Number field search results

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

Results (1-50 of 63129 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
18.0.107...375.1	$x^{18} - x^{17} + 20 x^{16} - 20 x^{15} + 172 x^{14} - 172 x^{13} + 837 x^{12} - 837 x^{11} + 2566 x^{10} - 2566 x^{9} + 5283 x^{8} - 5283 x^{7} + 7791 x^{6} - 7791 x^{5} + 9045 x^{4} - 9045 x^{3} + 9330 x^{2} - 9330 x + 9349$	$18$	[0,9]	$-\,5^{9}\cdot 19^{17}$	$2$	$36.0742022981$	$36.07420229809253$	✓	✓	?	$C_{18}$ (as 18T1)	$[152]$	$2$	$8$	$22305.8950792$
18.0.116...367.1	$x^{18} - x^{17} + 26 x^{16} - 19 x^{15} + 319 x^{14} - 179 x^{13} + 2258 x^{12} - 914 x^{11} + 9881 x^{10} - 2825 x^{9} + 26418 x^{8} - 4536 x^{7} + 41176 x^{6} - 4496 x^{5} + 32480 x^{4} + 10240 x^{2} - 1280 x + 512$	$18$	[0,9]	$-\,7^{9}\cdot 19^{16}$	$2$	$36.2425617492$	$36.24256174919533$	✓	✓	?	$C_{18}$ (as 18T1)	$[2, 74]$	$2$	$8$	$22305.8950792$
18.0.124...503.1	$x^{18} - 8 x^{17} + 44 x^{16} - 148 x^{15} + 337 x^{14} - 355 x^{13} - 409 x^{12} + 2535 x^{11} - 3290 x^{10} - 6263 x^{9} + 43736 x^{8} - 119075 x^{7} + 221321 x^{6} - 296751 x^{5} + 303777 x^{4} - 226521 x^{3} + 141287 x^{2} - 71712 x + 44507$	$18$	[0,9]	$-\,7^{15}\cdot 138041^{3}$	$2$	$36.3844976233$	$1880.4094066508408$	✓		?	$S_3^3:C_6$ (as 18T285)	$[2, 56]$	$2$	$8$	$22017.7641526$
18.0.182...303.1	$x^{18} + 18 x^{16} - x^{15} + 153 x^{14} - 57 x^{13} + 953 x^{12} - 900 x^{11} + 5709 x^{10} - 6035 x^{9} + 24372 x^{8} - 20892 x^{7} + 52768 x^{6} - 34272 x^{5} + 26304 x^{4} - 12160 x^{3} + 5760 x^{2} - 1536 x + 512$	$18$	[0,9]	$-\,3^{24}\cdot 7^{12}\cdot 167^{3}$	$3$	$37.15464460376029$	$204.6061115516297$	✓			$C_6\times A_4$ (as 18T25)	$[111]$	$2$	$8$	$54408.48888868202$
18.0.308...919.1	$x^{18} + 15 x^{16} - 4 x^{15} + 132 x^{14} - 12 x^{13} + 806 x^{12} + 21 x^{11} + 2952 x^{10} + 311 x^{9} + 7530 x^{8} + 12328 x^{6} - 432 x^{5} + 6432 x^{4} - 704 x^{3} + 2304 x^{2} + 512$	$18$	[0,9]	$-\,3^{24}\cdot 7^{12}\cdot 199^{3}$	$3$	$38.25626311288771$	$223.35048738562688$	✓			$C_6\times A_4$ (as 18T25)	$[147]$	$2$	$8$	$54408.48888868202$
18.0.387...768.1	$x^{18} + 34 x^{16} + 480 x^{14} + 3640 x^{12} + 16016 x^{10} + 41184 x^{8} + 59136 x^{6} + 42240 x^{4} + 11520 x^{2} + 512$	$18$	[0,9]	$-\,2^{27}\cdot 19^{16}$	$2$	$38.7449282527$	$38.74492825271069$	✓	✓	?	$C_{18}$ (as 18T1)	$[171]$	$2$	$8$	$22305.8950792$
