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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
12.0.117236328125.1	$x^{12} - 4 x^{11} + 9 x^{10} - 20 x^{9} + 40 x^{8} - 64 x^{7} + 81 x^{6} - 81 x^{5} + 65 x^{4} - 40 x^{3} + 19 x^{2} - 6 x + 1$	$12$	[0,6]	$5^{11}\cdot 7^{4}$	$2$	$8.36415073054$	$11.568352777429151$			?	$S_3 \times C_4$ (as 12T11)	trivial	$10$	$5$	$11.9978872283$
12.0.200000000000.1	$x^{12} - 4 x^{11} + 9 x^{10} - 15 x^{9} + 15 x^{8} + x^{7} - 19 x^{6} + 14 x^{5} + 5 x^{4} - 10 x^{3} + 4 x^{2} - x + 1$	$12$	[0,6]	$2^{12}\cdot 5^{11}$	$2$	$8.74485272221$	$12.367089320707036$			?	$S_3 \times C_4$ (as 12T11)	trivial	$10$	$5$	$16.6769530035$
12.0.546564453125.1	$x^{12} - x^{11} + x^{10} - x^{8} - 2 x^{7} + 2 x^{6} - 3 x^{5} + x^{4} + x^{3} + x^{2} + 1$	$12$	[0,6]	$5^{9}\cdot 23^{4}$	$2$	$9.50904235709$	$16.03582917757843$			✓	$S_3 \times C_4$ (as 12T11)	trivial	$10$	$5$	$32.3656237465$
12.0.1012500000000.1	$x^{12} - 3 x^{11} + 11 x^{10} - 25 x^{9} + 55 x^{8} - 88 x^{7} + 119 x^{6} - 118 x^{5} + 95 x^{4} - 55 x^{3} + 26 x^{2} - 8 x + 1$	$12$	[0,6]	$2^{8}\cdot 3^{4}\cdot 5^{11}$	$3$	$10.0103574601$	$12.021808208412303$			?	$S_3 \times C_4$ (as 12T11)	trivial	$10$	$5$	$46.6043886559$
12.0.1037970703125.1	$x^{12} - 2 x^{9} + 4 x^{6} - 3 x^{3} + 1$	$12$	[0,6]	$3^{12}\cdot 5^{9}$	$2$	$10.0311045746$	$12.046724184927836$			✓	$S_3 \times C_4$ (as 12T11)	trivial	$10$	$5$	$46.5914285344$
12.0.1200500000000.1	$x^{12} - 2 x^{11} + 2 x^{10} - x^{9} + 5 x^{8} + 2 x^{7} - 3 x^{6} + 2 x^{5} + 5 x^{4} + 9 x^{3} + 7 x^{2} + 3 x + 1$	$12$	[0,6]	$2^{8}\cdot 5^{9}\cdot 7^{4}$	$3$	$10.1534471757$	$14.043106421634382$			?	$S_3 \times C_4$ (as 12T11)	trivial	$10$	$5$	$44.4179208274$
12.0.1803751953125.3	$x^{12} - x^{10} - x^{9} + x^{8} - 3 x^{7} + 2 x^{5} + 3 x^{4} - 2 x^{3} + x^{2} - x + 1$	$12$	[0,6]	$5^{9}\cdot 31^{4}$	$2$	$10.5038392776$	$18.616942190179014$			✓	$S_3 \times C_4$ (as 12T11)	trivial	$10$	$5$	$55.7455420814$
12.4.5744580078125.1	$x^{12} - 2 x^{11} + x^{10} + 5 x^{9} - 12 x^{7} - x^{6} + 18 x^{5} - 20 x^{4} - 5 x^{3} + 16 x^{2} - 7 x + 1$	$12$	[4,4]	$5^{11}\cdot 7^{6}$	$2$	$11.5683527774$	$11.568352777429151$			?	$S_3 \times C_4$ (as 12T11)	trivial	$2$	$7$	$41.9630859692$
