Number field search results

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

Results (1-50 of 61 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
18.0.382...992.2	$x^{18} - 3 x^{17} - 42 x^{16} + 12 x^{15} + 1512 x^{14} + 1572 x^{13} - 5418 x^{12} - 3414 x^{11} + 258483 x^{10} + 481455 x^{9} + 4287204 x^{8} + 13613802 x^{7} + 73994292 x^{6} + 146257296 x^{5} + 667973280 x^{4} + 855399936 x^{3} + 3840924672 x^{2} + 1876512768 x + 11595603968$	$18$	[0,9]	$-\,2^{18}\cdot 3^{30}\cdot 13^{14}\cdot 23^{9}$	$4$	$440.044290026$	$762.788024220569$	✓			$S_3 \times C_6$ (as 18T6)	$[3, 3, 3, 6, 236316906]$	$2$	$8$	$3533133948.6916637$
18.0.134...631.6	$x^{18} - 666 x^{15} + 10989 x^{14} - 132534 x^{13} + 504828 x^{12} + 267732 x^{11} - 2869461 x^{10} - 2521772 x^{9} + 77298624 x^{8} + 21004974 x^{7} - 459144729 x^{6} + 1801890306 x^{5} + 9112996548 x^{4} - 24669932040 x^{3} + 41395363200 x^{2} + 65283984000 x + 33270400000$	$18$	[0,9]	$-\,3^{45}\cdot 37^{17}$	$2$	$471.935386691$	$471.9353866914472$	✓	✓		$C_{18}$ (as 18T1)	$[14802753096]$	$2$	$8$	$23654456315312.36$
18.0.196...616.1	$x^{18} - 7 x^{17} + 4 x^{16} + 184 x^{15} + 128 x^{14} - 8092 x^{13} + 51598 x^{12} - 134342 x^{11} + 478943 x^{10} - 3007341 x^{9} + 21773822 x^{8} - 92692658 x^{7} + 352111696 x^{6} - 1127712400 x^{5} + 4235753024 x^{4} - 12494373536 x^{3} + 32946159232 x^{2} - 50298266368 x + 59975185408$	$18$	[0,9]	$-\,2^{18}\cdot 31^{9}\cdot 127^{14}$	$3$	$481.950711271$	$892.0631670322495$	✓			$S_3 \times C_6$ (as 18T6)	$[9, 9, 244021806]$	$2$	$8$	$5546046730.2947445$
18.0.155...664.2	$x^{18} - 7 x^{17} + 22 x^{16} + 72 x^{15} + 648 x^{14} - 9060 x^{13} + 72318 x^{12} - 272982 x^{11} + 1442715 x^{10} - 7028429 x^{9} + 45186124 x^{8} - 191602578 x^{7} + 838542252 x^{6} - 2810738664 x^{5} + 10903299792 x^{4} - 31071279168 x^{3} + 87450314880 x^{2} - 137349245952 x + 194888648704$	$18$	[0,9]	$-\,2^{18}\cdot 3^{9}\cdot 13^{9}\cdot 127^{14}$	$4$	$540.572666348$	$1000.5690488183127$	✓			$S_3 \times C_6$ (as 18T6)	$[2, 84, 357158172]$	$2$	$8$	$5546046730.2947445$
18.0.172...792.1	$x^{18} - 9 x^{17} - 420 x^{16} + 1984 x^{15} + 73770 x^{14} - 37218 x^{13} - 6149376 x^{12} - 16784976 x^{11} + 237244221 x^{10} + 1419179555 x^{9} - 2094160692 x^{8} - 40253540568 x^{7} - 102727801808 x^{6} + 224932172208 x^{5} + 2034413940288 x^{4} + 5797665555712 x^{3} + 9183109401600 x^{2} + 8595850543104 x + 4021085863936$	$18$	[0,9]	$-\,2^{12}\cdot 3^{24}\cdot 7^{9}\cdot 79^{14}$	$4$	$543.662701528$	$873.1655608199176$	✓			$S_3 \times C_6$ (as 18T6)	$[2, 2, 4, 12, 84, 1009932]$	$2$	$8$	$32038743174.66701$
18.0.224...000.1	$x^{18} - 9 x^{17} - 402 x^{16} + 1840 x^{15} + 69018 x^{14} - 10914 x^{13} - 5537100 x^{12} - 17815248 x^{11} + 205547661 x^{10} + 1433969187 x^{9} - 1050471018 x^{8} - 39884181384 x^{7} - 128655698368 x^{6} + 185836782000 x^{5} + 2638164247776 x^{4} + 9516122868224 x^{3} + 19470659444736 x^{2} + 24153643711488 x + 15157286557696$	$18$	[0,9]	$-\,2^{12}\cdot 3^{27}\cdot 5^{9}\cdot 79^{14}$	$4$	$551.805125483$	$886.2429416276534$	✓			$S_3 \times C_6$ (as 18T6)	$[6, 84, 45051972]$	$2$	$8$	$32038743174.66701$
