Number field search results

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

Results (1-50 of 201 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
18.0.549...559.5	$x^{18} + 120 x^{16} - 100 x^{15} + 5202 x^{14} - 6276 x^{13} + 216480 x^{12} - 393084 x^{11} + 3932949 x^{10} - 12808812 x^{9} + 44404560 x^{8} - 291814320 x^{7} + 1659031088 x^{6} + 12409534080 x^{5} + 110919615744 x^{4} + 424503642112 x^{3} + 1332058521600 x^{2} + 2249313484800 x + 2772434944000$	$18$	[0,9]	$-\,3^{27}\cdot 7^{15}\cdot 19^{15}$	$3$	$305.885048594$	$305.8850485944082$	✓	✓		$C_6 \times C_3$ (as 18T2)	$[2, 2, 2, 2, 2, 277909656]$	$2$	$8$	$10681224266.072006$
18.0.102...136.1	$x^{18} - x^{17} + 191 x^{16} + 237 x^{15} + 24585 x^{14} + 119723 x^{13} + 2169003 x^{12} + 13020561 x^{11} + 116404855 x^{10} + 597868077 x^{9} + 3990653485 x^{8} + 18385432151 x^{7} + 99487490867 x^{6} + 368692180073 x^{5} + 1482883758697 x^{4} + 3744823323947 x^{3} + 10112290341964 x^{2} + 13574001819584 x + 22784958920704$	$18$	[0,9]	$-\,2^{12}\cdot 3^{9}\cdot 7^{15}\cdot 11^{6}\cdot 19^{15}$	$5$	$359.960257369$	$676.3372901115204$	✓			$S_3 \times C_6$ (as 18T6)	$[2, 2, 2, 6, 88705224]$	$2$	$8$	$2494653063.4840164$
18.0.213...000.1	$x^{18} + 570 x^{16} + 123975 x^{14} + 13922250 x^{12} + 890161875 x^{10} + 32905743750 x^{8} + 667386281250 x^{6} + 6305250937500 x^{4} + 16368106640625 x^{2} + 121236328125$	$18$	[0,9]	$-\,2^{18}\cdot 3^{27}\cdot 5^{9}\cdot 19^{17}$	$4$	$374.894107337$	$374.89410733688527$	✓	✓		$C_{18}$ (as 18T1)	$[2, 2, 682763844]$	$2$	$8$	$15010229.973756868$
18.0.213...000.2	$x^{18} + 570 x^{16} + 123975 x^{14} + 13494750 x^{12} + 809364375 x^{10} + 27846281250 x^{8} + 553885031250 x^{6} + 6230705625000 x^{4} + 36516983203125 x^{2} + 86016673828125$	$18$	[0,9]	$-\,2^{18}\cdot 3^{27}\cdot 5^{9}\cdot 19^{17}$	$4$	$374.894107337$	$374.89410733688527$	✓	✓		$C_{18}$ (as 18T1)	$[2, 2, 618423708]$	$2$	$8$	$22027035.20428972$
18.0.232...976.2	$x^{18} + 75 x^{16} - 76 x^{15} + 6471 x^{14} + 409951 x^{12} + 501372 x^{11} + 21240672 x^{10} + 32240074 x^{9} + 787133106 x^{8} + 1165841862 x^{7} + 21242025193 x^{6} + 22617048924 x^{5} + 398164960137 x^{4} + 246611628030 x^{3} + 4852747373220 x^{2} + 345736733040 x + 30985776501229$	$18$	[0,9]	$-\,2^{18}\cdot 3^{27}\cdot 7^{9}\cdot 19^{16}$	$4$	$376.643750076$	$376.6437500763521$	✓	✓		$C_{18}$ (as 18T1)	$[2, 2, 12, 55575756]$	$2$	$8$	$15010229.973756868$
18.0.351...791.4	$x^{18} + 69 x^{16} - 342 x^{15} + 4842 x^{14} - 20664 x^{13} + 299506 x^{12} - 884196 x^{11} + 9112317 x^{10} - 21399912 x^{9} + 191614905 x^{8} - 98215254 x^{7} + 3750331288 x^{6} - 3908734704 x^{5} + 65580672912 x^{4} - 101131530336 x^{3} + 545791014144 x^{2} - 452406256128 x + 1509470846976$	$18$	[0,9]	$-\,3^{27}\cdot 7^{12}\cdot 37^{15}$	$3$	$385.403225913$	$385.4032259125891$	✓	✓		$C_6 \times C_3$ (as 18T2)	$[6, 126, 4356072]$	$2$	$8$	$958454033532.8324$