12.0.7320500000000.2	$x^{12} - x^{11} + 2 x^{9} - 3 x^{8} + 2 x^{7} + 3 x^{6} - 8 x^{5} + 7 x^{4} + 4 x^{3} + 2 x^{2} + x + 1$	$12$	[0,6]	$2^{8}\cdot 5^{9}\cdot 11^{4}$	$3$	$11.8044311122$	$17.603965534028475$			?	$S_3 \times C_4$ (as 12T11)	trivial	$10$	$5$	$141.9815003$
12.4.9112500000000.1	$x^{12} - 6 x^{11} + 14 x^{10} - 15 x^{9} + 5 x^{8} + 4 x^{7} - 9 x^{6} + 16 x^{5} - 15 x^{4} + 5 x^{3} - x^{2} + x + 1$	$12$	[4,4]	$2^{8}\cdot 3^{6}\cdot 5^{11}$	$3$	$12.0218082084$	$12.021808208412303$			?	$S_3 \times C_4$ (as 12T11)	trivial	$2$	$7$	$56.4359851616$
12.4.9341736328125.1	$x^{12} - 6 x^{11} + 15 x^{10} - 11 x^{9} - 27 x^{8} + 69 x^{7} - 40 x^{6} - 45 x^{5} + 57 x^{4} + 8 x^{3} - 24 x^{2} - 3 x + 1$	$12$	[4,4]	$3^{14}\cdot 5^{9}$	$2$	$12.0467241849$	$12.046724184927836$			?	$S_3 \times C_4$ (as 12T11)	trivial	$2$	$7$	$56.4202909911$
12.4.12800000000000.1	$x^{12} - 2 x^{11} + x^{10} - 10 x^{8} + 18 x^{7} - 26 x^{6} + 8 x^{5} + 15 x^{4} - 20 x^{3} + 6 x^{2} + 8 x - 4$	$12$	[4,4]	$2^{18}\cdot 5^{11}$	$2$	$12.3670893207$	$12.367089320707036$			?	$S_3 \times C_4$ (as 12T11)	trivial	$2$	$7$	$78.0328195859$
12.0.13213283203125.1	$x^{12} - 4 x^{11} + 5 x^{10} - 9 x^{8} + 30 x^{7} - 41 x^{6} - 20 x^{5} + 106 x^{4} - 95 x^{3} + 30 x^{2} + x + 1$	$12$	[0,6]	$3^{4}\cdot 5^{9}\cdot 17^{4}$	$3$	$12.399882274413569$	$23.87880512635518$			?	$S_3 \times C_4$ (as 12T11)	trivial	$10$	$5$	$205.6035190856011$
12.0.25949267578125.1	$x^{12} - 5 x^{9} + 15 x^{6} - 15 x^{3} + 5$	$12$	[0,6]	$3^{12}\cdot 5^{11}$	$2$	$13.1172790833$	$15.753025202513207$			?	$S_3 \times C_4$ (as 12T11)	trivial	$10$	$5$	$277.288481269$
12.0.39357658203125.1	$x^{12} - 4 x^{11} + 7 x^{10} - 10 x^{9} + 9 x^{8} - 8 x^{7} + 21 x^{6} - 14 x^{5} + 6 x^{4} - 31 x^{3} + 16 x^{2} + 7 x + 1$	$12$	[0,6]	$5^{9}\cdot 67^{4}$	$2$	$13.580604576842257$	$27.369376545007917$			?	$S_3 \times C_4$ (as 12T11)	$[2]$	$10$	$5$	$172.1554240836862$
12.0.43436029431808.1	$x^{12} - 6 x^{11} + 19 x^{10} - 39 x^{9} + 63 x^{8} - 77 x^{7} + 71 x^{6} - 44 x^{5} + 39 x^{4} - 10 x^{3} + 8 x^{2} + x + 1$	$12$	[0,6]	$2^{12}\cdot 13^{9}$	$2$	$13.692650084$	$19.364331453687083$			?	$S_3 \times C_4$ (as 12T11)	trivial	$2$	$5$	$54.6840897429$
12.4.51200000000000.2	$x^{12} + 10 x^{6} - 20 x^{2} + 5$	$12$	[4,4]	$2^{20}\cdot 5^{11}$	$2$	$13.8815884105$	$17.489705444423358$				$S_3 \times C_4$ (as 12T11)	trivial	$2$	$7$	$197.800498269$