18.0.147...712.1	$x^{18} - 2 x^{17} - 127 x^{16} - 1370 x^{15} + 1071 x^{14} + 162946 x^{13} + 2249906 x^{12} + 19230652 x^{11} + 121957908 x^{10} + 608611962 x^{9} + 2449633407 x^{8} + 8020398008 x^{7} + 21278039105 x^{6} + 45104419528 x^{5} + 74302857419 x^{4} + 90626337302 x^{3} + 75780975570 x^{2} + 38197162944 x + 8660565481$	$18$	[0,9]	$-\,2^{12}\cdot 7^{15}\cdot 19^{9}\cdot 31^{15}$	$4$	$612.510083153$	$612.5100831527393$		✓	?	$S_3 \times C_3$ (as 18T3)	$[2, 2, 2, 4, 4, 4, 4, 12, 156, 9516]$	$2$	$8$	$36950112.38519628$
18.0.123...792.1	$x^{18} - 9 x^{17} + 384 x^{16} - 2272 x^{15} + 88605 x^{14} - 658197 x^{13} + 12846028 x^{12} - 64843719 x^{11} + 865327146 x^{10} - 5579169113 x^{9} + 77246982246 x^{8} - 512686378569 x^{7} + 3789040141804 x^{6} - 15288000079185 x^{5} + 92885783574705 x^{4} - 423518882731740 x^{3} + 2727446539429518 x^{2} - 8733433478069253 x + 23845975839012979$	$18$	[0,9]	$-\,2^{12}\cdot 3^{27}\cdot 17^{9}\cdot 37^{15}$	$4$	$689.330947541$	$689.3309475411555$	✓		?	$S_3 \times C_6$ (as 18T6)	$[2, 78, 70196490]$	$2$	$8$	$118546543.87559307$
18.0.217...656.6	$x^{18} + 684 x^{16} + 145692 x^{14} + 10824528 x^{12} + 377384688 x^{10} + 6981100992 x^{8} + 70338466944 x^{6} + 363270583296 x^{4} + 755493868800 x^{2} + 40292160000$	$18$	[0,9]	$-\,2^{27}\cdot 3^{45}\cdot 19^{17}$	$3$	$711.311556336$	$711.3115563361192$	✓	✓		$C_{18}$ (as 18T1)	$[2, 14851834524]$	$2$	$8$	$5772307958.489205$
18.0.271...008.1	$x^{18} + 75 x^{16} - 518 x^{15} + 14895 x^{14} + 38628 x^{13} + 1453312 x^{12} + 695970 x^{11} + 97733346 x^{10} + 422945816 x^{9} + 8555002947 x^{8} + 33622267188 x^{7} + 365903950891 x^{6} + 1580920554276 x^{5} + 17528600923959 x^{4} + 88916584556742 x^{3} + 542518369755228 x^{2} + 1475998825390308 x + 4052214442111177$	$18$	[0,9]	$-\,2^{24}\cdot 3^{27}\cdot 11^{9}\cdot 37^{14}$	$4$	$720.218054753$	$880.2100486914904$	✓		?	$S_3 \times C_6$ (as 18T6)	$[2, 6, 210, 4951590]$	$2$	$8$	$118546543.87559307$
18.0.326...187.2	$x^{18} + 109359 x^{12} + 354417390 x^{6} + 291038813883$	$18$	[0,9]	$-\,3^{27}\cdot 1657^{12}$	$2$	$727.607032028$	$727.6070320279168$		✓	?	$S_3 \times C_3$ (as 18T3)	$[2, 2, 1050, 2470650]$	$6$	$8$	$1266915384.7466033$
18.0.408...232.1	$x^{18} - 9 x^{17} + 12 x^{16} - 410 x^{15} + 10995 x^{14} - 9861 x^{13} + 162726 x^{12} - 3204009 x^{11} + 24015348 x^{10} + 104943021 x^{9} + 1568694924 x^{8} - 152631309 x^{7} + 19476958064 x^{6} + 109343418069 x^{5} + 2476828380501 x^{4} + 13611173843684 x^{3} + 68512294190292 x^{2} + 162135328484937 x + 329489799094441$	$18$	[0,9]	$-\,2^{12}\cdot 3^{27}\cdot 29^{9}\cdot 37^{14}$	$4$	$736.681895462$	$900.3312299599922$	✓		?	$S_3 \times C_6$ (as 18T6)	$[3, 3, 378, 4455864]$	$2$	$8$	$118546543.87559307$