18.0.397...767.1	$x^{18} + 27 x^{16} + 351 x^{14} + 2646 x^{12} + 12465 x^{10} - 5 x^{9} + 35964 x^{8} + 468 x^{7} + 61488 x^{6} + 4752 x^{5} + 51840 x^{4} + 9600 x^{3} + 20736 x^{2} + 2304 x + 512$	$18$	[0,9]	$-\,3^{44}\cdot 7^{9}$	$2$	$38.8012235203$	$38.80122352031639$	✓	✓	?	$C_{18}$ (as 18T1)	$[163]$	$2$	$8$	$40934.0329443$
18.0.413...352.1	$x^{18} + 12 x^{16} - 40 x^{15} + 96 x^{14} - 444 x^{13} + 1674 x^{12} - 2472 x^{11} + 16878 x^{10} - 19734 x^{9} + 64794 x^{8} - 118380 x^{7} + 147569 x^{6} - 491256 x^{5} + 1646274 x^{4} - 2357414 x^{3} + 7131054 x^{2} - 6384660 x + 1632457$	$18$	[0,9]	$-\,2^{27}\cdot 3^{27}\cdot 7^{9}$	$3$	$38.8844441904$	$38.88444419044716$			?	$S_3 \times C_6$ (as 18T6)	$[2, 2, 26]$	$2$	$8$	$55250.70198920589$
18.0.478...000.1	$x^{18} - 4 x^{17} + 18 x^{16} - 92 x^{15} + 137 x^{14} - 262 x^{13} + 928 x^{12} + 1544 x^{11} - 1155 x^{10} - 2378 x^{9} - 11207 x^{8} - 11994 x^{7} + 36962 x^{6} - 121254 x^{5} + 174674 x^{4} - 268108 x^{3} + 686430 x^{2} - 163192 x + 580021$	$18$	[0,9]	$-\,2^{18}\cdot 3^{9}\cdot 5^{9}\cdot 7^{15}$	$4$	$39.2034232971$	$39.20342329707507$			?	$S_3 \times C_6$ (as 18T6)	$[2, 2, 26]$	$2$	$8$	$90069.70392878134$
18.0.533...839.2	$x^{18} + 21 x^{16} - 2 x^{15} + 234 x^{14} - 54 x^{13} + 1696 x^{12} - 711 x^{11} + 8328 x^{10} - 3849 x^{9} + 26856 x^{8} - 11544 x^{7} + 49208 x^{6} - 16848 x^{5} + 20640 x^{4} - 5312 x^{3} + 4608 x^{2} - 768 x + 512$	$18$	[0,9]	$-\,3^{24}\cdot 7^{12}\cdot 239^{3}$	$3$	$39.44209878373271$	$244.7706362685197$	✓			$C_6\times A_4$ (as 18T25)	$[3, 63]$	$2$	$8$	$54408.48888868202$
18.0.543...931.1	$x^{18} - 8 x^{17} + 27 x^{16} - 81 x^{15} + 291 x^{14} - 804 x^{13} + 1229 x^{12} + 793 x^{11} + 3756 x^{10} + 1662 x^{9} + 4817 x^{8} + 2413 x^{7} + 2650 x^{6} - 147 x^{5} + 464 x^{4} - 14 x^{3} + 28 x^{2} - x + 1$	$18$	[0,9]	$-\,3^{9}\cdot 13^{12}\cdot 17^{9}$	$3$	$39.4833496294$	$39.483349629417994$		✓	?	$S_3 \times C_3$ (as 18T3)	$[3, 3, 18]$	$2$	$8$	$48887.8339977$
18.0.621...176.1	$x^{18} + 30 x^{16} + 349 x^{14} + 2085 x^{12} + 7021 x^{10} + 13685 x^{8} + 15239 x^{6} + 9016 x^{4} + 2254 x^{2} + 49$	$18$	[0,9]	$-\,2^{18}\cdot 7^{14}\cdot 769^{4}$	$3$	$39.7782282675$		✓		?	$A_4^3:C_6$ (as 18T552)	$[6, 24]$	$2$	$8$	$60132.7264179$