12.4.58824500000000.1	$x^{12} - x^{11} - 2 x^{10} + 8 x^{9} - 5 x^{8} - 14 x^{7} + 33 x^{6} + 24 x^{5} - 25 x^{4} + 12 x^{3} + 18 x^{2} - 29 x - 19$	$12$	[4,4]	$2^{8}\cdot 5^{9}\cdot 7^{6}$	$3$	$14.0431064216$	$14.043106421634382$			?	$S_3 \times C_4$ (as 12T11)	trivial	$2$	$7$	$155.35343805$
12.4.85465283203125.1	$x^{12} - 4 x^{11} + 9 x^{10} - 10 x^{9} + 16 x^{7} - 24 x^{6} - 41 x^{5} + 45 x^{4} - 10 x^{3} - 6 x^{2} + 14 x + 1$	$12$	[4,4]	$3^{6}\cdot 5^{11}\cdot 7^{4}$	$3$	$14.4871340275$	$20.036974770387825$			?	$S_3 \times C_4$ (as 12T11)	trivial	$2$	$7$	$210.207248027$
12.0.117128000000000.2	$x^{12} - 2 x^{11} + 7 x^{10} - 11 x^{9} + 30 x^{8} - 13 x^{7} + 32 x^{6} + 67 x^{5} + 20 x^{4} - 11 x^{3} - 3 x^{2} + 3 x + 1$	$12$	[0,6]	$2^{12}\cdot 5^{9}\cdot 11^{4}$	$3$	$14.872651240288148$	$31.366700656905365$			?	$S_3 \times C_4$ (as 12T11)	trivial	$10$	$5$	$769.2278076585833$
12.4.118919548828125.1	$x^{12} - 6 x^{11} + 17 x^{10} - 22 x^{9} - 12 x^{8} + 83 x^{7} - 127 x^{6} + 83 x^{5} - 12 x^{4} - 22 x^{3} + 17 x^{2} - 6 x + 1$	$12$	[4,4]	$3^{6}\cdot 5^{9}\cdot 17^{4}$	$3$	$14.89147686317512$	$23.87880512635518$			?	$S_3 \times C_4$ (as 12T11)	trivial	$2$	$7$	$301.86432812746887$
12.0.139920500000000.1	$x^{12} - x^{11} - x^{10} + x^{9} + 13 x^{8} - 62 x^{7} + 89 x^{6} - 16 x^{5} - 53 x^{4} - 33 x^{3} + 198 x^{2} - 216 x + 81$	$12$	[0,6]	$2^{8}\cdot 5^{9}\cdot 23^{4}$	$3$	$15.09466384085731$	$25.455292105670352$			?	$S_3 \times C_4$ (as 12T11)	$[2]$	$10$	$5$	$291.9505434072523$
12.4.145800000000000.1	$x^{12} - 4 x^{11} + 9 x^{10} - 5 x^{9} - 10 x^{8} + 21 x^{7} - 24 x^{6} - 31 x^{5} + 10 x^{4} + 15 x^{3} - 31 x^{2} - 11 x + 1$	$12$	[4,4]	$2^{12}\cdot 3^{6}\cdot 5^{11}$	$3$	$15.1465292196$	$21.42042704520706$			?	$S_3 \times C_4$ (as 12T11)	trivial	$2$	$7$	$256.4625112$
12.0.204800000000000.2	$x^{12} + 10 x^{10} + 35 x^{8} + 70 x^{6} + 85 x^{4} + 60 x^{2} + 20$	$12$	[0,6]	$2^{22}\cdot 5^{11}$	$2$	$15.5815561611$	$17.489705444423358$				$S_3 \times C_4$ (as 12T11)	$[2]$	$2$	$5$	$102.745462078$
12.0.219825939453125.1	$x^{12} + 2 x^{10} - 5 x^{9} + 4 x^{8} - 10 x^{7} + 23 x^{6} - 40 x^{5} + 56 x^{4} - 65 x^{3} + 60 x^{2} - 50 x + 25$	$12$	[0,6]	$5^{9}\cdot 103^{4}$	$2$	$15.673761889267645$	$33.93486420206204$			?	$S_3 \times C_4$ (as 12T11)	$[2]$	$10$	$5$	$438.3305767013016$