18.0.888...187.2	$x^{18} + 118863 x^{12} + 418673070 x^{6} + 373714754427$	$18$	[0,9]	$-\,3^{27}\cdot 1801^{12}$	$2$	$769.173577976$	$769.1735779760147$		✓	?	$S_3 \times C_3$ (as 18T3)	$[26, 26, 312, 67704]$	$6$	$8$	$1321946620.3369434$
18.0.211...776.1	$x^{18} - 388 x^{16} - 1770 x^{15} + 79167 x^{14} + 461226 x^{13} - 7119103 x^{12} - 69040572 x^{11} + 412426863 x^{10} + 4399169196 x^{9} - 18676098374 x^{8} - 265581279066 x^{7} + 550446017812 x^{6} + 17062555046622 x^{5} + 128931293649937 x^{4} + 697432636061526 x^{3} + 2270159537466107 x^{2} + 2634341655131550 x + 6328125825565187$	$18$	[0,9]	$-\,2^{12}\cdot 7^{12}\cdot 37^{15}\cdot 47^{9}$	$4$	$807.177516104$	$807.1775161036906$		✓	?	$S_3 \times C_3$ (as 18T3)	$[3, 3, 3, 3, 3, 3, 777, 46620]$	$2$	$8$	$508181773.5034319$
18.0.766...000.1	$x^{18} - 4 x^{17} - 161 x^{16} + 122 x^{15} + 12163 x^{14} + 26048 x^{13} - 396092 x^{12} - 1847422 x^{11} + 4445026 x^{10} + 49750964 x^{9} + 101924407 x^{8} - 223146292 x^{7} - 1210841585 x^{6} + 1527209132 x^{5} + 28187586667 x^{4} + 108856477778 x^{3} + 256578470140 x^{2} + 342514005968 x + 299674652229$	$18$	[0,9]	$-\,2^{30}\cdot 3^{6}\cdot 5^{9}\cdot 7^{14}\cdot 43^{14}$	$5$	$866.993858056$	$1801.2653737007222$	✓			$S_3 \times C_6$ (as 18T6)	$[3, 3, 6, 12, 252, 212688]$	$2$	$8$	$58418500973.81414$
18.0.125...192.1	$x^{18} + 242604 x^{12} + 14701076640 x^{6} + 1728$	$18$	[0,9]	$-\,2^{12}\cdot 3^{27}\cdot 1123^{12}$	$3$	$891.158697427$	$891.1586974269279$		✓	?	$S_3 \times C_3$ (as 18T3)	$[301, 4515, 58695]$	$6$	$8$	$1065094301.6985265$
18.0.844...000.1	$x^{18} - 3 x^{17} - 552 x^{16} + 6240 x^{15} + 53364 x^{14} - 1530168 x^{13} + 13275402 x^{12} - 60135330 x^{11} + 149804439 x^{10} - 232194769 x^{9} + 966780294 x^{8} - 7176130086 x^{7} + 33707047332 x^{6} - 107168086212 x^{5} + 257696335560 x^{4} - 491003942664 x^{3} + 736717649280 x^{2} - 788668438368 x + 499240711936$	$18$	[0,9]	$-\,2^{18}\cdot 3^{31}\cdot 5^{9}\cdot 7^{14}\cdot 13^{14}$	$5$	$990.65557087$	$1800.003364360441$	✓			$S_3 \times C_6$ (as 18T6)	$[2, 2, 2, 2, 30, 154037940]$	$2$	$8$	$1784332202668.8357$
18.0.987...907.4	$x^{18} - 9 x^{17} + 45 x^{16} + 36 x^{15} - 1026 x^{14} + 4590 x^{13} - 12816 x^{12} + 26028 x^{11} + 90828 x^{10} - 1489446 x^{9} + 5627718 x^{8} - 12557430 x^{7} + 49427415 x^{6} - 103026411 x^{5} + 91894095 x^{4} - 352468422 x^{3} + 573552900 x^{2} + 396747072 x + 780420096$	$18$	[0,9]	$-\,3^{39}\cdot 7^{12}\cdot 127^{12}$	$3$	$999.30307977$	$999.3030797698304$		✓		$S_3 \times C_3$ (as 18T3)	$[3, 18, 18, 18, 18, 252, 252]$	$6$	$8$	$59097926601.30937$
18.0.116...216.1	$x^{18} + 762 x^{16} + 218313 x^{14} + 30376749 x^{12} + 2249058240 x^{10} + 89192075616 x^{8} + 1757405549952 x^{6} + 14140144366848 x^{4} + 39992306079744 x^{2} + 9792653414400$	$18$	[0,9]	$-\,2^{18}\cdot 3^{27}\cdot 127^{17}$	$3$	$1008.41109236$	$1008.4110923638796$	✓	✓		$C_{18}$ (as 18T1)	$[2, 2, 2, 2217190170]$	$2$	$8$	$88513037217.36226$