18.0.757...248.1	$x^{18} + 30 x^{16} + 357 x^{14} + 2216 x^{12} + 7917 x^{10} + 16836 x^{8} + 21078 x^{6} + 14613 x^{4} + 4866 x^{2} + 577$	$18$	[0,9]	$-\,2^{18}\cdot 3^{24}\cdot 73^{2}\cdot 577^{3}$	$4$	$40.2182816187$		✓		?	$D_6\wr C_3$ (as 18T472)	$[3, 84]$	$2$	$8$	$26510.9946997$
18.0.757...248.2	$x^{18} + 33 x^{16} + 432 x^{14} + 2878 x^{12} + 10569 x^{10} + 22212 x^{8} + 26600 x^{6} + 17148 x^{4} + 5193 x^{2} + 577$	$18$	[0,9]	$-\,2^{18}\cdot 3^{24}\cdot 73^{2}\cdot 577^{3}$	$4$	$40.2182816187$		✓		?	$C_2\times S_4^3.A_4$ (as 18T879)	$[240]$	$2$	$8$	$26510.9946997$
18.0.845...064.1	$x^{18} + 40 x^{16} + 606 x^{14} + 4498 x^{12} + 17745 x^{10} + 37370 x^{8} + 40081 x^{6} + 20600 x^{4} + 4112 x^{2} + 64$	$18$	[0,9]	$-\,2^{18}\cdot 7^{12}\cdot 13^{12}$	$3$	$40.4629544903$	$40.46295449025258$	✓	✓		$C_6 \times C_3$ (as 18T2)	$[3, 6, 6]$	$4$	$8$	$205236.825908$
18.0.923...912.1	$x^{18} + 27 x^{16} + 289 x^{14} + 1645 x^{12} + 5523 x^{10} + 11298 x^{8} + 13839 x^{6} + 9334 x^{4} + 2678 x^{2} + 13$	$18$	[0,9]	$-\,2^{18}\cdot 7^{16}\cdot 13^{9}$	$3$	$40.6630480432$	$160.8003083167751$	✓		?	$C_6^2.C_6$ (as 18T92)	$[3, 42]$	$2$	$8$	$89545.2892541$
18.0.923...912.2	$x^{18} + 26 x^{16} + 274 x^{14} + 1498 x^{12} + 4522 x^{10} + 7469 x^{8} + 6433 x^{6} + 2652 x^{4} + 429 x^{2} + 13$	$18$	[0,9]	$-\,2^{18}\cdot 7^{16}\cdot 13^{9}$	$3$	$40.6630480432$	$160.8003083167751$	✓		?	$C_6^2.C_6$ (as 18T92)	$[114]$	$2$	$8$	$89545.2892541$
18.0.948...568.4	$x^{18} + 6 x^{16} + 24 x^{14} - 156 x^{13} + 181 x^{12} - 168 x^{11} - 12 x^{10} + 864 x^{9} + 1956 x^{8} - 1968 x^{7} - 773 x^{6} + 384 x^{5} + 810 x^{4} + 14112 x^{3} + 32844 x^{2} + 27720 x + 9075$	$18$	[0,9]	$-\,2^{12}\cdot 3^{21}\cdot 19^{12}$	$3$	$40.7221339612$	$40.722133961240765$		✓		$C_3^2 : C_2$ (as 18T4)	$[6, 18]$	$6$	$8$	$2038760.66718$
18.0.102...199.1	$x^{18} - 9 x^{17} + 62 x^{16} - 292 x^{15} + 1146 x^{14} - 3626 x^{13} + 9891 x^{12} - 22842 x^{11} + 46111 x^{10} - 80086 x^{9} + 121818 x^{8} - 159244 x^{7} + 180716 x^{6} - 173115 x^{5} + 140578 x^{4} - 91800 x^{3} + 48036 x^{2} - 17345 x + 4181$	$18$	[0,9]	$-\,19^{17}\cdot 37\cdot 151\cdot 3343$	$4$	$40.8953266395$	$69721.90715986823$	✓		✓	$C_2\wr C_9$ (as 18T460)	$[2, 2, 76]$	$2$	$8$	$22305.8950792$
