Number field search results

Note: Search results may be incomplete. Given $p$-adic completions contain an unramified field and completions are only searched for ramified primes.

Results (1-50 of 120 matches)

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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
14.2.497...168.1	$x^{14} - 2 x - 1$	$14$	[2,6]	$2^{15}\cdot 11\cdot 587\cdot 23505755743$	$4$	$21.650870026$	$58603019.42500222$			✓	$S_{14}$ (as 14T63)	trivial	$2$	$7$	$11877.3098365$
14.4.170...179.1	$x^{14} - 7 x^{13} + 28 x^{12} - 77 x^{11} + 136 x^{10} - 141 x^{9} + 5 x^{8} + 265 x^{7} - 464 x^{6} + 419 x^{5} - 140 x^{4} - 99 x^{3} + 153 x^{2} - 79 x + 18$	$14$	[4,5]	$-\,7^{8}\cdot 11\cdot 173^{6}$	$3$	$32.8443728152$	$159.63131361268375$			?	$C_2\wr F_7$ (as 14T48)	trivial	$2$	$8$	$1070462.31054$
14.0.932...440.1	$x^{14} - 4 x + 8$	$14$	[0,7]	$-\,2^{12}\cdot 5\cdot 11\cdot 18313\cdot 84551\cdot 267224171$	$6$	$43.719672639$	$9045491670.484062$			?	$S_{14}$ (as 14T63)	trivial	$2$	$6$	$2710415.55319$
14.2.990...536.1	$x^{14} - 4 x - 3$	$14$	[2,6]	$2^{14}\cdot 11\cdot 549419308234664489$	$3$	$43.9087609048$	$4916751932.15249$			✓	$S_{14}$ (as 14T63)	trivial	$2$	$7$	$3830413.60885$
14.2.745...077.1	$x^{14} - x - 4$	$14$	[2,6]	$11\cdot 3121\cdot 21721305966220608967$	$3$	$50.7205252003$	$863547424943.3668$			✓	$S_{14}$ (as 14T63)	trivial	$2$	$7$	$7369523.38966$
14.2.171...125.1	$x^{14} - 5 x - 5$	$14$	[2,6]	$5^{13}\cdot 11\cdot 887\cdot 1109\cdot 129654793$	$5$	$53.8238486826$	$166940530.4363459$			?	$S_{14}$ (as 14T63)	$[2]$	$2$	$7$	$5774585.27649$
14.0.119...251.1	$x^{14} - x + 7$	$14$	[0,7]	$-\,3\cdot 11\cdot 89\cdot 7883\cdot 12457\cdot 414777865853633$	$6$	$72.8956731426$	$10937353655980.158$			?	$S_{14}$ (as 14T63)	$[2]$	$2$	$6$	$20591792.7745$
14.0.121...968.1	$x^{14} - 6 x + 6$	$14$	[0,7]	$-\,2^{14}\cdot 3^{13}\cdot 11\cdot 3259\cdot 6823\cdot 19000087$	$6$	$72.9722012053$				✓	$S_{14}$ (as 14T63)	$[2]$	$2$	$6$	$22083348.4505$
14.0.143...131.1	$x^{14} - 5 x + 6$	$14$	[0,7]	$-\,11\cdot 31\cdot 152922151\cdot 2747682891446041$	$4$	$73.8413086353$	$11970042527360.018$			✓	$S_{14}$ (as 14T63)	trivial	$2$	$6$	$315283522.312$