12.4.233543408203125.2	$x^{12} - 6 x^{11} + 9 x^{10} - 6 x^{7} - 4 x^{6} + 6 x^{5} + 9 x^{2} + 6 x + 1$	$12$	[4,4]	$3^{14}\cdot 5^{11}$	$2$	$15.7530252025$	$15.753025202513207$			?	$S_3 \times C_4$ (as 12T11)	trivial	$2$	$7$	$335.784870604$
12.4.259200000000000.1	$x^{12} - 10 x^{10} + 35 x^{8} - 60 x^{6} + 55 x^{4} - 10 x^{2} + 5$	$12$	[4,4]	$2^{16}\cdot 3^{4}\cdot 5^{11}$	$3$	$15.8904519628$	$19.083430996593624$			?	$S_3 \times C_4$ (as 12T11)	trivial	$2$	$7$	$368.977181234$
12.0.265720500000000.3	$x^{12} - 2 x^{9} + 4 x^{6} - 8 x^{3} + 16$	$12$	[0,6]	$2^{8}\cdot 3^{12}\cdot 5^{9}$	$3$	$15.9233859542$	$19.122982643925198$			?	$S_3 \times C_4$ (as 12T11)	trivial	$10$	$5$	$1053.91768271$
12.4.289132595703125.1	$x^{12} - 2 x^{11} + 3 x^{10} - 5 x^{9} - 6 x^{8} + 6 x^{7} - 51 x^{6} + 87 x^{5} - 104 x^{4} + 172 x^{3} - 181 x^{2} + 94 x - 19$	$12$	[4,4]	$5^{9}\cdot 23^{6}$	$2$	$16.0358291776$	$16.03582917757843$			?	$S_3 \times C_4$ (as 12T11)	trivial	$2$	$7$	$330.426451282$
12.4.307328000000000.1	$x^{12} - 4 x^{11} + x^{10} + 14 x^{9} - 28 x^{8} + 4 x^{7} + 61 x^{6} - 68 x^{5} - 36 x^{4} + 122 x^{3} + 53 x^{2} - 60 x - 19$	$12$	[4,4]	$2^{16}\cdot 5^{9}\cdot 7^{4}$	$3$	$16.1175927278$	$22.292041906603796$			?	$S_3 \times C_4$ (as 12T11)	trivial	$2$	$7$	$456.668824888$
12.0.357012500000000.1	$x^{12} - x^{11} - x^{10} + 25 x^{9} - 15 x^{8} - 86 x^{7} + 141 x^{6} + 76 x^{5} - 365 x^{4} + 195 x^{3} + 244 x^{2} - 384 x + 181$	$12$	[0,6]	$2^{8}\cdot 5^{11}\cdot 13^{4}$	$3$	$16.3201301752$	$25.025389399554754$	✓		?	$S_3 \times C_4$ (as 12T11)	trivial	$10$	$5$	$1008.69816141$
12.0.458793060873472.1	$x^{12} - 3 x^{11} + 9 x^{10} - 27 x^{9} + 55 x^{8} - 100 x^{7} + 157 x^{6} - 185 x^{5} + 152 x^{4} - 40 x^{3} - 36 x^{2} - 9 x + 27$	$12$	[0,6]	$2^{8}\cdot 13^{11}$	$2$	$16.6648497871$	$20.99639504015924$				$S_3 \times C_4$ (as 12T11)	$[3]$	$2$	$5$	$295.950151185$
12.0.461760500000000.2	$x^{12} - 4 x^{11} + 8 x^{10} - 5 x^{9} + x^{8} + 10 x^{7} + 7 x^{6} - 8 x^{5} + 31 x^{4} - 15 x^{3} + 35 x^{2} - 25 x + 25$	$12$	[0,6]	$2^{8}\cdot 5^{9}\cdot 31^{4}$	$3$	$16.67380551902469$	$29.552553617121323$			?	$S_3 \times C_4$ (as 12T11)	trivial	$10$	$5$	$1782.1558033475317$