18.0.134...048.1	$x^{18} - 7 x^{17} - 14 x^{16} + 296 x^{15} - 104 x^{14} - 8692 x^{13} + 40510 x^{12} - 31030 x^{11} - 103469 x^{10} - 883965 x^{9} + 10462064 x^{8} - 42389938 x^{7} + 122868164 x^{6} - 348451720 x^{5} + 1353700784 x^{4} - 4306452928 x^{3} + 10681441664 x^{2} - 15402059776 x + 14816731136$	$18$	[0,9]	$-\,2^{18}\cdot 23^{9}\cdot 127^{14}$	$3$	$415.131507581$	$768.3846474898045$	✓			$S_3 \times C_6$ (as 18T6)	$[12, 252, 1888488]$	$2$	$8$	$5546046730.2947445$
18.0.174...000.2	$x^{18} - x^{15} + 59536 x^{12} + 118341 x^{9} + 1171847088 x^{6} - 387420489 x^{3} + 7625597484987$	$18$	[0,9]	$-\,2^{12}\cdot 3^{27}\cdot 5^{12}\cdot 73^{12}$	$4$	$421.273158475$	$421.27315847500523$		✓	?	$S_3 \times C_3$ (as 18T3)	$[3, 3, 9, 9, 9, 9, 54, 378]$	$6$	$8$	$66851395.5778903$
18.0.195...787.2	$x^{18} - 9 x^{17} + 45 x^{16} - 156 x^{15} + 411 x^{14} - 861 x^{13} - 521793 x^{12} + 3137505 x^{11} - 10201200 x^{10} + 22236314 x^{9} - 35056719 x^{8} + 41336523 x^{7} + 68414239629 x^{6} - 205328532297 x^{5} + 410694739059 x^{4} - 479154240201 x^{3} + 319438195035 x^{2} - 114085331286 x + 17746624531$	$18$	[0,9]	$-\,3^{31}\cdot 7^{12}\cdot 73^{12}$	$3$	$423.957928025$	$423.957928025228$		✓	?	$S_3 \times C_3$ (as 18T3)	$[3, 3, 3, 3, 9, 684, 4788]$	$6$	$8$	$49147979.00484934$
18.0.219...983.4	$x^{18} - 3 x^{17} - 126 x^{16} - 550 x^{15} + 9855 x^{14} + 58947 x^{13} + 2403572 x^{12} + 4265028 x^{11} + 133354239 x^{10} + 69650435 x^{9} + 3774087570 x^{8} - 459373590 x^{7} + 64122556561 x^{6} - 16181516019 x^{5} + 751115946456 x^{4} + 45178635864 x^{3} + 5972918763024 x^{2} - 618217616304 x + 22504454258688$	$18$	[0,9]	$-\,3^{24}\cdot 13^{15}\cdot 19^{15}$	$3$	$426.653979425$	$426.6539794250053$	✓	✓		$C_6 \times C_3$ (as 18T2)	$[21, 42, 378, 11718]$	$2$	$8$	$931139254937.0632$
18.0.330...503.1	$x^{18} - 218 x^{15} + 8829 x^{14} + 1962 x^{13} + 3052 x^{12} - 2601612 x^{11} + 4236939 x^{10} - 23442412 x^{9} + 250790688 x^{8} - 356748498 x^{7} + 5184150199 x^{6} - 18049683870 x^{5} + 61464190068 x^{4} - 380206748136 x^{3} + 665349107904 x^{2} + 398639222784 x + 381578493952$	$18$	[0,9]	$-\,3^{27}\cdot 109^{17}$	$2$	$436.43343972$	$436.43343972012116$	✓	✓		$C_{18}$ (as 18T1)	$[3, 593413236]$	$2$	$8$	$3866670056388.9624$
18.0.420...672.2	$x^{18} - 6 x^{17} + 345 x^{16} - 1778 x^{15} + 50028 x^{14} - 219576 x^{13} + 3899592 x^{12} - 14341668 x^{11} + 171878073 x^{10} - 515196144 x^{9} + 4026740871 x^{8} - 9350526024 x^{7} + 37334377373 x^{6} - 58803238512 x^{5} - 60150628077 x^{4} + 133588777454 x^{3} + 167812083477 x^{2} - 218068968786 x + 185027482261$	$18$	[0,9]	$-\,2^{18}\cdot 3^{27}\cdot 7^{12}\cdot 19^{15}$	$4$	$442.32203182$	$442.32203181987285$	✓	✓		$C_6 \times C_3$ (as 18T2)	$[2, 2, 2, 2, 52, 1217892]$	$2$	$8$	$42198260.232521206$