14.2.205...965.1	$x^{14} - 7 x - 3$	$14$	[2,6]	$5\cdot 7^{14}\cdot 11\cdot 33623\cdot 163795469$	$5$	$75.7664057275$	$166283540.95220524$			✓	$S_{14}$ (as 14T63)	trivial	$2$	$7$	$147942156.473$
14.2.133...240.1	$x^{14} - 8 x + 2$	$14$	[2,6]	$2^{27}\cdot 5\cdot 11\cdot 59\cdot 307\cdot 28081\cdot 354770777$	$7$	$86.5896441514$				✓	$S_{14}$ (as 14T63)	trivial	$2$	$7$	$249718463.726$
14.2.313...269.1	$x^{14} - 3 x - 9$	$14$	[2,6]	$3^{12}\cdot 11\cdot 19\cdot 2713\cdot 6829\cdot 414521\cdot 3679153$	$7$	$92.0555947483$	$211857288193.03763$			?	$S_{14}$ (as 14T63)	trivial	$2$	$7$	$304124096.669$
14.0.590...411.1	$x^{14} - 7 x + 8$	$14$	[0,7]	$-\,7^{14}\cdot 11\cdot 284111\cdot 2785186759$	$4$	$96.3053788432$	$891386956.7343488$			✓	$S_{14}$ (as 14T63)	$[3]$	$2$	$6$	$125082578.005$
14.2.692...149.1	$x^{14} - 9 x - 1$	$14$	[2,6]	$11\cdot 101\cdot 1777\cdot 27017\cdot 129903275709416051$	$5$	$97.4133501458$	$83239479535231.8$			✓	$S_{14}$ (as 14T63)	$[2]$	$2$	$7$	$319996332.387$
16.0.41268653593021184.1	$x^{16} - 5 x^{15} + 15 x^{14} - 31 x^{13} + 52 x^{12} - 75 x^{11} + 97 x^{10} - 107 x^{9} + 91 x^{8} - 49 x^{7} + 5 x^{6} + 16 x^{5} - 12 x^{4} + x^{3} + 5 x^{2} - 4 x + 1$	$16$	[0,8]	$2^{8}\cdot 11\cdot 73^{2}\cdot 229^{4}$	$4$	$10.9263792031$	$1572.9204384800132$			?	$C_4^4.C_2\wr S_4$ (as 16T1879)	trivial	$2$	$7$	$35.4102036342$
16.0.203...617.1	$x^{16} - 3 x^{13} + 4 x^{12} + 3 x^{10} - 9 x^{9} + 6 x^{8} - x^{7} + 6 x^{6} - 9 x^{5} + 5 x^{4} - x^{3} + 3 x^{2} - 3 x + 1$	$16$	[0,8]	$11\cdot 23\cdot 229^{4}\cdot 1307\cdot 22367$	$5$	$16.0979884327$	$1301426.556073373$			✓	$C_2^8.S_3\wr S_4$ (as 16T1947)	trivial	$2$	$7$	$1694.15164906$
16.0.566...424.1	$x^{16} + 8 x^{14} + 28 x^{12} + 48 x^{10} + 26 x^{8} - 24 x^{6} - 28 x^{4} + 21$	$16$	[0,8]	$2^{32}\cdot 3^{3}\cdot 7^{9}\cdot 11^{2}$	$4$	$19.8180974563$				?	$C_4^4.C_2\wr A_4$ (as 16T1845)	trivial	$2$	$7$	$16328.1416818$
16.0.566...424.2	$x^{16} - 8 x^{14} + 28 x^{12} - 48 x^{10} + 26 x^{8} + 24 x^{6} - 28 x^{4} + 21$	$16$	[0,8]	$2^{32}\cdot 3^{3}\cdot 7^{9}\cdot 11^{2}$	$4$	$19.8180974563$				?	$C_4^4.C_2\wr A_4$ (as 16T1845)	trivial	$2$	$7$	$13649.7153446$