18.0.103...616.1	$x^{18} + 25 x^{16} + 263 x^{14} + 1528 x^{12} + 5404 x^{10} + 12064 x^{8} + 16994 x^{6} + 14559 x^{4} + 6882 x^{2} + 1369$	$18$	[0,9]	$-\,2^{18}\cdot 19^{16}\cdot 37^{2}$	$3$	$40.9208361463$	$329.7062100438573$	✓		?	$C_2^6:C_{18}$ (as 18T264)	$[2, 162]$	$2$	$8$	$22305.8950792$
18.0.132...368.2	$x^{18} + 36 x^{16} + 540 x^{14} + 4368 x^{12} + 20592 x^{10} + 57024 x^{8} + 88704 x^{6} + 69120 x^{4} + 20736 x^{2} + 512$	$18$	[0,9]	$-\,2^{27}\cdot 3^{44}$	$2$	$41.480252743$	$41.48025274304532$	✓	✓	?	$C_{18}$ (as 18T1)	$[333]$	$2$	$8$	$40934.0329443$
18.0.141...064.1	$x^{18} + 24 x^{16} + 220 x^{14} + 1010 x^{12} + 2543 x^{10} + 3581 x^{8} + 2690 x^{6} + 905 x^{4} + 66 x^{2} + 1$	$18$	[0,9]	$-\,2^{18}\cdot 257^{6}\cdot 43237^{2}$	$3$	$41.6328458223$	$11212.354761299932$	✓		?	$D_6\wr S_3$ (as 18T556)	$[2, 68]$	$2$	$8$	$95074.4744327$
18.0.143...000.1	$x^{18} + 20 x^{16} + 167 x^{14} + 757 x^{12} + 2025 x^{10} + 3248 x^{8} + 3022 x^{6} + 1477 x^{4} + 293 x^{2} + 5$	$18$	[0,9]	$-\,2^{30}\cdot 5^{3}\cdot 37^{6}\cdot 107^{2}\cdot 191^{2}$	$5$	$41.6754988053$		✓		✓	$D_6\wr S_3$ (as 18T556)	$[2, 60]$	$2$	$8$	$165397.421579$
18.0.147...047.1	$x^{18} + 28 x^{16} - 31 x^{15} + 343 x^{14} - 560 x^{13} + 2535 x^{12} - 4606 x^{11} + 14791 x^{10} - 17924 x^{9} + 29428 x^{8} + 15897 x^{7} - 50004 x^{6} + 185423 x^{5} - 114961 x^{4} + 122123 x^{3} + 237580 x^{2} - 217679 x + 451879$	$18$	[0,9]	$-\,7^{12}\cdot 97^{3}\cdot 22679^{3}$	$3$	$41.7315612338$	$5427.458494884186$			?	$D_6\wr C_3$ (as 18T472)	$[104]$	$2$	$8$	$99994.2543337$
18.0.158...559.1	$x^{18} - 2 x^{17} + 7 x^{16} - 10 x^{15} + 66 x^{14} - 104 x^{13} + 252 x^{12} + 15 x^{11} + 1120 x^{10} - 603 x^{9} + 2562 x^{8} + 8 x^{7} + 7896 x^{6} - 6768 x^{5} + 4896 x^{4} - 1984 x^{3} + 1792 x^{2} - 1024 x + 512$	$18$	[0,9]	$-\,7^{12}\cdot 13^{12}\cdot 79^{3}$	$3$	$41.90817770140314$	$179.82130310417884$	✓			$C_6\times A_4$ (as 18T25)	$[127]$	$2$	$8$	$205236.82590785183$
18.0.164...064.1	$x^{18} - x^{17} + 13 x^{16} - 2 x^{15} + 115 x^{14} - 91 x^{13} + 1177 x^{12} - 1431 x^{11} + 6780 x^{10} - 7238 x^{9} + 35125 x^{8} - 55927 x^{7} + 162275 x^{6} - 210997 x^{5} + 444163 x^{4} - 469025 x^{3} + 586289 x^{2} - 145088 x + 90787$	$18$	[0,9]	$-\,2^{12}\cdot 3^{6}\cdot 11^{9}\cdot 13^{12}$	$4$	$41.9809561856$	$50.41648169689674$				$S_3 \times C_6$ (as 18T6)	$[126]$	$2$	$8$	$368294.41393950605$