18.0.420...672.4	$x^{18} + 45 x^{16} - 210 x^{15} + 3024 x^{14} + 10080 x^{13} - 53472 x^{12} - 1285200 x^{11} - 5355135 x^{10} + 39238850 x^{9} + 452260827 x^{8} + 590724540 x^{7} - 9047417835 x^{6} - 42861762090 x^{5} + 7539888843 x^{4} + 615461531370 x^{3} + 2224622720133 x^{2} + 3640164079860 x + 2551664661337$	$18$	[0,9]	$-\,2^{18}\cdot 3^{27}\cdot 7^{12}\cdot 19^{15}$	$4$	$442.32203182$	$442.32203181987285$	✓	✓		$C_6 \times C_3$ (as 18T2)	$[2, 2, 2, 2, 28, 2261532]$	$2$	$8$	$110172188.8644179$
18.0.739...984.1	$x^{18} - 2 x^{17} - 87 x^{16} + 1202 x^{15} - 2841 x^{14} - 80238 x^{13} + 1287658 x^{12} - 11262660 x^{11} + 70706700 x^{10} - 344420830 x^{9} + 1342940679 x^{8} - 4240439604 x^{7} + 10825160241 x^{6} - 22066150836 x^{5} + 35004517519 x^{4} - 41292548918 x^{3} + 33626242626 x^{2} - 16638384612 x + 3731618953$	$18$	[0,9]	$-\,2^{12}\cdot 17^{9}\cdot 163^{15}$	$3$	$456.457970324$	$456.4579703237679$		✓	?	$S_3 \times C_3$ (as 18T3)	$[26, 1612, 30628]$	$2$	$8$	$24241802.06091236$
18.0.957...375.2	$x^{18} - x^{17} - 282 x^{16} + 42 x^{15} + 30077 x^{14} + 18035 x^{13} - 1363905 x^{12} - 1533003 x^{11} + 25199154 x^{10} + 38273266 x^{9} - 19380689 x^{8} + 151200629 x^{7} + 2370420196 x^{6} + 1825666152 x^{5} + 11737837080 x^{4} + 16619785184 x^{3} + 87416317952 x^{2} - 2937968128 x + 305535379456$	$18$	[0,9]	$-\,3^{9}\cdot 5^{9}\cdot 7^{14}\cdot 67^{14}$	$4$	$463.046394786$	$651.6629025455062$	✓			$S_3 \times C_6$ (as 18T6)	$[2, 2, 2, 4, 77184492]$	$2$	$8$	$4641319478.753615$
18.0.137...944.2	$x^{18} - 3 x^{17} - 36 x^{16} + 408 x^{15} + 576 x^{14} - 18684 x^{13} + 145350 x^{12} - 556254 x^{11} + 2697543 x^{10} - 14553153 x^{9} + 105217326 x^{8} - 548111610 x^{7} + 2645917704 x^{6} - 9783568800 x^{5} + 34090131744 x^{4} - 89371535328 x^{3} + 211735347840 x^{2} - 307300490496 x + 380974814208$	$18$	[0,9]	$-\,2^{18}\cdot 3^{31}\cdot 13^{9}\cdot 19^{14}$	$4$	$472.385581692$	$786.7803377295565$	✓			$S_3 \times C_6$ (as 18T6)	$[2, 6, 724765860]$	$2$	$8$	$15773424688.63964$
18.0.239...384.2	$x^{18} - 6 x^{17} - 159 x^{16} - 1410 x^{15} + 7527 x^{14} + 280182 x^{13} + 3597450 x^{12} + 30551556 x^{11} + 196786164 x^{10} + 1007188198 x^{9} + 4180850511 x^{8} + 14164032300 x^{7} + 38939538201 x^{6} + 85555837932 x^{5} + 145837576599 x^{4} + 183224962614 x^{3} + 156763071546 x^{2} + 80259221724 x + 18360337249$	$18$	[0,9]	$-\,2^{12}\cdot 3^{31}\cdot 7^{9}\cdot 31^{15}$	$4$	$487.243352689$	$487.24335268924307$		✓	?	$S_3 \times C_3$ (as 18T3)	$[3, 1638, 219492]$	$2$	$8$	$52651214.56199736$
18.0.250...063.6	$x^{18} - x^{17} + 20 x^{16} - 58 x^{15} + 4523 x^{14} - 44727 x^{13} + 156314 x^{12} + 565724 x^{11} + 5297847 x^{10} - 62092191 x^{9} - 87377712 x^{8} + 2705060950 x^{7} - 3711440771 x^{6} - 44238428233 x^{5} + 171707544098 x^{4} + 136367346344 x^{3} - 1463520329344 x^{2} + 355897168384 x + 11080414060544$	$18$	[0,9]	$-\,19^{17}\cdot 37^{17}$	$2$	$488.417414498$	$488.4174144979954$	✓	✓		$C_{18}$ (as 18T1)	$[7801759098]$	$2$	$8$	$4738886400565.654$