16.4.419...201.1	$x^{16} - x^{14} - 4 x^{13} + 10 x^{12} - 3 x^{11} - 36 x^{10} - 9 x^{9} + 80 x^{8} + 158 x^{7} - 435 x^{6} + 196 x^{5} - 157 x^{4} + 1115 x^{3} - 1630 x^{2} + 879 x - 163$	$16$	[4,6]	$11^{2}\cdot 277^{8}$	$2$	$22.4602181524$	$140.93413315990728$			?	$C_2^4.\SL(2,3)$ (as 16T732)	trivial	$2$	$9$	$24226.3247022$
16.8.592...112.1	$x^{16} - 7 x^{14} - 63 x^{13} - 540 x^{12} + 170 x^{11} + 3039 x^{10} - 8087 x^{9} - 3223 x^{8} + 80302 x^{7} + 38032 x^{6} - 7974 x^{5} + 535319 x^{4} + 454564 x^{3} - 354541 x^{2} - 139271 x + 9317$	$16$	[8,4]	$2^{18}\cdot 3^{2}\cdot 11^{2}\cdot 163^{8}\cdot 41617$	$5$	$83.8052474913$	$136879.02259935232$			?	$C_2^8.S_3\wr A_4$ (as 16T1941)	trivial	$2$	$11$	$17171207118.8$
16.16.755...296.1	$x^{16} - 156 x^{14} - 336 x^{13} + 9018 x^{12} + 36768 x^{11} - 202764 x^{10} - 1361808 x^{9} + 427479 x^{8} + 18733312 x^{7} + 36576468 x^{6} - 47516496 x^{5} - 246543254 x^{4} - 292281696 x^{3} - 89635896 x^{2} + 40007520 x + 15752961$	$16$	[16,0]	$2^{48}\cdot 3^{12}\cdot 11^{2}\cdot 149^{2}\cdot 1171^{4}$	$5$	$269.086878652$				?	$C_2^8.S_3\wr S_3$ (as 16T1914)	$[2]$	$2$	$15$	$366148614643000$
16.12.345...536.1	$x^{16} - 132 x^{14} - 48 x^{13} + 7686 x^{12} + 11232 x^{11} - 358552 x^{10} - 62496 x^{9} + 11208243 x^{8} - 30488960 x^{7} - 78633864 x^{6} + 538072416 x^{5} - 946188978 x^{4} + 238508064 x^{3} + 1154305404 x^{2} - 1289280240 x + 387105561$	$16$	[12,2]	$2^{40}\cdot 3^{14}\cdot 7^{2}\cdot 11^{2}\cdot 17^{2}\cdot 31^{8}\cdot 67^{2}$	$7$	$341.675422495$				?	$A_4\wr A_4.C_2$ (as 16T1917)	$[2, 2]$	$2$	$13$	$548343223841000$
16.16.259...208.1	$x^{16} - 504 x^{14} - 1968 x^{13} + 96282 x^{12} + 735936 x^{11} - 7087182 x^{10} - 94175928 x^{9} - 20877525 x^{8} + 4095482272 x^{7} + 19598712930 x^{6} + 2275521240 x^{5} - 194421420157 x^{4} - 370914894912 x^{3} + 287689134942 x^{2} + 1001981333736 x + 183522103461$	$16$	[16,0]	$2^{22}\cdot 3^{16}\cdot 11^{2}\cdot 2777^{5}\cdot 848761^{2}$	$5$	$689.330070114$	$5590865.673588891$			?	$C_2^8.C_3^4:\GL(2,3)$ (as 16T1930)	$[2]$	$2$	$15$	$358242232809000000$
18.0.111...771.1	$x^{18} - 8 x^{17} + 28 x^{16} - 54 x^{15} + 55 x^{14} - 8 x^{13} - 55 x^{12} + 69 x^{11} - 19 x^{10} - 37 x^{9} + 44 x^{8} - 16 x^{7} - 6 x^{6} + 15 x^{5} - 14 x^{4} + 3 x^{3} + 7 x^{2} - 5 x + 1$	$18$	[0,9]	$-\,3^{4}\cdot 11^{5}\cdot 31^{8}$	$3$	$11.432207825$	$167.845280953044$			?	$C_6^3:S_4$ (as 18T485)	trivial	$2$	$8$	$80.526625464$