18.0.168...632.1	$x^{18} - 2 x^{17} + 47 x^{16} - 74 x^{15} + 907 x^{14} - 1134 x^{13} + 9377 x^{12} - 9216 x^{11} + 56719 x^{10} - 43522 x^{9} + 205793 x^{8} - 125158 x^{7} + 442963 x^{6} - 223626 x^{5} + 549366 x^{4} - 241380 x^{3} + 372456 x^{2} - 127008 x + 74088$	$18$	[0,9]	$-\,2^{18}\cdot 3^{9}\cdot 7^{12}\cdot 11^{9}$	$4$	$42.0422217881$	$42.04222178812256$		✓		$S_3 \times C_3$ (as 18T3)	$[3, 6, 18]$	$2$	$8$	$130703.898439$
18.0.188...064.1	$x^{18} - 6 x^{17} + 31 x^{16} - 124 x^{15} + 403 x^{14} - 1144 x^{13} + 2830 x^{12} - 6420 x^{11} + 13956 x^{10} - 27780 x^{9} + 51861 x^{8} - 91584 x^{7} + 173635 x^{6} - 319924 x^{5} + 597495 x^{4} - 843778 x^{3} + 865576 x^{2} - 666536 x + 330469$	$18$	[0,9]	$-\,2^{24}\cdot 37^{6}\cdot 16361^{3}$	$3$	$42.3066732557$		✓		?	$S_3^3:D_6$ (as 18T394)	$[4, 68]$	$2$	$8$	$45363.6836572$
18.0.202...067.1	$x^{18} - 6 x^{17} + 6 x^{16} + 6 x^{15} + 267 x^{14} - 1599 x^{13} + 3156 x^{12} - 267 x^{11} - 4575 x^{10} - 6847 x^{9} + 34635 x^{8} + 2436 x^{7} - 52743 x^{6} - 51519 x^{5} + 250608 x^{4} + 227274 x^{3} - 605661 x^{2} - 261210 x + 836587$	$18$	[0,9]	$-\,3^{31}\cdot 41^{9}$	$2$	$42.4718086735$	$42.47180867347496$		✓		$S_3 \times C_3$ (as 18T3)	$[2, 2, 38]$	$2$	$8$	$269015.233286$
18.0.206...375.1	$x^{18} - 6 x^{17} + 21 x^{16} - 38 x^{15} + 72 x^{14} - 72 x^{13} + 82 x^{12} + 540 x^{11} - 123 x^{10} - 880 x^{9} + 17883 x^{8} - 34212 x^{7} + 79951 x^{6} - 92796 x^{5} + 178851 x^{4} - 124326 x^{3} + 112827 x^{2} - 54930 x + 114211$	$18$	[0,9]	$-\,3^{27}\cdot 5^{9}\cdot 7^{12}$	$3$	$42.5172902208$	$42.517290220802025$	✓	✓		$C_6 \times C_3$ (as 18T2)	$[2, 2, 74]$	$2$	$8$	$54408.4888887$
18.0.216...751.1	$x^{18} - 9 x^{17} + 60 x^{16} - 276 x^{15} + 1040 x^{14} - 3164 x^{13} + 8190 x^{12} - 17914 x^{11} + 33819 x^{10} - 54695 x^{9} + 76338 x^{8} - 90906 x^{7} + 92078 x^{6} - 77770 x^{5} + 53800 x^{4} - 29270 x^{3} + 11843 x^{2} - 3165 x + 433$	$18$	[0,9]	$-\,7^{16}\cdot 13^{8}\cdot 8000831$	$3$	$42.6374965758$	$88184.99768067754$	✓		✓	$C_2\wr C_9.C_3$ (as 18T586)	$[165]$	$2$	$8$	$89545.2892541$