18.0.300...000.1	$x^{18} - 4 x^{17} - 77 x^{16} - 186 x^{15} + 6112 x^{14} + 26100 x^{13} - 79910 x^{12} - 856236 x^{11} - 1687355 x^{10} - 3787964 x^{9} + 93538987 x^{8} + 176088726 x^{7} + 8509113946 x^{6} - 42706675732 x^{5} + 161608733256 x^{4} + 230802504368 x^{3} + 6364008129664 x^{2} - 7002971574528 x + 29398869968896$	$18$	[0,9]	$-\,2^{18}\cdot 5^{9}\cdot 7^{15}\cdot 13^{15}\cdot 17^{6}$	$5$	$493.399984934$	$1118.894012821775$	✓			$S_3 \times C_6$ (as 18T6)	$[2, 6, 472686840]$	$2$	$8$	$55972376075.29769$
18.0.337...488.1	$x^{18} - 46827 x^{12} + 3634057251 x^{6} + 747377296875$	$18$	[0,9]	$-\,2^{12}\cdot 3^{37}\cdot 11^{12}\cdot 17^{12}$	$4$	$496.588868956$	$496.5888689560723$		✓		$C_3^2 : C_2$ (as 18T4)	$[2, 2, 2, 6, 6, 6, 12, 12, 72, 72]$	$6$	$8$	$795492382.7560022$
18.0.533...648.7	$x^{18} + 273 x^{16} - 168 x^{15} + 38934 x^{14} - 4704 x^{13} + 3256078 x^{12} - 740880 x^{11} + 177123093 x^{10} + 94202304 x^{9} + 8415651069 x^{8} + 10024559160 x^{7} + 241142568884 x^{6} + 271774244448 x^{5} + 6941687396868 x^{4} + 23218361290432 x^{3} + 193558495474176 x^{2} + 420721169799168 x + 1331820844863488$	$18$	[0,9]	$-\,2^{18}\cdot 3^{24}\cdot 7^{15}\cdot 19^{15}$	$4$	$509.410668522$	$509.41066852186157$	✓	✓		$C_6 \times C_3$ (as 18T2)	$[2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 28, 25284]$	$2$	$8$	$10681224266.072006$
18.0.533...648.9	$x^{18} + 57 x^{16} - 114 x^{15} + 25992 x^{14} + 17328 x^{13} + 1534972 x^{12} - 1975392 x^{11} + 167764281 x^{10} + 223754298 x^{9} + 17029175391 x^{8} + 4324050780 x^{7} + 341322297569 x^{6} - 127425006738 x^{5} + 58784088299895 x^{4} + 125502023684818 x^{3} + 3925005531309753 x^{2} + 3316967769886236 x + 43904083722291521$	$18$	[0,9]	$-\,2^{18}\cdot 3^{24}\cdot 7^{15}\cdot 19^{15}$	$4$	$509.410668522$	$509.41066852186157$	✓	✓		$C_6 \times C_3$ (as 18T2)	$[2, 2, 2, 2, 28, 4299204]$	$2$	$8$	$42198260.232521206$
18.0.187...232.1	$x^{18} - 9 x^{17} - 132 x^{16} + 742 x^{15} + 12147 x^{14} - 13221 x^{13} - 634314 x^{12} - 1579305 x^{11} + 17018340 x^{10} + 109842349 x^{9} - 17013828 x^{8} - 2482374477 x^{7} - 9152309280 x^{6} + 6179192277 x^{5} + 169228552005 x^{4} + 703629239684 x^{3} + 1596953609076 x^{2} + 2096104977033 x + 1343941011449$	$18$	[0,9]	$-\,2^{12}\cdot 3^{24}\cdot 23^{9}\cdot 37^{14}$	$4$	$546.291831598$	$667.6471889561029$	✓		?	$S_3 \times C_6$ (as 18T6)	$[3, 3, 3, 3, 14783202]$	$2$	$8$	$118546543.87559307$
18.0.465...816.1	$x^{18} - 33 x^{16} - 518 x^{15} + 7551 x^{14} + 57276 x^{13} + 279460 x^{12} - 2117214 x^{11} + 6831186 x^{10} + 177967040 x^{9} + 2070194571 x^{8} + 6463629012 x^{7} + 23205936379 x^{6} + 142282696212 x^{5} + 2468568430875 x^{4} + 16826397242406 x^{3} + 81392406986196 x^{2} + 210401935775676 x + 360860185926073$	$18$	[0,9]	$-\,2^{24}\cdot 3^{27}\cdot 7^{9}\cdot 37^{14}$	$4$	$574.535252874$	$702.1647118811377$	✓		?	$S_3 \times C_6$ (as 18T6)	$[3, 6, 6, 12, 1076556]$	$2$	$8$	$118546543.87559307$