18.0.201...688.1	$x^{18} - 9 x^{17} + 45 x^{16} + 636 x^{15} - 5526 x^{14} + 21690 x^{13} - 29010 x^{12} - 57708 x^{11} + 2184723 x^{10} - 57195115 x^{9} + 237549663 x^{8} - 590965020 x^{7} + 7075342842 x^{6} - 18851833098 x^{5} + 11484916434 x^{4} - 293292196752 x^{3} + 462523978377 x^{2} + 433013473827 x + 4995175830121$	$18$	[0,9]	$-\,2^{12}\cdot 3^{33}\cdot 19^{12}\cdot 43^{12}$	$4$	$1039.65760591$	$1039.6576059055951$		✓	?	$S_3 \times C_3$ (as 18T3)	$[3, 9, 9, 9, 1386, 26334]$	$6$	$8$	$2105795997.736377$
18.0.267...000.1	$x^{18} - 3 x^{17} - 807 x^{16} + 1005 x^{15} + 269049 x^{14} + 73797 x^{13} - 46410555 x^{12} - 66738279 x^{11} + 4474849215 x^{10} + 10471753955 x^{9} - 240910122405 x^{8} - 759018551721 x^{7} + 6760093363683 x^{6} + 26905061270919 x^{5} - 81820212046617 x^{4} - 419376128500893 x^{3} + 286839979293732 x^{2} + 2932106044957716 x + 3159025422781024$	$18$	[0,9]	$-\,2^{12}\cdot 3^{31}\cdot 5^{9}\cdot 7^{14}\cdot 19^{14}$	$5$	$1056.24606292$	$1746.2249651383675$	✓			$S_3 \times C_6$ (as 18T6)	$[3, 6, 12, 220646244]$	$2$	$8$	$5963727865967.527$
18.0.521...000.1	$x^{18} - 8 x^{17} - 517 x^{16} + 1678 x^{15} + 96179 x^{14} + 34920 x^{13} - 5376324 x^{12} + 5188354 x^{11} + 148150274 x^{10} - 258684356 x^{9} - 628744217 x^{8} - 3685397192 x^{7} + 30254061027 x^{6} - 6887580648 x^{5} + 43144941139 x^{4} - 488373903890 x^{3} + 1226187715060 x^{2} + 1982246556352 x + 9154324841549$	$18$	[0,9]	$-\,2^{24}\cdot 5^{9}\cdot 877^{14}$	$3$	$1096.11977641$	$1597.1951797930046$	✓		?	$S_3 \times C_6$ (as 18T6)	$[2, 2, 54, 61400052]$	$2$	$8$	$11318340440.066559$
18.0.858...336.1	$x^{18} - 8 x^{17} - 172 x^{16} - 1382 x^{15} + 11784 x^{14} + 353158 x^{13} + 4437353 x^{12} + 37700470 x^{11} + 245003955 x^{10} + 1270005030 x^{9} + 5351249319 x^{8} + 18426951344 x^{7} + 51518737541 x^{6} + 115116872056 x^{5} + 199374151874 x^{4} + 253917378998 x^{3} + 219504667881 x^{2} + 113162419542 x + 25987884553$	$18$	[0,9]	$-\,2^{27}\cdot 11^{9}\cdot 313^{15}$	$3$	$1126.83834568$	$1126.8383456793752$		✓		$S_3 \times C_3$ (as 18T3)	$[9, 9, 27, 54, 151956]$	$2$	$8$	$5926891982.334674$
18.0.221...032.1	$x^{18} - 2 x^{17} - 475 x^{16} - 2764 x^{15} + 35862 x^{14} + 811404 x^{13} + 11671470 x^{12} + 80449872 x^{11} + 381518397 x^{10} + 414420542 x^{9} + 1059157049 x^{8} + 62716099132 x^{7} + 708210563500 x^{6} + 5574455143176 x^{5} + 57576694070148 x^{4} + 257270466657168 x^{3} + 1724517820231056 x^{2} + 176904804349440 x + 19989274074918912$	$18$	[0,9]	$-\,2^{27}\cdot 3^{9}\cdot 727^{15}$	$3$	$1187.72973682$	$1187.72973682315$		✓		$S_3 \times C_3$ (as 18T3)	$[2, 2, 6, 6, 2922, 61362]$	$2$	$8$	$49077055635172.75$