18.0.155...643.1	$x^{18} - 2 x^{17} + 2 x^{16} + x^{15} - 5 x^{14} + 5 x^{13} + x^{12} - 7 x^{11} + 9 x^{10} - 6 x^{9} + 4 x^{8} - 7 x^{7} + 6 x^{6} - 5 x^{5} + 2 x^{4} + x^{2} + 1$	$18$	[0,9]	$-\,11^{3}\cdot 31^{6}\cdot 6673\cdot 19681$	$4$	$13.2344675213$	$211622.25245233547$			?	$C_3^6.C_2\wr (C_2\times S_4)$ (as 18T945)	trivial	$2$	$8$	$354.340635376$
18.0.317...471.1	$x^{18} - 3 x^{16} - 3 x^{15} + 8 x^{14} + 13 x^{13} + 3 x^{12} - 9 x^{11} + x^{10} + 9 x^{9} + x^{8} - 9 x^{7} + 3 x^{6} + 13 x^{5} + 8 x^{4} - 3 x^{3} - 3 x^{2} + 1$	$18$	[0,9]	$-\,11^{4}\cdot 31\cdot 37^{4}\cdot 139^{4}$	$4$	$13.7717397577$	$1974.926326620088$			?	$C_2^9.A_9$ (as 18T966)	trivial	$2$	$8$	$977.467803568$
18.6.378...917.1	$x^{18} - 3 x^{17} + 2 x^{16} - 5 x^{15} + 4 x^{14} + 29 x^{13} - 5 x^{12} - 83 x^{11} + 7 x^{10} + 105 x^{9} + 7 x^{8} - 83 x^{7} - 5 x^{6} + 29 x^{5} + 4 x^{4} - 5 x^{3} + 2 x^{2} - 3 x + 1$	$18$	[6,6]	$11^{4}\cdot 37^{5}\cdot 139^{4}$	$3$	$13.9077763398$	$874.823585606666$			?	$C_2^9.A_9$ (as 18T966)	trivial	$2$	$11$	$1568.66869653$
18.6.144...981.1	$x^{18} - x^{17} + 4 x^{16} + 4 x^{15} - 2 x^{14} + 12 x^{13} - 8 x^{12} - 12 x^{11} - 29 x^{10} - 52 x^{9} - 36 x^{8} - 46 x^{7} - 21 x^{6} - 2 x^{5} + 5 x^{4} + 11 x^{3} + 3 x^{2} + x + 1$	$18$	[6,6]	$3\cdot 11^{4}\cdot 37^{4}\cdot 47\cdot 139^{4}$	$5$	$14.9808495225$	$4211.915101066578$			?	$C_2^9.A_9$ (as 18T966)	trivial	$2$	$11$	$4227.82306897$
18.4.154...391.1	$x^{18} - 8 x^{16} - 5 x^{15} + 27 x^{14} + 36 x^{13} - 49 x^{12} - 95 x^{11} + 31 x^{10} + 147 x^{9} + 7 x^{8} - 126 x^{7} - 35 x^{6} + 76 x^{5} + 17 x^{4} - 24 x^{3} - 3 x^{2} + 5 x - 1$	$18$	[4,7]	$-\,11^{4}\cdot 37^{4}\cdot 139^{4}\cdot 151$	$4$	$15.0379852577$	$4358.715530432155$			?	$C_2^9.A_9$ (as 18T966)	trivial	$2$	$10$	$4246.06379679$
18.2.270...353.1	$x^{18} - x^{17} + x^{16} - 3 x^{15} - 8 x^{14} + 5 x^{13} + 8 x^{12} + 18 x^{11} + 25 x^{10} - 34 x^{9} - 49 x^{8} + 6 x^{7} + 16 x^{6} + 10 x^{5} + 7 x^{4} - 7 x^{3} - 6 x^{2} + x + 1$	$18$	[2,8]	$3^{9}\cdot 11^{5}\cdot 31^{8}$	$3$	$15.5118570101$	$167.845280953044$			?	$C_6^3:S_4$ (as 18T485)	trivial	$2$	$9$	$2751.63626644$