12.0.503060929445888.2	$x^{12} - 12 x^{8} + 20 x^{6} + 4 x^{4} - 8 x^{2} + 2$	$12$	[0,6]	$2^{35}\cdot 11^{4}$	$2$	$16.7932614352$	$25.04381555535815$			?	$S_3 \times C_4$ (as 12T11)	trivial	$2$	$5$	$503.341863638$
12.4.503060929445888.6	$x^{12} - 12 x^{8} - 20 x^{6} + 4 x^{4} + 8 x^{2} + 2$	$12$	[4,4]	$2^{35}\cdot 11^{4}$	$2$	$16.7932614352$	$25.04381555535815$			?	$S_3 \times C_4$ (as 12T11)	trivial	$2$	$7$	$775.482114835$
12.0.575195158203125.1	$x^{12} + x^{10} - 5 x^{9} + x^{8} - 5 x^{7} + 16 x^{6} - 10 x^{5} + 21 x^{4} - 30 x^{3} + 15 x^{2} - 25 x + 25$	$12$	[0,6]	$5^{9}\cdot 131^{4}$	$2$	$16.981834411852024$	$38.2704131838469$			?	$S_3 \times C_4$ (as 12T11)	trivial	$10$	$5$	$1244.0220590230213$
12.0.668168000000000.1	$x^{12} - x^{11} - 7 x^{10} + 15 x^{9} + 21 x^{8} - 60 x^{7} - 23 x^{6} + 163 x^{5} - 54 x^{4} - 240 x^{3} + 290 x^{2} - 75 x + 25$	$12$	[0,6]	$2^{12}\cdot 5^{9}\cdot 17^{4}$	$3$	$17.195196351170477$	$38.99392548461692$			?	$S_3 \times C_4$ (as 12T11)	trivial	$10$	$5$	$2014.8871293984223$
12.0.729103595703125.1	$x^{12} - x^{10} - 5 x^{9} + x^{8} + 5 x^{7} + 14 x^{6} - 10 x^{5} - 19 x^{4} - 20 x^{3} + 15 x^{2} + 25 x + 25$	$12$	[0,6]	$5^{9}\cdot 139^{4}$	$2$	$17.32071317552354$	$39.42165958407071$			?	$S_3 \times C_4$ (as 12T11)	trivial	$10$	$5$	$2002.9878211135294$
12.4.885780500000000.1	$x^{12} - x^{11} + 3 x^{10} + x^{9} + 9 x^{8} - 18 x^{7} - 33 x^{6} + 46 x^{5} - 15 x^{4} - 21 x^{3} + 20 x^{2} - 22 x + 11$	$12$	[4,4]	$2^{8}\cdot 5^{9}\cdot 11^{6}$	$3$	$17.603965534$	$17.603965534028475$			?	$S_3 \times C_4$ (as 12T11)	trivial	$2$	$7$	$781.064333478$
12.0.937080500000000.1	$x^{12} - x^{11} + 4 x^{10} - 6 x^{9} + 17 x^{8} + 10 x^{7} + 35 x^{6} + 12 x^{5} + 103 x^{4} - 32 x^{3} + 10 x^{2} - 3 x + 1$	$12$	[0,6]	$2^{8}\cdot 5^{9}\cdot 37^{4}$	$3$	$17.6867515429$	$32.28605847922135$	✓		?	$S_3 \times C_4$ (as 12T11)	$[2]$	$10$	$5$	$503.981234285$
12.4.981348487528448.4	$x^{12} - 4 x^{10} + 6 x^{8} + 8 x^{6} - 7 x^{4} - 4 x^{2} + 2$	$12$	[4,4]	$2^{35}\cdot 13^{4}$	$2$	$17.7549152981$	$28.844410203711913$			?	$S_3 \times C_4$ (as 12T11)	trivial	$2$	$7$	$1918.43223703$
12.0.981348487528448.5	$x^{12} + 4 x^{10} + 6 x^{8} - 8 x^{6} - 7 x^{4} + 4 x^{2} + 2$	$12$	[0,6]	$2^{35}\cdot 13^{4}$	$2$	$17.7549152981$	$28.844410203711913$			?	$S_3 \times C_4$ (as 12T11)	trivial	$2$	$5$	$695.749093895$
