} - 20759 x^{3} + 14724 x^{2} - 2412 x + 216$	$18$	[0,9]	$-\,7^{12}\cdot 53^{6}\cdot 139^{3}$	$3$	$31.2843005782$	$314.08270911399967$	✓		?	$C_6\times S_4$ (as 18T61)	$[2, 2, 10]$	$2$	$8$	$23621.7133529$
18.0.977...007.3	$x^{18} - 3 x^{17} + 36 x^{15} - 72 x^{14} - 108 x^{13} + 498 x^{12} - 390 x^{11} - 1764 x^{10} + 1160 x^{9} + 4896 x^{8} + 828 x^{7} - 3579 x^{6} - 4479 x^{5} + 756 x^{4} + 2892 x^{3} + 1056 x^{2} - 1728 x + 512$	$18$	[0,9]	$-\,3^{30}\cdot 7^{15}$	$2$	$31.5827874738$	$33.57045242721829$				$S_3 \times C_6$ (as 18T6)	$[21]$	$2$	$8$	$9447907.468229258$
18.0.102...064.1	$x^{18} + 30 x^{16} + 333 x^{14} + 1712 x^{12} + 4164 x^{10} + 4500 x^{8} + 2316 x^{6} + 561 x^{4} + 54 x^{2} + 1$	$18$	[0,9]	$-\,2^{18}\cdot 3^{24}\cdot 7^{12}$	$3$	$31.6657925274$	$31.66579252742446$	✓	✓		$C_6 \times C_3$ (as 18T2)	$[2, 14]$	$4$	$8$	$54408.4888887$
18.0.105...856.1	$x^{18} - 4 x^{17} + 6 x^{16} + 2 x^{15} + 3 x^{14} - 96 x^{13} + 400 x^{12} - 598 x^{11} + 361 x^{10} + 1116 x^{9} - 1796 x^{8} + 1670 x^{7} + 1665 x^{6} - 1256 x^{5} + 1240 x^{4} + 1374 x^{3} + 1474 x^{2} - 2208 x + 534$	$18$	[0,9]	$-\,2^{20}\cdot 3^{9}\cdot 13^{15}$	$3$	$31.7193681251$	$37.001564034934304$				$S_3\times D_6$ (as 18T29)	$[12]$	$2$	$8$	$4564456.230782871$
18.0.125...256.2	$x^{18} + x^{16} - 36 x^{14} + 81 x^{12} + 37 x^{10} - 176 x^{8} - 84 x^{6} + 192 x^{4} + 208 x^{2} + 64$	$18$	[0,9]	$-\,2^{18}\cdot 3^{6}\cdot 37^{12}$	$3$	$32.0286202283$	$38.464353655440554$				$S_3^2$ (as 18T11)	$[2, 6]$	$4$	$8$	$4024769.0899026883$
18.0.127...131.1	$x^{18} - 2 x^{17} - 8 x^{16} + 22 x^{15} + 34 x^{14} - 139 x^{13} + 411 x^{12} - 1297 x^{11} + 2584 x^{10} - 3316 x^{9} + 3809 x^{8} - 3584 x^{7} + 1488 x^{6} - 1255 x^{5} + 2103 x^{4} - 1121 x^{3} + 2048 x^{2} - 368 x + 415$	$18$	[0,9]	$-\,13^{14}\cdot 19^{9}$	$2$	$32.04624772796207$	$36.95412533099223$				$S_3 \times C_6$ (as 18T6)	$[13]$	$2$	$8$	$270913.8657066776$
18.0.127...272.1	$x^{18} + 22 x^{16} + 195 x^{14} + 905 x^{12} + 2407 x^{10} + 3777 x^{8} + 3444 x^{6} + 1699 x^{4} + 374 x^{2} + 17$	$18$	[0,9]	$-\,2^{18}\cdot 17^{3}\cdot 994046201^{2}$	$3$	$32.0491604229$		✓		?	$C_2^9.S_9$ (as 18T968)	$[32]$	$2$	$8$	$22244.2712354$
18.0.130...375.1	$x^{18} - 9 x^{16} - 24 x^{15} + 57 x^{14} + 171 x^{13} + 78 x^{12} - 1398 x^{11} - 354 x^{10} + 2370 x^{9} + 7326 x^{8} - 11433 x^{7} + 823 x^{6} + 783 x^{5} + 55563 x^{4} + 3137 x^{3} + 48636 x^{2} - 42972 x + 9784$	$18$	[0,9]	$-\,3^{24}\cdot 5^{9}\cdot 11^{9}$	$3$	$32.088027244$	$32.08802724398451$			?	$S_3 \times C_6$ (as 18T6)	$[28]$	$2$	$8$	$56262.000163134624$
18.0.136...007.1	$x^{18} - x^{17} + 5 x^{16} - 6 x^{15} + 23 x^{14} - 32 x^{13} + 106 x^{12} - 10 x^{11} + 338 x^{10} - 60 x^{9} + 1382 x^{8} - 608 x^{7} + 5956 x^{6} - 4242 x^{5} + 3033 x^{4} - 2133 x^{3} + 1539 x^{2} - 972 x + 729$	$18$	[0,9]	$-\,7^{15}\cdot 257^{6}$	$2$	$32.17802670610972$	$81.13624943470906$	✓			$S_3 \times C_6$ (as 18T6)	$[38]$	$14$	$8$	$397993.7481250477$