18.0.488...000.3	$x^{18} - 3 x^{17} - 354 x^{16} + 2172 x^{15} + 44394 x^{14} - 428718 x^{13} - 1669332 x^{12} + 31785648 x^{11} - 47149131 x^{10} - 927212375 x^{9} + 4765541070 x^{8} + 972777468 x^{7} - 70540733496 x^{6} + 158074945248 x^{5} + 512148044928 x^{4} - 3757461785088 x^{3} + 9971179180032 x^{2} - 13774599094272 x + 8983456251904$	$18$	[0,9]	$-\,2^{12}\cdot 3^{31}\cdot 5^{9}\cdot 61^{14}$	$4$	$576.063508565$	$912.0080840017521$	✓			$S_3 \times C_6$ (as 18T6)	$[3, 3, 18, 18436230]$	$2$	$8$	$248523426321.35065$
18.0.647...536.1	$x^{18} - x^{17} - 46 x^{16} + 6 x^{15} + 1875 x^{14} - 149 x^{13} + 3114 x^{12} + 58411 x^{11} + 742416 x^{10} + 1083121 x^{9} + 13778320 x^{8} - 7527429 x^{7} + 296925420 x^{6} - 102044671 x^{5} + 3365343059 x^{4} - 1720750208 x^{3} + 25382044532 x^{2} + 3807287761 x + 105185281361$	$18$	[0,9]	$-\,2^{18}\cdot 31^{9}\cdot 163^{14}$	$3$	$585.195801436$	$1098.2861596333155$	✓			$S_3 \times C_6$ (as 18T6)	$[300, 9960300]$	$2$	$8$	$87986390.20265311$
18.0.658...904.2	$x^{18} - 4 x^{17} - 256 x^{16} + 1138 x^{15} + 24231 x^{14} - 118856 x^{13} - 825357 x^{12} + 4506790 x^{11} + 14933513 x^{10} - 100422380 x^{9} + 48529363 x^{8} + 706102334 x^{7} + 3550027525 x^{6} - 19415573440 x^{5} + 48699532177 x^{4} + 4438727658 x^{3} + 333518260810 x^{2} - 1171630181320 x + 3405745481641$	$18$	[0,9]	$-\,2^{27}\cdot 3^{9}\cdot 7^{14}\cdot 67^{14}$	$4$	$585.712507941$	$824.2956154720551$	✓			$S_3 \times C_6$ (as 18T6)	$[2, 2, 2, 6, 6, 6, 42, 27006]$	$2$	$8$	$4641319478.753615$
18.0.720...304.1	$x^{18} + 762 x^{16} + 163449 x^{14} + 12079605 x^{12} + 378579888 x^{10} + 5811085152 x^{8} + 45949843584 x^{6} + 184059502848 x^{4} + 339802159104 x^{2} + 226534772736$	$18$	[0,9]	$-\,2^{18}\cdot 3^{27}\cdot 127^{15}$	$3$	$588.683204379$	$588.6832043794094$	✓	✓		$C_6 \times C_3$ (as 18T2)	$[2, 2, 2, 2, 8, 8, 728, 3640]$	$2$	$8$	$139246964.12762704$
18.0.110...528.1	$x^{18} - 9 x^{17} + 249 x^{16} - 1210 x^{15} + 46269 x^{14} - 388629 x^{13} + 5761489 x^{12} - 23816085 x^{11} + 231643500 x^{10} - 1868512448 x^{9} + 27515504667 x^{8} - 192359931897 x^{7} + 1114840641631 x^{6} - 3682933439697 x^{5} + 19540700837241 x^{4} - 110436829949061 x^{3} + 710612754783045 x^{2} - 2315082332910126 x + 5065118682021109$	$18$	[0,9]	$-\,2^{12}\cdot 3^{27}\cdot 13^{9}\cdot 37^{15}$	$4$	$602.802426812$	$602.802426811825$	✓		?	$S_3 \times C_6$ (as 18T6)	$[2, 12, 77388948]$	$2$	$8$	$118546543.87559307$
18.0.114...824.2	$x^{18} - 288 x^{16} - 684 x^{15} + 25407 x^{14} + 114912 x^{13} - 134160 x^{12} - 332424 x^{11} + 13658103 x^{10} + 37696646 x^{9} + 4537944 x^{8} + 95193990 x^{7} + 2434990194 x^{6} + 2758880142 x^{5} + 9735437304 x^{4} + 20624060568 x^{3} + 135663898545 x^{2} - 38029861350 x + 1084361854375$	$18$	[0,9]	$-\,2^{27}\cdot 3^{45}\cdot 19^{16}$	$3$	$603.973658424$	$603.9736584237519$	✓	✓		$C_{18}$ (as 18T1)	$[7, 409181346]$	$2$	$8$	$5772307958.489205$