18.0.220...016.1	$x^{18} + 28 x^{16} - 6 x^{15} + 294 x^{14} - 98 x^{13} + 2049 x^{12} - 490 x^{11} + 9401 x^{10} + 62 x^{9} + 25921 x^{8} + 5572 x^{7} + 50645 x^{6} + 13328 x^{5} + 75068 x^{4} + 19698 x^{3} + 60025 x^{2} + 17150 x + 42875$	$18$	[0,9]	$-\,2^{27}\cdot 7^{12}\cdot 17^{9}$	$3$	$42.6744711274$	$42.67447112735335$		✓		$S_3 \times C_3$ (as 18T3)	$[2, 2, 28]$	$2$	$8$	$194089.946384$
18.0.240...639.1	$x^{18} - 6 x^{17} + 6 x^{16} + 45 x^{15} - 123 x^{14} - 117 x^{13} + 1266 x^{12} - 3357 x^{11} + 6558 x^{10} - 13742 x^{9} + 34728 x^{8} - 78768 x^{7} + 145971 x^{6} - 211194 x^{5} + 255198 x^{4} - 241821 x^{3} + 197232 x^{2} - 106644 x + 46808$	$18$	[0,9]	$-\,3^{30}\cdot 23^{6}\cdot 199^{3}$	$3$	$42.879878811919184$	$448.74464988853384$	✓		?	$A_4\times D_6$ (as 18T60)	$[150]$	$2$	$8$	$118867.59391303241$
18.0.242...603.1	$x^{18} - x^{17} + 17 x^{16} - 6 x^{15} + 201 x^{14} - 76 x^{13} + 999 x^{12} - 218 x^{11} + 3519 x^{10} - 623 x^{9} + 5540 x^{8} + 1505 x^{7} + 5069 x^{6} - 129 x^{5} + 528 x^{4} - 97 x^{3} + 56 x^{2} - 7 x + 1$	$18$	[0,9]	$-\,3^{9}\cdot 37^{16}$	$2$	$42.9059690768$	$42.90596907675813$	✓	✓	?	$C_{18}$ (as 18T1)	$[171]$	$6$	$8$	$409151.310213$
18.0.285...703.1	$x^{18} - 8 x^{17} + 18 x^{16} + 15 x^{15} - 36 x^{14} - 377 x^{13} + 1110 x^{12} - 523 x^{11} - 209 x^{10} - 3573 x^{9} + 11860 x^{8} - 24128 x^{7} + 36096 x^{6} - 20522 x^{5} + 19123 x^{4} - 72857 x^{3} + 132651 x^{2} - 161631 x + 186759$	$18$	[0,9]	$-\,7^{14}\cdot 67^{6}\cdot 167^{3}$	$3$	$43.29550619889824$	$535.3576385241264$	✓		?	$A_4\times D_6$ (as 18T60)	$[228]$	$2$	$8$	$122519.13430794713$
18.0.314...304.1	$x^{18} + 32 x^{16} + 392 x^{14} + 2337 x^{12} + 7216 x^{10} + 11256 x^{8} + 7946 x^{6} + 2128 x^{4} + 120 x^{2} + 1$	$18$	[0,9]	$-\,2^{18}\cdot 13^{12}\cdot 61^{6}$	$3$	$43.5280129601$	$86.36222339339257$	✓		?	$S_3 \times C_6$ (as 18T6)	$[3, 3, 12]$	$4$	$8$	$230602.64598601736$
18.0.333...896.1	$x^{18} + 24 x^{16} + 228 x^{14} + 1129 x^{12} + 3177 x^{10} + 5133 x^{8} + 4523 x^{6} + 1874 x^{4} + 231 x^{2} + 1$	$18$	[0,9]	$-\,2^{30}\cdot 19^{6}\cdot 137^{6}$	$3$	$43.6724995284$		✓		?	$S_4^2:C_2^2$ (as 18T370)	$[2, 64]$	$2$	$8$	$138588.252508$
18.0.396...104.1	$x^{18} + 36 x^{16} + 540 x^{14} + 4368 x^{12} + 20592 x^{10} + 57024 x^{8} + 88704 x^{6} + 69120 x^{4} + 20736 x^{2} + 1536$	$18$	[0,9]	$-\,2^{27}\cdot 3^{45}$	$2$	$44.0908153701$	$44.090815370097204$	✓	✓	?	$C_{18}$ (as 18T1)	$[542]$	$2$	$8$	$40934.0329443$