18.0.139...551.1	$x^{18} - 6 x^{17} + 33 x^{16} - 132 x^{15} + 398 x^{14} - 878 x^{13} + 1591 x^{12} - 2720 x^{11} + 5300 x^{10} - 9712 x^{9} + 11716 x^{8} - 6585 x^{7} + 6401 x^{6} - 25670 x^{5} + 32584 x^{4} + 6876 x^{3} - 33816 x^{2} - 3691 x + 27971$	$18$	[0,9]	$-\,7^{12}\cdot 13^{5}\cdot 43^{7}$	$3$	$32.2155192012$	$712.7029119734025$	✓		?	$C_6\wr C_3$ (as 18T188)	$[2, 2, 6]$	$2$	$8$	$35085.5946511$
18.0.139...391.1	$x^{18} - 3 x^{17} + 15 x^{16} - 53 x^{15} + 207 x^{14} - 648 x^{13} + 1867 x^{12} - 5094 x^{11} + 12642 x^{10} - 27983 x^{9} + 54783 x^{8} - 96642 x^{7} + 152588 x^{6} - 201378 x^{5} + 203559 x^{4} - 147022 x^{3} + 71619 x^{2} - 21321 x + 3079$	$18$	[0,9]	$-\,3^{24}\cdot 7^{12}\cdot 71^{3}$	$3$	$32.2183595933$	$133.41035526120362$	✓		?	$C_6\times A_4$ (as 18T25)	$[2, 10]$	$2$	$8$	$54408.4888887$
18.0.139...391.2	$x^{18} - 3 x^{17} + 27 x^{16} - 52 x^{15} + 249 x^{14} - 378 x^{13} + 1144 x^{12} - 1320 x^{11} + 2610 x^{10} - 2630 x^{9} + 3594 x^{8} - 2052 x^{7} + 2454 x^{6} - 1296 x^{5} + 1647 x^{4} - 963 x^{3} + 567 x^{2} - 162 x + 27$	$18$	[0,9]	$-\,3^{24}\cdot 7^{12}\cdot 71^{3}$	$3$	$32.2183595933$	$133.41035526120362$	✓			$C_6\times A_4$ (as 18T25)	$[2, 14]$	$2$	$8$	$54408.4888887$
18.0.151...088.1	$x^{18} + 6 x^{16} - 12 x^{14} + 28 x^{12} + 345 x^{10} + 138 x^{8} + 14812 x^{6} + 39675 x^{4} + 36501 x^{2} + 12167$	$18$	[0,9]	$-\,2^{12}\cdot 3^{18}\cdot 23^{11}$	$3$	$32.3574977313$	$75.67759754192122$			?	$S_3\times S_4$ (as 18T65)	$[14]$	$2$	$8$	$153649.289639$
18.0.152...976.1	$x^{18} - 12 x^{16} - 10 x^{15} + 108 x^{14} + 42 x^{13} - 447 x^{12} + 222 x^{11} + 2181 x^{10} - 4754 x^{9} - 5631 x^{8} + 19452 x^{7} + 1661 x^{6} - 32016 x^{5} + 66060 x^{4} - 105666 x^{3} + 112833 x^{2} - 91314 x + 53433$	$18$	[0,9]	$-\,2^{27}\cdot 3^{24}\cdot 7^{9}$	$3$	$32.3784225499$	$32.37842254987355$		✓		$S_3 \times C_3$ (as 18T3)	$[12]$	$2$	$8$	$793654.483575$
18.0.160...696.1	$x^{18} - 6 x^{17} + 31 x^{16} - 126 x^{15} + 449 x^{14} - 1344 x^{13} + 3523 x^{12} - 8124 x^{11} + 16814 x^{10} - 30804 x^{9} + 50122 x^{8} - 71112 x^{7} + 87448 x^{6} - 89688 x^{5} + 73686 x^{4} - 45720 x^{3} + 20178 x^{2} - 5832 x + 918$	$18$	[0,9]	$-\,2^{34}\cdot 3^{9}\cdot 7^{15}$	$3$	$32.4654336372$	$39.35869146874217$			?	$S_3\times D_6$ (as 18T29)	$[2, 6]$	$2$	$8$	$1486658.4572439173$
18.0.161...407.1	$x^{18} - 9 x^{17} + 16 x^{16} + 76 x^{15} - 304 x^{14} + 84 x^{13} + 1122 x^{12} - 1714 x^{11} - 220 x^{10} + 2464 x^{9} - 1596 x^{8} - 1124 x^{7} + 1128 x^{6} + 1970 x^{5} - 851 x^{4} - 3175 x^{3} + 5544 x^{2} - 3412 x + 968$	$18$	[0,9]	$-\,7^{9}\cdot 43^{12}$	$2$	$32.4734170696$	$32.473417069603315$		✓		$S_3 \times C_3$ (as 18T3)	$[19]$	$2$	$8$	$386705.621198$