18.0.329...848.2	$x^{18} - 6 x^{17} - 588 x^{16} + 2730 x^{15} + 140388 x^{14} - 535026 x^{13} - 15515850 x^{12} + 66139470 x^{11} + 839143659 x^{10} - 4277544184 x^{9} - 17718435114 x^{8} + 79245803352 x^{7} + 350741017488 x^{6} - 605392710048 x^{5} - 6069527174496 x^{4} - 1091786217216 x^{3} + 57382505628672 x^{2} + 110075105415168 x + 64478748483584$	$18$	[0,9]	$-\,2^{18}\cdot 3^{30}\cdot 7^{9}\cdot 103^{14}$	$4$	$1214.28651067$	$2361.3871467062645$	✓			$S_3 \times C_6$ (as 18T6)	$[2, 6, 1010271384]$	$2$	$8$	$135497086932398.42$
18.0.516...544.1	$x^{18} - x^{17} - 339 x^{16} - 46 x^{15} + 47557 x^{14} + 56007 x^{13} - 3490681 x^{12} - 7365053 x^{11} + 144682296 x^{10} + 437794222 x^{9} - 3261383845 x^{8} - 13326944589 x^{7} + 32763269619 x^{6} + 195609354075 x^{5} - 27367760547 x^{4} - 1043363367495 x^{3} + 187960310919 x^{2} + 6621321395790 x + 10883991773043$	$18$	[0,9]	$-\,2^{18}\cdot 3^{6}\cdot 11^{9}\cdot 523^{14}$	$4$	$1244.96447471$	$2993.781066708205$	✓			$S_3 \times C_6$ (as 18T6)	$[2, 7931527162]$	$2$	$8$	$1120251490200.2412$
18.0.317...888.1	$x^{18} - x^{17} - 984 x^{16} + 2510 x^{15} + 399126 x^{14} - 1518902 x^{13} - 79528672 x^{12} + 365710044 x^{11} + 8041909773 x^{10} - 37726851253 x^{9} - 388634200160 x^{8} + 1634195356934 x^{7} + 9217764115764 x^{6} - 27873163776444 x^{5} - 74670398987968 x^{4} - 46074585055336 x^{3} + 719202938309504 x^{2} + 674017524612704 x + 783773403510784$	$18$	[0,9]	$-\,2^{12}\cdot 7^{15}\cdot 19^{6}\cdot 211^{14}$	$4$	$1377.0873022$	$3815.5505259090596$	✓			$S_3 \times C_6$ (as 18T6)	$[3, 3, 3, 9, 9, 6906690]$	$2$	$8$	$182929425339792.53$
18.0.924...048.1	$x^{18} - x^{17} + 470 x^{16} + 2513 x^{15} + 149163 x^{14} + 956039 x^{13} + 28464247 x^{12} + 225068368 x^{11} + 3988265085 x^{10} + 28542470943 x^{9} + 336726026476 x^{8} + 2290282965516 x^{7} + 19375023447318 x^{6} + 96784777040119 x^{5} + 380485121195032 x^{4} + 969083882090814 x^{3} + 1861722334970505 x^{2} + 2126907556454464 x + 1628413597910449$	$18$	[0,9]	$-\,2^{12}\cdot 3^{9}\cdot 7^{6}\cdot 19^{14}\cdot 73^{14}$	$5$	$1461.44974325$	$3021.2966005615217$	✓			$S_3 \times C_6$ (as 18T6)	$[3, 3, 3, 12, 12, 5992980]$	$6$	$8$	$1270819096089.6284$
18.0.243...000.1	$x^{18} + 1302 x^{16} + 537075 x^{14} + 87091648 x^{12} + 7014895419 x^{10} + 308465253054 x^{8} + 7475073472013 x^{6} + 92453456727660 x^{4} + 451572633759492 x^{2} + 194277433462336$	$18$	[0,9]	$-\,2^{30}\cdot 3^{24}\cdot 5^{6}\cdot 7^{14}\cdot 31^{14}$	$5$	$1542.10801187$	$3425.756139012853$	✓			$S_3 \times C_6$ (as 18T6)	$[2, 2, 4, 12, 77921736]$	$4$	$8$	$162297974877455.78$
18.0.733...443.1	$x^{18} - 9 x^{17} + 45 x^{16} + 1902 x^{15} - 15021 x^{14} + 57771 x^{13} - 5041232 x^{12} + 29633925 x^{11} - 22759602 x^{10} - 6203302885 x^{9} + 27813323421 x^{8} - 57748921875 x^{7} + 9019520363287 x^{6} - 26874825967038 x^{5} + 52528838073972 x^{4} - 300600540176057 x^{3} + 412931389362222 x^{2} + 333613339887189 x + 1397069806495609$	$18$	[0,9]	$-\,3^{21}\cdot 7^{12}\cdot 19^{12}\cdot 73^{12}$	$4$	$1639.67508621$	$1639.6750862110014$		✓	?	$S_3 \times C_3$ (as 18T3)	$[3, 3, 3, 3, 3, 3, 3, 9, 9, 36, 2052]$	$6$	$8$	$2508774324153.621$