18.0.442...432.1	$x^{18} - 6 x^{17} + 29 x^{16} - 102 x^{15} + 336 x^{14} - 890 x^{13} + 2170 x^{12} - 4566 x^{11} + 9356 x^{10} - 15604 x^{9} + 22168 x^{8} - 24046 x^{7} + 21992 x^{6} - 15918 x^{5} + 17462 x^{4} - 15366 x^{3} + 13571 x^{2} - 3898 x + 6053$	$18$	[0,9]	$-\,2^{26}\cdot 37^{6}\cdot 13693^{3}$	$3$	$44.3579480099$		✓		?	$S_3^3:D_6$ (as 18T394)	$[2, 100]$	$2$	$8$	$146523.090266$
18.0.450...000.1	$x^{18} - 171 x^{12} + 9747 x^{6} + 27$	$18$	[0,9]	$-\,2^{12}\cdot 3^{37}\cdot 5^{12}$	$3$	$44.4033679831$	$44.40336798307826$		✓		$C_3^2 : C_2$ (as 18T4)	$[3, 6, 6]$	$6$	$8$	$16809351.5152$
18.0.450...000.2	$x^{18} - 9 x^{17} + 45 x^{16} - 126 x^{15} + 189 x^{14} - 27 x^{13} - 216 x^{12} - 729 x^{11} + 3807 x^{10} - 5414 x^{9} - 423 x^{8} + 17991 x^{7} - 36621 x^{6} + 11718 x^{5} + 99414 x^{4} - 188676 x^{3} + 121500 x^{2} + 11016 x + 1156$	$18$	[0,9]	$-\,2^{12}\cdot 3^{37}\cdot 5^{12}$	$3$	$44.4033679831$	$44.40336798307826$		✓		$C_3^2 : C_2$ (as 18T4)	$[3, 6, 6]$	$6$	$8$	$2396291.4248$
18.0.453...968.2	$x^{18} - x^{17} + 5 x^{16} + 19 x^{15} + 8 x^{14} + 68 x^{13} + 90 x^{12} - 118 x^{11} + 653 x^{10} + 1339 x^{9} - 771 x^{8} + 51 x^{7} + 4810 x^{6} + 2562 x^{5} + 2212 x^{4} + 7728 x^{3} + 4256 x^{2} + 2688 x + 7168$	$18$	[0,9]	$-\,2^{12}\cdot 7^{15}\cdot 13^{12}$	$3$	$44.4185044524$	$55.96380876440059$				$S_3 \times C_6$ (as 18T6)	$[156]$	$2$	$8$	$392092503.6861413$
18.0.500...864.1	$x^{18} - x^{17} + 13 x^{16} - 14 x^{15} + 102 x^{14} - 85 x^{13} + 597 x^{12} - 117 x^{11} + 2104 x^{10} - 147 x^{9} + 5814 x^{8} - 1244 x^{7} + 10992 x^{6} - 4320 x^{5} + 5856 x^{4} - 2240 x^{3} + 2176 x^{2} - 512 x + 512$	$18$	[0,9]	$-\,2^{12}\cdot 7^{12}\cdot 37^{6}\cdot 151^{3}$	$4$	$44.66651712937576$	$434.1848772346385$	✓		?	$C_6\times S_4$ (as 18T61)	$[171]$	$2$	$8$	$146431.64361735608$
18.0.519...867.2	$x^{18} - 6 x^{17} + 12 x^{16} - 28 x^{15} + 171 x^{14} - 192 x^{13} - 252 x^{12} + 624 x^{11} + 537 x^{10} + 4550 x^{9} + 11598 x^{8} + 23070 x^{7} + 61893 x^{6} + 117033 x^{5} + 211056 x^{4} + 282511 x^{3} + 269637 x^{2} + 183555 x + 59273$	$18$	[0,9]	$-\,3^{24}\cdot 107^{9}$	$2$	$44.7562366782$	$44.75623667824389$		✓	?	$S_3 \times C_3$ (as 18T3)	$[2, 2, 2, 18]$	$2$	$8$	$146101.088241$