18.2.310...109.1	$x^{18} - 6 x^{17} + 20 x^{16} - 45 x^{15} + 68 x^{14} - 71 x^{13} + 52 x^{12} - 53 x^{11} + 123 x^{10} - 205 x^{9} + 218 x^{8} - 156 x^{7} + 48 x^{6} - 26 x^{5} + 43 x^{4} - 20 x^{3} - x + 1$	$18$	[2,8]	$3^{6}\cdot 11^{5}\cdot 31^{9}$	$3$	$15.6313688455$	$167.845280953044$			?	$C_6^3:S_4$ (as 18T485)	trivial	$2$	$9$	$2687.87073054$
18.0.500...611.1	$x^{18} - 9 x^{17} + 26 x^{16} - 3 x^{15} - 119 x^{14} + 155 x^{13} + 176 x^{12} - 444 x^{11} - 20 x^{10} + 529 x^{9} - 152 x^{8} - 355 x^{7} + 189 x^{6} + 118 x^{5} - 104 x^{4} - 5 x^{3} + 26 x^{2} - 9 x + 1$	$18$	[0,9]	$-\,11^{3}\cdot 31^{6}\cdot 65101^{2}$	$3$	$16.0519975745$	$29883.786795970114$			✓	$C_3\wr (C_2\times S_4)$ (as 18T672)	trivial	$2$	$8$	$2242.85297359$
18.2.866...528.1	$x^{18} - 3 x^{15} - 18 x^{13} + 30 x^{12} + 9 x^{11} - 18 x^{10} - 61 x^{9} + 90 x^{8} + 90 x^{7} - 117 x^{6} - 18 x^{5} + 27 x^{4} + 9 x^{3} - 3$	$18$	[2,8]	$2^{3}\cdot 3^{44}\cdot 11$	$3$	$18.8071598378$	$165.21822254789458$			?	$C_2^4:A_4^2.D_6$ (as 18T658)	trivial	$2$	$9$	$52280.5304794$
18.0.141...304.1	$x^{18} - 7 x^{17} + 20 x^{16} - 25 x^{15} + x^{14} + 14 x^{13} + 27 x^{12} - 47 x^{11} - x^{10} + 50 x^{9} - x^{8} - 47 x^{7} + 27 x^{6} + 14 x^{5} + x^{4} - 25 x^{3} + 20 x^{2} - 7 x + 1$	$18$	[0,9]	$-\,2^{30}\cdot 11^{5}\cdot 13^{8}$	$3$	$19.3231684418$	$119.40721551831778$			?	$C_6^3:D_6$ (as 18T396)	trivial	$2$	$8$	$27090.8954165$
18.6.141...304.1	$x^{18} - 4 x^{17} + 6 x^{16} - 2 x^{15} - 17 x^{14} + 48 x^{13} - 36 x^{12} - 14 x^{11} + 85 x^{10} - 116 x^{9} - 56 x^{8} + 82 x^{7} - 87 x^{6} - 80 x^{5} + 140 x^{4} + 14 x^{3} - 74 x^{2} - 16 x + 2$	$18$	[6,6]	$2^{30}\cdot 11^{5}\cdot 13^{8}$	$3$	$19.3231684418$	$119.40721551831778$			?	$C_6^3:D_6$ (as 18T396)	trivial	$2$	$11$	$93137.3629249$
18.4.250...416.1	$x^{18} + 2 x^{16} - 6 x^{15} - 3 x^{14} - 10 x^{13} + 13 x^{12} + 12 x^{11} + 25 x^{10} - 14 x^{9} - 18 x^{8} - 30 x^{7} + 7 x^{6} + 12 x^{5} + 15 x^{4} - 4 x^{3} - 3 x^{2} - 2 x + 1$	$18$	[4,7]	$-\,2^{27}\cdot 11^{2}\cdot 17^{2}\cdot 3767^{3}$	$4$	$19.9512958521$	$2373.9064851000344$			?	$C_3^6.S_4^2:C_2^2$ (as 18T939)	trivial	$2$	$10$	$81195.1261492$