18.0.795...707.3	$x^{18} + 248166 x^{12} + 3825681705 x^{6} + 1855425871872$	$18$	[0,9]	$-\,3^{31}\cdot 7^{12}\cdot 13^{12}\cdot 43^{12}$	$4$	$1647.08265147$	$1647.0826514653338$		✓		$S_3 \times C_3$ (as 18T3)	$[3, 3, 3, 9, 9, 18, 18, 126, 126]$	$6$	$8$	$10228947091425.262$
18.0.619...688.1	$x^{18} + 51576 x^{12} + 306516240 x^{6} + 5159780352$	$18$	[0,9]	$-\,2^{12}\cdot 3^{33}\cdot 1933^{12}$	$3$	$1845.99363871$	$1845.9936387089674$		✓		$S_3 \times C_3$ (as 18T3)	$[3, 6, 6, 54, 54, 108, 1404]$	$6$	$8$	$4462230161839.376$
18.0.663...472.1	$x^{18} - 3024 x^{15} + 1165924 x^{12} + 2022824160 x^{9} + 951986143216 x^{6} + 208357877056896 x^{3} + 19780262567688384$	$18$	[0,9]	$-\,2^{12}\cdot 3^{27}\cdot 7^{12}\cdot 13^{12}\cdot 37^{12}$	$5$	$1852.95109355$	$1852.951093547014$		✓		$S_3 \times C_3$ (as 18T3)	$[3, 3, 3, 3, 3, 3, 9, 117, 15561]$	$6$	$8$	$87969966278262.44$
18.0.691...000.1	$x^{18} - 126 x^{16} - 1506 x^{15} + 13413 x^{14} + 94968 x^{13} + 606345 x^{12} + 23306106 x^{11} + 362900991 x^{10} + 207124472 x^{9} - 20638244151 x^{8} - 55026746730 x^{7} + 964213213642 x^{6} + 1142790467772 x^{5} - 26838014382981 x^{4} + 4275378675392 x^{3} + 597733410996390 x^{2} - 2203214877726000 x + 2708125245357200$	$18$	[0,9]	$-\,2^{27}\cdot 3^{18}\cdot 5^{12}\cdot 11^{15}\cdot 103^{9}$	$5$	$1857.34294756$	$2230.55178415808$				$S_3^2$ (as 18T11)	$[3, 3, 6, 18, 18, 18, 234, 702]$	$2$	$8$	$11922805943498.25$
18.0.753...191.1	$x^{18} - 6 x^{17} - 1527 x^{16} + 8808 x^{15} + 927642 x^{14} - 5120388 x^{13} - 288098278 x^{12} + 1510843992 x^{11} + 49548274205 x^{10} - 244055933606 x^{9} - 4575731495955 x^{8} + 20737038801648 x^{7} + 221396206694440 x^{6} - 911575249761792 x^{5} - 3926480656027888 x^{4} + 16967797388265088 x^{3} - 74294080126316288 x^{2} - 74967510509588480 x + 3741267643296382976$	$18$	[0,9]	$-\,7^{12}\cdot 97^{15}\cdot 127^{9}$	$3$	$1866.13761003$	$1866.1376100312793$		✓		$S_3 \times C_3$ (as 18T3)	$[3, 3, 3, 3, 42, 84, 86268]$	$2$	$8$	$141934307507722030$
18.0.914...328.1	$x^{18} - 9 x^{17} + 255 x^{16} - 1824 x^{15} + 24423 x^{14} - 137697 x^{13} + 1727788 x^{12} - 8466441 x^{11} - 43796637 x^{10} + 269577198 x^{9} + 5420996661 x^{8} - 22405758879 x^{7} + 238912851253 x^{6} - 660557469432 x^{5} - 10676966704536 x^{4} + 23268587608140 x^{3} + 505306443813876 x^{2} - 547038123493644 x + 948137416523604$	$18$	[0,9]	$-\,2^{12}\cdot 3^{21}\cdot 7^{14}\cdot 13^{14}\cdot 19^{14}$	$5$	$1886.31024012$	$2854.240879731732$				$S_3^2$ (as 18T11)	$[3, 3, 3, 3, 9, 9, 18, 54, 54, 54]$	$6$	$8$	$34782068743257.96$
18.0.262...568.1	$x^{18} - 2 x^{17} + 501 x^{16} + 14648 x^{15} + 272582 x^{14} + 3144591 x^{13} + 27063010 x^{12} + 177529456 x^{11} + 942236178 x^{10} + 4085550909 x^{9} + 15020023463 x^{8} + 47124023126 x^{7} + 130555515789 x^{6} + 316870835959 x^{5} + 684237290359 x^{4} + 1237214238291 x^{3} + 1844496811058 x^{2} + 1914036738569 x + 1310138919769$	$18$	[0,9]	$-\,2^{12}\cdot 3^{9}\cdot 29^{6}\cdot 1129^{14}$	$4$	$2000.00370789$	$5180.335750362452$	✓		?	$S_3 \times C_6$ (as 18T6)	$[5, 105, 86358510]$	$6$	$8$	$2974025056676.291$