12.0.1015401564453125.2	$x^{12} - x^{11} + 5 x^{10} + 10 x^{9} - 9 x^{8} + 44 x^{6} + 100 x^{5} + 81 x^{4} - 40 x^{3} - 40 x^{2} + 24 x + 16$	$12$	[0,6]	$5^{9}\cdot 151^{4}$	$2$	$17.805458126184142$	$41.088092228921276$			?	$S_3 \times C_4$ (as 12T11)	trivial	$10$	$5$	$1971.95634084061$
12.4.1119448865964032.6	$x^{12} - 16 x^{8} - 40 x^{6} - 32 x^{4} + 8$	$12$	[4,4]	$2^{33}\cdot 19^{4}$	$2$	$17.9507950469$	$29.323059968612448$			?	$S_3 \times C_4$ (as 12T11)	trivial	$2$	$7$	$1325.92180197$
12.0.1119448865964032.15	$x^{12} - 16 x^{8} + 40 x^{6} - 32 x^{4} + 8$	$12$	[0,6]	$2^{33}\cdot 19^{4}$	$2$	$17.9507950469$	$29.323059968612448$			?	$S_3 \times C_4$ (as 12T11)	$[2]$	$2$	$5$	$195.463564584$
12.0.1156720500000000.1	$x^{12} - 3 x^{11} - 3 x^{10} + 25 x^{9} + 11 x^{8} - 60 x^{7} - 27 x^{6} + 36 x^{5} + 71 x^{4} + 85 x^{3} + 60 x^{2} + 50 x + 25$	$12$	[0,6]	$2^{8}\cdot 3^{4}\cdot 5^{9}\cdot 13^{4}$	$4$	$17.999856219800858$	$33.14717113722765$			?	$S_3 \times C_4$ (as 12T11)	trivial	$10$	$5$	$1757.9316561444375$
12.0.1175078824045389.1	$x^{12} - 2 x^{11} + 3 x^{9} - 3 x^{8} + 17 x^{7} + 22 x^{6} - 25 x^{5} - 20 x^{4} + 91 x^{3} + 230 x^{2} + 228 x + 83$	$12$	[0,6]	$3^{4}\cdot 29^{9}$	$2$	$18.02349111$	$21.645076535339435$			?	$S_3 \times C_4$ (as 12T11)	$[2]$	$2$	$5$	$142.483768915$
12.0.1381988962788733.1	$x^{12} - 6 x^{11} + 22 x^{10} - 52 x^{9} + 100 x^{8} - 162 x^{7} + 268 x^{6} - 382 x^{5} + 459 x^{4} - 432 x^{3} + 459 x^{2} - 405 x + 243$	$12$	[0,6]	$13^{9}\cdot 19^{4}$	$2$	$18.268745029820636$	$29.84243899281031$				$S_3 \times C_4$ (as 12T11)	$[2]$	$2$	$5$	$800.6377392154858$
12.4.1733405626953125.1	$x^{12} - 6 x^{10} - x^{9} + 11 x^{8} + 17 x^{7} - 60 x^{6} - 43 x^{5} + 118 x^{4} + 138 x^{3} - 44 x^{2} - 31 x + 31$	$12$	[4,4]	$5^{9}\cdot 31^{6}$	$2$	$18.6169421902$	$18.616942190179014$			?	$S_3 \times C_4$ (as 12T11)	trivial	$2$	$7$	$676.99391235$
12.0.2332800000000000.1	$x^{12} + 5 x^{10} - 10 x^{8} - 35 x^{6} + 10 x^{4} + 105 x^{2} + 45$	$12$	[0,6]	$2^{16}\cdot 3^{6}\cdot 5^{11}$	$3$	$19.0834309966$	$19.083430996593624$			?	$S_3 \times C_4$ (as 12T11)	$[2, 2]$	$2$	$5$	$191.661453404$

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