18.0.148...368.1	$x^{18} + 553 x^{16} + 124978 x^{14} + 14852474 x^{12} + 993573441 x^{10} + 37101053689 x^{8} + 720817500956 x^{6} + 6348478632580 x^{4} + 20090550387600 x^{2} + 692684296192$	$18$	[0,9]	$-\,2^{30}\cdot 7^{15}\cdot 79^{15}$	$3$	$612.803074492$	$772.083492992753$	✓			$S_3 \times C_6$ (as 18T6)	$[2, 2, 2, 2, 4, 12, 1303020]$	$2$	$8$	$20721910881.979282$
18.0.193...000.1	$x^{18} - x^{17} - 37 x^{16} - 2 x^{15} + 1775 x^{14} - 175 x^{13} + 15397 x^{12} + 63753 x^{11} + 1006988 x^{10} + 1462242 x^{9} + 22067877 x^{8} - 5102579 x^{7} + 468059929 x^{6} - 138548203 x^{5} + 5750426701 x^{4} - 2439482531 x^{3} + 45599080719 x^{2} + 4718555316 x + 193437757489$	$18$	[0,9]	$-\,2^{18}\cdot 5^{9}\cdot 7^{9}\cdot 163^{14}$	$4$	$621.805238947$	$1166.994168869991$	✓		?	$S_3 \times C_6$ (as 18T6)	$[2, 2, 2, 28, 17819172]$	$2$	$8$	$87986390.20265311$
18.0.241...000.1	$x^{18} - 6 x^{17} - 75 x^{16} + 322 x^{15} + 4083 x^{14} - 13386 x^{13} - 47197 x^{12} + 222126 x^{11} + 755604 x^{10} - 6314064 x^{9} - 510672 x^{8} + 78891408 x^{7} - 257271072 x^{6} - 49951008 x^{5} + 1777895376 x^{4} - 3995186848 x^{3} + 22818506112 x^{2} + 35231984640 x + 27667283968$	$18$	[0,9]	$-\,2^{18}\cdot 3^{27}\cdot 5^{6}\cdot 13^{15}\cdot 73^{6}$	$5$	$629.644807417$	$2380.45203313063$	✓			$S_3 \times C_6$ (as 18T6)	$[2, 663415116]$	$2$	$8$	$915173418366.1372$
18.0.275...000.1	$x^{18} - 2 x^{17} - 140 x^{16} - 50 x^{15} + 9349 x^{14} + 23272 x^{13} - 295241 x^{12} - 1389596 x^{11} + 3702763 x^{10} + 37744642 x^{9} + 56319898 x^{8} - 328077626 x^{7} - 1540727786 x^{6} - 146306990 x^{5} + 20797548331 x^{4} + 87252708550 x^{3} + 210708993481 x^{2} + 282909781276 x + 245644707669$	$18$	[0,9]	$-\,2^{24}\cdot 3^{6}\cdot 5^{9}\cdot 271^{14}$	$4$	$634.173654885$	$1039.6648619016023$	✓			$S_3 \times C_6$ (as 18T6)	$[86, 21244580]$	$2$	$8$	$48005482170.92574$
18.0.275...144.1	$x^{18} - 9 x^{17} - 114 x^{16} + 598 x^{15} + 10995 x^{14} - 5745 x^{13} - 553500 x^{12} - 1804737 x^{11} + 14666778 x^{10} + 115321025 x^{9} + 72948210 x^{8} - 2489222517 x^{7} - 11063580650 x^{6} + 4354104129 x^{5} + 234790211235 x^{4} + 1131134296912 x^{3} + 2978310223176 x^{2} + 4545989325489 x + 3552952831147$	$18$	[0,9]	$-\,2^{12}\cdot 3^{24}\cdot 31^{9}\cdot 37^{14}$	$4$	$634.22248611$	$775.1110954468446$	✓		?	$S_3 \times C_6$ (as 18T6)	$[3, 3, 3, 117602388]$	$2$	$8$	$118546543.87559307$
18.0.286...032.1	$x^{18} + 123804 x^{12} + 455035104 x^{6} + 421875000000$	$18$	[0,9]	$-\,2^{12}\cdot 3^{31}\cdot 7^{12}\cdot 67^{12}$	$4$	$635.590484181$	$635.5904841808897$		✓	?	$S_3 \times C_3$ (as 18T3)	$[2, 6, 6, 6, 36, 36, 36, 108]$	$6$	$8$	$1305258438.9061162$