18.0.259...584.1	$x^{18} - 9 x^{15} + 9 x^{14} + 54 x^{12} - 135 x^{11} + 81 x^{10} - 6 x^{9} + 243 x^{8} - 729 x^{7} + 999 x^{6} - 756 x^{5} + 243 x^{4} + 81 x^{3} - 81 x^{2} + 9$	$18$	[0,9]	$-\,2^{3}\cdot 3^{45}\cdot 11$	$3$	$19.9907897664$				?	$C_2^4:A_4^2.D_6$ (as 18T658)	$[2]$	$2$	$8$	$34392.7400217$
18.2.666...528.2	$x^{18} - 4 x^{17} + 8 x^{16} - 6 x^{15} - 2 x^{14} + 18 x^{13} - 78 x^{12} + 176 x^{11} - 96 x^{10} - 316 x^{9} + 556 x^{8} + 168 x^{7} - 1640 x^{6} + 2632 x^{5} - 2424 x^{4} + 1472 x^{3} - 592 x^{2} + 144 x - 16$	$18$	[2,8]	$2^{32}\cdot 11^{4}\cdot 13^{9}$	$3$	$21.0647694197$	$165.79816173757717$			?	$A_4^3.(C_2\times S_4)$ (as 18T775)	trivial	$2$	$9$	$144577.390009$
18.8.194...131.1	$x^{18} - 5 x^{17} + 14 x^{16} - 18 x^{15} - x^{14} + 64 x^{13} - 144 x^{12} + 143 x^{11} + 46 x^{10} - 300 x^{9} + 345 x^{8} - 100 x^{7} - 300 x^{6} + 215 x^{5} + 133 x^{4} - 26 x^{3} - 69 x^{2} + 2 x + 9$	$18$	[8,5]	$-\,11^{4}\cdot 37^{6}\cdot 139^{5}$	$3$	$22.3581771921$	$874.823585606666$			?	$C_2^9.A_9$ (as 18T966)	trivial	$2$	$12$	$419992.659206$
18.6.266...112.1	$x^{18} - 4 x^{14} - 8 x^{12} - 72 x^{10} - 48 x^{8} + 340 x^{6} + 320 x^{4} - 208 x^{2} - 208$	$18$	[6,6]	$2^{34}\cdot 11^{4}\cdot 13^{9}$	$3$	$22.7512093593$	$261.2947270525209$			?	$A_4^3.(C_2\times S_4)$ (as 18T775)	trivial	$2$	$11$	$470216.319544$
18.0.268...704.2	$x^{18} + 4 x^{16} - x^{14} - 12 x^{12} - 12 x^{10} - 5 x^{8} + 19 x^{6} + 26 x^{4} + 10 x^{2} + 1$	$18$	[0,9]	$-\,2^{18}\cdot 11^{4}\cdot 37^{4}\cdot 139^{4}$	$4$	$22.7596393298$				?	$C_2^9.A_9$ (as 18T966)	trivial	$2$	$8$	$47368.0680883$
18.10.268...704.1	$x^{18} - 4 x^{16} - x^{14} + 12 x^{12} - 12 x^{10} + 5 x^{8} + 19 x^{6} - 26 x^{4} + 10 x^{2} - 1$	$18$	[10,4]	$2^{18}\cdot 11^{4}\cdot 37^{4}\cdot 139^{4}$	$4$	$22.7596393298$				?	$C_2^8.A_9$ (as 18T963)	trivial	$2$	$13$	$708366.596572$
18.2.268...704.1	$x^{18} + 6 x^{16} + 15 x^{14} + 16 x^{12} - x^{10} - 11 x^{8} - 20 x^{6} - 35 x^{4} - 17 x^{2} - 1$	$18$	[2,8]	$2^{18}\cdot 11^{4}\cdot 37^{4}\cdot 139^{4}$	$4$	$22.7596393298$				?	$C_2^8.A_9$ (as 18T963)	trivial	$2$	$9$	$65537.7829193$