18.0.524...768.4	$x^{18} - 12 x^{16} - 8 x^{15} + 117 x^{14} + 96 x^{13} + 246 x^{12} + 438 x^{11} + 2376 x^{10} + 3532 x^{9} + 21948 x^{8} + 13782 x^{7} + 114732 x^{6} + 44268 x^{5} + 331017 x^{4} + 87920 x^{3} + 531078 x^{2} + 90444 x + 386513$	$18$	[0,9]	$-\,2^{27}\cdot 3^{24}\cdot 7^{12}$	$3$	$44.7821932556$	$44.78219325557628$	✓	✓		$C_6 \times C_3$ (as 18T2)	$[18, 18]$	$2$	$8$	$54408.4888887$
18.0.537...696.1	$x^{18} + 26 x^{16} + 277 x^{14} + 1739 x^{12} + 8504 x^{10} + 34994 x^{8} + 100505 x^{6} + 170701 x^{4} + 150743 x^{2} + 52919$	$18$	[0,9]	$-\,2^{18}\cdot 7^{12}\cdot 52919^{3}$	$3$	$44.8432720341$				?	$S_3^3:A_4$ (as 18T401)	$[128]$	$2$	$8$	$174193.50455$
18.0.584...504.1	$x^{18} + 22 x^{16} + 204 x^{14} + 1040 x^{12} + 3188 x^{10} + 6032 x^{8} + 6943 x^{6} + 4582 x^{4} + 1508 x^{2} + 169$	$18$	[0,9]	$-\,2^{18}\cdot 7^{12}\cdot 13^{2}\cdot 41^{2}\cdot 23813^{2}$	$5$	$45.0516869843$		✓		?	$C_2\times S_4^3.A_4$ (as 18T879)	$[2, 2, 66]$	$2$	$8$	$73614.8297766$
18.0.602...563.2	$x^{18} + 26 x^{16} - 28 x^{15} + 495 x^{14} - 518 x^{13} + 4312 x^{12} - 5250 x^{11} + 27163 x^{10} - 25326 x^{9} + 69607 x^{8} - 33026 x^{7} + 104749 x^{6} - 50344 x^{5} + 66332 x^{4} - 14224 x^{3} + 19600 x^{2} - 4704 x + 3136$	$18$	[0,9]	$-\,3^{9}\cdot 7^{12}\cdot 19^{12}$	$3$	$45.1296246392$	$45.129624639238735$	✓	✓	?	$C_6 \times C_3$ (as 18T2)	$[6, 18]$	$6$	$8$	$833965.243856$
18.0.677...632.1	$x^{18} - 10 x^{16} - 5 x^{15} + 84 x^{14} - 15 x^{13} - 186 x^{12} - 92 x^{11} + 1232 x^{10} - 405 x^{9} + 2987 x^{8} - 2817 x^{7} + 13566 x^{6} + 895 x^{5} + 29602 x^{4} - 626 x^{3} + 31305 x^{2} - 11895 x + 61027$	$18$	[0,9]	$-\,2^{12}\cdot 7^{12}\cdot 37^{6}\cdot 167^{3}$	$4$	$45.4226021568$	$456.60898666664724$	✓		?	$A_4\times D_6$ (as 18T60)	$[216]$	$2$	$8$	$146431.643617$
18.0.683...103.1	$x^{18} + 9 x^{16} - 10 x^{15} + 18 x^{14} - 48 x^{13} + 26 x^{12} + 315 x^{11} + 786 x^{10} + 2839 x^{9} + 10872 x^{8} + 6360 x^{7} + 40168 x^{6} + 15408 x^{5} + 9888 x^{4} + 8000 x^{3} + 2304 x^{2} + 768 x + 512$	$18$	[0,9]	$-\,3^{24}\cdot 13^{12}\cdot 47^{3}$	$3$	$45.443686048598465$	$163.9983593898171$	✓			$C_6\times A_4$ (as 18T25)	$[111]$	$2$	$8$	$400417.1364448253$