18.0.336...848.1	$x^{18} - 3 x^{17} - 372 x^{16} + 2220 x^{15} + 48642 x^{14} - 446046 x^{13} - 2086968 x^{12} + 34431120 x^{11} - 33488187 x^{10} - 1049976215 x^{9} + 4500825492 x^{8} + 5096936940 x^{7} - 78281565936 x^{6} + 152818776720 x^{5} + 343019618880 x^{4} - 2247082834368 x^{3} + 4853863902720 x^{2} - 5257925494272 x + 2489858275328$	$18$	[0,9]	$-\,2^{12}\cdot 3^{30}\cdot 7^{9}\cdot 61^{14}$	$4$	$641.250396505$	$1079.1025175572363$	✓			$S_3 \times C_6$ (as 18T6)	$[6, 1039665942]$	$2$	$8$	$248523426321.35065$
18.0.724...552.1	$x^{18} + 684 x^{16} + 182628 x^{14} + 24835584 x^{12} + 1856540160 x^{10} + 76187049984 x^{8} + 1609060073472 x^{6} + 14569818292224 x^{4} + 27472624091136 x^{2} + 163208757248$	$18$	[0,9]	$-\,2^{27}\cdot 3^{44}\cdot 19^{17}$	$3$	$669.19567915$	$669.1956791500382$	✓	✓		$C_{18}$ (as 18T1)	$[2, 2, 2, 2, 2, 2, 2, 36, 781596]$	$2$	$8$	$373976932305.4817$
18.0.724...552.3	$x^{18} + 684 x^{16} + 145692 x^{14} + 12701424 x^{12} + 553659696 x^{10} + 13065198912 x^{8} + 168726690432 x^{6} + 1120116736512 x^{4} + 3069202731264 x^{2} + 985095890432$	$18$	[0,9]	$-\,2^{27}\cdot 3^{44}\cdot 19^{17}$	$3$	$669.19567915$	$669.1956791500382$	✓	✓	?	$C_{18}$ (as 18T1)	$[9, 261743454]$	$2$	$8$	$771793981.9189847$
18.0.724...552.4	$x^{18} + 684 x^{16} + 182628 x^{14} + 24322584 x^{12} + 1730990592 x^{10} + 66282292224 x^{8} + 1283370835968 x^{6} + 10319094448128 x^{4} + 17155059351552 x^{2} + 8032970866688$	$18$	[0,9]	$-\,2^{27}\cdot 3^{44}\cdot 19^{17}$	$3$	$669.19567915$	$669.1956791500382$	✓	✓		$C_{18}$ (as 18T1)	$[2, 36, 26617356]$	$2$	$8$	$780956274.3587214$
18.0.724...552.5	$x^{18} + 684 x^{16} + 182628 x^{14} + 25307544 x^{12} + 2016760320 x^{10} + 95935104000 x^{8} + 2718287880192 x^{6} + 44181664137216 x^{4} + 376568116936704 x^{2} + 1297774555430912$	$18$	[0,9]	$-\,2^{27}\cdot 3^{44}\cdot 19^{17}$	$3$	$669.19567915$	$669.1956791500382$	✓	✓		$C_{18}$ (as 18T1)	$[2, 36, 36763092]$	$2$	$8$	$1907649489.937839$
18.0.724...552.6	$x^{18} + 684 x^{16} + 145692 x^{14} + 10156944 x^{12} + 313986096 x^{10} + 4682204352 x^{8} + 31999796352 x^{6} + 81048287232 x^{4} + 69983771904 x^{2} + 14550451712$	$18$	[0,9]	$-\,2^{27}\cdot 3^{44}\cdot 19^{17}$	$3$	$669.19567915$	$669.1956791500382$	✓	✓	?	$C_{18}$ (as 18T1)	$[9, 271391526]$	$2$	$8$	$658443956.5015022$
18.0.855...712.4	$x^{18} - 306 x^{16} - 708 x^{15} + 40104 x^{14} + 202284 x^{13} - 2674572 x^{12} - 20110392 x^{11} + 86941944 x^{10} + 949735792 x^{9} - 423343152 x^{8} - 19766135520 x^{7} - 18882531552 x^{6} + 193086664128 x^{5} + 780864960960 x^{4} + 3330748799808 x^{3} + 16521840365184 x^{2} + 51445398142656 x + 65006631218368$	$18$	[0,9]	$-\,2^{12}\cdot 3^{39}\cdot 13^{12}\cdot 19^{12}$	$4$	$675.430525812$	$675.430525812495$		✓		$S_3 \times C_3$ (as 18T3)	$[3, 3, 3, 3, 585, 25155]$	$6$	$8$	$32762378537.631496$
18.0.113...424.2	$x^{18} - 8 x^{17} - 206 x^{16} - 6 x^{15} + 17550 x^{14} + 124802 x^{13} + 359127 x^{12} + 659382 x^{11} + 4974933 x^{10} + 36876810 x^{9} + 180850253 x^{8} + 695406524 x^{7} + 2546248545 x^{6} + 7978959520 x^{5} + 22847752382 x^{4} + 51046721698 x^{3} + 110400751965 x^{2} + 153363319298 x + 222285198247$	$18$	[0,9]	$-\,2^{33}\cdot 3^{9}\cdot 7^{14}\cdot 61^{14}$	$4$	$686.020825852$	$1078.0622724781153$	✓		?	$S_3 \times C_6$ (as 18T6)	$[6, 18, 108, 137484]$	$2$	$8$	$1363491204.97286$