18.10.268...704.2	$x^{18} - 8 x^{16} + 26 x^{14} - 51 x^{12} + 67 x^{10} - 50 x^{8} + 35 x^{6} - 57 x^{4} + 37 x^{2} - 1$	$18$	[10,4]	$2^{18}\cdot 11^{4}\cdot 37^{4}\cdot 139^{4}$	$4$	$22.7596393298$				?	$C_2^8.A_9$ (as 18T963)	trivial	$2$	$13$	$359712.575666$
18.0.656...968.1	$x^{18} + 12 x^{16} + 48 x^{14} + 184 x^{12} + 308 x^{10} + 216 x^{8} + 62 x^{6} + 24 x^{4} + 24 x^{2} + 8$	$18$	[0,9]	$-\,2^{39}\cdot 11^{4}\cdot 13^{8}$	$3$	$23.9187339602$	$134.65969308045723$				$C_6^2.S_3^2$ (as 18T299)	trivial	$2$	$8$	$392823.494818$
18.2.866...864.1	$x^{18} - 4 x^{17} + 13 x^{16} - 24 x^{15} + 53 x^{14} - 46 x^{13} + 139 x^{12} - 72 x^{11} + 268 x^{10} - 48 x^{9} + 142 x^{8} + 232 x^{7} - 12 x^{6} + 256 x^{5} + 280 x^{4} + 144 x^{3} + 68 x^{2} + 24 x + 4$	$18$	[2,8]	$2^{32}\cdot 11^{4}\cdot 13^{10}$	$3$	$24.290835414227942$	$165.79816173757717$			?	$A_4^3.(C_2\times S_4)$ (as 18T771)	$[2]$	$2$	$9$	$306524.3723401248$
18.6.131...936.1	$x^{18} + 2 x^{16} - 15 x^{14} - 12 x^{12} + 67 x^{10} - 74 x^{8} - 25 x^{6} + 48 x^{4} + 20 x^{2} - 4$	$18$	[6,6]	$2^{40}\cdot 11^{4}\cdot 13^{8}$	$3$	$24.8577649431$	$127.10182525224437$			?	$C_6^2.S_3^2$ (as 18T316)	trivial	$2$	$11$	$1592093.93315$
18.6.281...808.1	$x^{18} - 3 x^{17} + 9 x^{15} - 30 x^{14} + 7 x^{13} + 61 x^{12} - 114 x^{11} - 2 x^{10} + 268 x^{9} - 54 x^{8} - 178 x^{7} + 164 x^{6} + 174 x^{5} + 32 x^{4} + 18 x^{3} - 10 x - 2$	$18$	[6,6]	$2^{30}\cdot 11^{4}\cdot 13^{11}$	$3$	$25.9346514642$	$152.03758466926027$			?	$C_6^2.S_3^2$ (as 18T310)	trivial	$2$	$11$	$1399836.51268$
18.6.346...456.1	$x^{18} - 14 x^{16} + 87 x^{14} - 324 x^{12} + 819 x^{10} - 1622 x^{8} + 2713 x^{6} - 3380 x^{4} + 2392 x^{2} - 676$	$18$	[6,6]	$2^{34}\cdot 11^{4}\cdot 13^{10}$	$3$	$26.235553355$	$261.2947270525209$				$A_4^3.(C_2\times S_4)$ (as 18T771)	$[2]$	$2$	$11$	$2141289.03866$
18.6.346...456.2	$x^{18} - 4 x^{17} + 10 x^{16} - 24 x^{15} + 29 x^{14} - 18 x^{13} + 4 x^{12} + 88 x^{11} - 235 x^{10} + 426 x^{9} - 836 x^{8} + 1004 x^{7} + 37 x^{6} - 1526 x^{5} + 1592 x^{4} - 740 x^{3} + 290 x^{2} - 34 x - 2$	$18$	[6,6]	$2^{34}\cdot 11^{4}\cdot 13^{10}$	$3$	$26.235553354967013$	$219.7217993031626$			?	$A_4^3.(C_2\times S_4)$ (as 18T771)	trivial	$2$	$11$	$2234149.927501244$

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