18.0.335...000.1	$x^{18} + 912 x^{16} + 310692 x^{14} + 52656708 x^{12} + 4846114662 x^{10} + 244755477132 x^{8} + 6554580709188 x^{6} + 88881650645340 x^{4} + 561033372337329 x^{2} + 1286936844705604$	$18$	[0,9]	$-\,2^{30}\cdot 3^{6}\cdot 5^{6}\cdot 7^{14}\cdot 181^{14}$	$5$	$2027.76573256$	$5966.955512699272$	✓			$S_3 \times C_6$ (as 18T6)	$[2, 6, 12, 12, 12, 12, 391740]$	$4$	$8$	$49926751662940.16$
18.0.490...488.1	$x^{18} + 3 x^{16} + 1008 x^{14} + 195268 x^{12} - 268014 x^{10} - 64460646 x^{8} + 2448021928 x^{6} + 5576982228 x^{4} - 170682814251 x^{2} + 832184947467$	$18$	[0,9]	$-\,2^{12}\cdot 3^{9}\cdot 7^{12}\cdot 2953^{12}$	$4$	$2070.88007292$	$2070.880072921307$		✓		$S_3 \times C_3$ (as 18T3)	$[2, 6, 6, 18, 36, 36, 36, 468]$	$6$	$8$	$63617903134123.17$
18.0.490...000.1	$x^{18} - 6 x^{17} - 687 x^{16} + 5406 x^{15} + 272031 x^{14} - 1075578 x^{13} - 45303006 x^{12} + 153139332 x^{11} + 4227681804 x^{10} - 17494139554 x^{9} - 302274108753 x^{8} + 1253829209316 x^{7} + 18917369006865 x^{6} - 93984714115572 x^{5} - 281050838668113 x^{4} + 2951327570583606 x^{3} + 17012485372731978 x^{2} - 151213514911900860 x + 463589489758381849$	$18$	[0,9]	$-\,2^{12}\cdot 3^{31}\cdot 5^{9}\cdot 7^{9}\cdot 67^{15}$	$5$	$2070.89708014$	$2070.897080137092$		✓		$S_3 \times C_3$ (as 18T3)	$[6, 6, 6, 378, 145908]$	$2$	$8$	$7232933732765.735$
18.0.679...336.1	$x^{18} - 8 x^{17} - 404 x^{16} + 10918 x^{15} + 91669 x^{14} - 3015554 x^{13} + 1101203 x^{12} + 468459422 x^{11} - 1783988569 x^{10} - 51385464532 x^{9} + 77131235840 x^{8} + 3937918314038 x^{7} + 16704551289024 x^{6} - 53767855256436 x^{5} - 391238980093323 x^{4} + 512206086889224 x^{3} + 9961068503950641 x^{2} + 26421806277378576 x + 22113695846279691$	$18$	[0,9]	$-\,2^{12}\cdot 23^{9}\cdot 853^{15}$	$3$	$2108.66751586$	$2108.6675158623016$		✓		$S_3 \times C_3$ (as 18T3)	$[2, 2, 42, 294, 328104]$	$2$	$8$	$2283911350493462.0$
18.0.733...827.1	$x^{18} + 530694 x^{12} + 13431802185 x^{6} + 23917744283328$	$18$	[0,9]	$-\,3^{27}\cdot 19^{12}\cdot 433^{12}$	$3$	$2117.59488996$	$2117.594889959028$		✓		$S_3 \times C_3$ (as 18T3)	$[3, 3, 3, 3, 3, 3, 21, 63, 126, 378]$	$6$	$8$	$81466624347417.27$
18.0.138...227.1	$x^{18} + 485982 x^{12} + 46823693841 x^{6} + 195920474112$	$18$	[0,9]	$-\,3^{27}\cdot 8677^{12}$	$2$	$2194.12625231$	$2194.126252307399$		✓		$S_3 \times C_3$ (as 18T3)	$[3, 3, 3, 9, 9, 1386, 18018]$	$6$	$8$	$98053733517680.33$