18.0.115...000.1	$x^{18} + 48 x^{16} - 518 x^{15} + 12087 x^{14} + 43290 x^{13} + 1053253 x^{12} - 49284 x^{11} + 62693295 x^{10} + 334422428 x^{9} + 5992436430 x^{8} + 23739397950 x^{7} + 222938790160 x^{6} + 1003108842378 x^{5} + 11209338881445 x^{4} + 60709569882666 x^{3} + 349997531677587 x^{2} + 954995916305826 x + 2359097078790079$	$18$	[0,9]	$-\,2^{33}\cdot 3^{27}\cdot 5^{9}\cdot 37^{14}$	$4$	$686.700971306$	$839.2473521053773$	✓		?	$S_3 \times C_6$ (as 18T6)	$[6, 6, 258317202]$	$2$	$8$	$118546543.87559307$
18.0.118...944.1	$x^{18} - 6 x^{17} + 427 x^{16} - 108 x^{15} + 75140 x^{14} + 192596 x^{13} + 7791772 x^{12} + 41131796 x^{11} + 324233435 x^{10} + 3688040186 x^{9} + 7170164721 x^{8} + 86405002144 x^{7} + 487968322552 x^{6} - 1781407473888 x^{5} + 19811453012448 x^{4} - 93030379477632 x^{3} + 300717932225024 x^{2} - 470177345986688 x + 723973068517952$	$18$	[0,9]	$-\,2^{33}\cdot 7^{15}\cdot 79^{15}$	$3$	$687.848194205$	$772.083492992753$	✓			$S_3 \times C_6$ (as 18T6)	$[2, 2, 2, 2, 12, 12, 2880360]$	$2$	$8$	$20721910881.979282$
18.0.190...496.2	$x^{18} - 276 x^{16} - 1580 x^{15} + 28422 x^{14} + 355500 x^{13} + 1078822 x^{12} - 9046764 x^{11} + 26855961 x^{10} + 1152845420 x^{9} + 7033272066 x^{8} - 33229098816 x^{7} - 580604160344 x^{6} - 1796953824576 x^{5} + 22616881415904 x^{4} + 273825317586768 x^{3} + 1395378492366564 x^{2} + 3660812605939536 x + 4363300165325176$	$18$	[0,9]	$-\,2^{33}\cdot 3^{27}\cdot 79^{15}$	$3$	$706.197404195$	$792.6797848235244$	✓			$S_3 \times C_6$ (as 18T6)	$[2, 2, 2, 2, 4, 12, 3407460]$	$2$	$8$	$32038743174.66701$
18.0.192...928.2	$x^{18} + 798 x^{16} + 242991 x^{14} + 36093274 x^{12} + 2831149587 x^{10} + 119120371902 x^{8} + 2538023959562 x^{6} + 22440538637328 x^{4} + 39871239158709 x^{2} + 18624704126077$	$18$	[0,9]	$-\,2^{18}\cdot 3^{24}\cdot 7^{15}\cdot 19^{17}$	$4$	$706.564428733$	$706.5644287326527$	✓	✓	?	$C_{18}$ (as 18T1)	$[2, 2, 12, 30537876]$	$2$	$8$	$824118633.8968437$
18.0.192...928.3	$x^{18} + 798 x^{16} + 242991 x^{14} + 38032414 x^{12} + 3369081387 x^{10} + 171403421490 x^{8} + 4744178127122 x^{6} + 59920722735636 x^{4} + 179088217142121 x^{2} + 32131593339013$	$18$	[0,9]	$-\,2^{18}\cdot 3^{24}\cdot 7^{15}\cdot 19^{17}$	$4$	$706.564428733$	$706.5644287326527$	✓	✓	?	$C_{18}$ (as 18T1)	$[2, 2, 12, 33681324]$	$2$	$8$	$1305382696.1857498$
18.0.217...656.1	$x^{18} + 684 x^{16} + 145692 x^{14} + 11366256 x^{12} + 426862512 x^{10} + 8467405632 x^{8} + 88486683264 x^{6} + 444387949056 x^{4} + 829422602496 x^{2} + 188728521216$	$18$	[0,9]	$-\,2^{27}\cdot 3^{45}\cdot 19^{17}$	$3$	$711.311556336$	$711.3115563361192$	✓	✓	?	$C_{18}$ (as 18T1)	$[2, 791649756]$	$2$	$8$	$771793981.9189847$