18.0.209...483.1	$x^{18} - 3 x^{17} - 416 x^{16} + 1257 x^{15} + 288337 x^{14} - 10786920 x^{13} + 157669824 x^{12} - 1816888320 x^{11} + 30380700672 x^{10} - 623446253568 x^{9} + 11510437699584 x^{8} - 113780248805376 x^{7} + 677775794503680 x^{6} - 3079806388273152 x^{5} + 18983977004040192 x^{4} - 90314630466895872 x^{3} + 453434281285386240 x^{2} - 722517043735166976 x + 436217609315155968$	$18$	[0,9]	$-\,3^{9}\cdot 13^{12}\cdot 37^{12}\cdot 97^{12}$	$4$	$2244.76992151$	$2244.7699215096413$		✓		$S_3 \times C_3$ (as 18T3)	$[2, 2, 2, 6, 18, 18, 396, 8316]$	$6$	$8$	$723879812207986.1$
18.0.227...003.1	$x^{18} + 27592275 x^{12} + 25321119032448 x^{6} + 1418640313495891968$	$18$	[0,9]	$-\,3^{33}\cdot 17^{12}\cdot 307^{12}$	$3$	$2254.83014112$	$2254.8301411195744$		✓		$S_3 \times C_3$ (as 18T3)	$[2, 2, 6, 6, 12, 12, 12, 36, 36, 36]$	$6$	$8$	$392363527634279.25$
18.0.691...307.2	$x^{18} - 9919 x^{15} + 103266244 x^{12} + 25079348385 x^{9} + 2032589480652 x^{6} - 3842823830391 x^{3} + 7625597484987$	$18$	[0,9]	$-\,3^{27}\cdot 7^{12}\cdot 13^{12}\cdot 109^{12}$	$4$	$2398.79872273$	$2398.7987227316275$		✓	?	$S_3 \times C_3$ (as 18T3)	$[3, 3, 3, 3, 3, 6, 18, 990, 2970]$	$6$	$8$	$78066072406331.89$
18.0.130...375.1	$x^{18} + 606 x^{16} - 42 x^{15} + 153015 x^{14} - 8484 x^{13} + 22856695 x^{12} - 428442 x^{11} + 2469822387 x^{10} + 729775284 x^{9} + 200774929287 x^{8} + 139597980018 x^{7} + 12034816391578 x^{6} + 8756629556136 x^{5} + 575675484948417 x^{4} + 8578727481828 x^{3} + 17233229874363636 x^{2} - 6266059191729120 x + 421748783514829120$	$18$	[0,9]	$-\,3^{18}\cdot 5^{9}\cdot 7^{15}\cdot 11^{9}\cdot 487^{9}$	$5$	$2484.9373668$	$2984.253115084941$				$S_3^2$ (as 18T11)	$[2, 2, 2, 6, 6, 6, 246, 64944]$	$2$	$8$	$5044715737238670.0$
18.0.147...283.1	$x^{18} - 3 x^{17} - 440 x^{16} + 437 x^{15} - 337117 x^{14} + 23671983 x^{13} - 368833646 x^{12} - 6602474036 x^{11} + 387409454753 x^{10} - 8399255282261 x^{9} + 115084114183121 x^{8} - 1118467036430126 x^{7} + 8043217290890512 x^{6} - 43369484085540759 x^{5} + 174370588263468377 x^{4} - 510173162432207521 x^{3} + 1031399763020665000 x^{2} - 1294085044187005725 x + 762516782753267677$	$18$	[0,9]	$-\,3^{9}\cdot 13^{12}\cdot 41^{12}\cdot 103^{12}$	$4$	$2501.90174398$	$2501.9017439796276$		✓	?	$S_3 \times C_3$ (as 18T3)	$[3, 63, 6867, 20601]$	$6$	$8$	$54845796471897.65$
18.0.267...952.1	$x^{18} + 1465272 x^{12} + 63795390480 x^{6} + 699092182315008$	$18$	[0,9]	$-\,2^{12}\cdot 3^{27}\cdot 7^{12}\cdot 13^{12}\cdot 61^{12}$	$5$	$2585.92563074$	$2585.925630736131$		✓		$S_3 \times C_3$ (as 18T3)	$[3, 3, 3, 3, 3, 3, 3, 3, 3, 57, 15561]$	$6$	$8$	$973307437394863.9$
18.0.480...816.1	$x^{18} + 141 x^{16} - 360 x^{15} + 13683 x^{14} - 71064 x^{13} + 1291103 x^{12} - 11920464 x^{11} + 77297904 x^{10} - 445448336 x^{9} + 1752021792 x^{8} - 13129615872 x^{7} + 55401409440 x^{6} - 99026005248 x^{5} + 847107279360 x^{4} - 3040844951808 x^{3} + 2031770407680 x^{2} - 19444819046400 x + 63555755265792$	$18$	[0,9]	$-\,2^{12}\cdot 3^{18}\cdot 17^{12}\cdot 23^{9}\cdot 313^{9}$	$5$	$2671.42684709$	$3208.2152237219734$				$S_3^2$ (as 18T11)	$[2, 6, 6, 6, 6, 6, 36, 36, 3420]$	$2$	$8$	$342971481898070.0$