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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
12.0.17547210909508096.1	$x^{12} - x^{11} + 4 x^{10} - 20 x^{9} + 25 x^{8} - 43 x^{7} + 122 x^{6} - 101 x^{5} + 168 x^{4} - 78 x^{3} + 81 x^{2} - 19 x + 13$	$12$	[0,6]	$2^{9}\cdot 17^{11}$	$2$	$22.577924062$	$37.971390815226314$			?	$S_3^2:C_4$ (as 12T80)	$[2]$	$2$	$5$	$2115.49319292$
12.0.24984212408264457.1	$x^{12} - 6 x^{11} + 25 x^{10} - 70 x^{9} + 134 x^{8} - 182 x^{7} + 211 x^{6} - 224 x^{5} + 189 x^{4} - 110 x^{3} + 8 x^{2} + 24 x + 16$	$12$	[0,6]	$3^{6}\cdot 17^{11}$	$2$	$23.252633080277057$	$23.252633080277057$				$S_3 \times C_4$ (as 12T11)	$[10]$	$2$	$5$	$4214.360188795258$
12.2.70188843638032384.1	$x^{12} - 3 x^{11} - 15 x^{10} + 55 x^{9} + 19 x^{8} - 147 x^{7} - 57 x^{6} + 181 x^{5} + 104 x^{4} - 38 x^{3} - 100 x^{2} - 48 x - 16$	$12$	[2,5]	$-\,2^{11}\cdot 17^{11}$	$2$	$25.3428628892$	$53.69965587306223$			?	$D_6\wr C_2$ (as 12T125)	$[2]$	$2$	$6$	$7284.49812494$
12.0.70188843638032384.1	$x^{12} - 5 x^{11} + 15 x^{10} - 35 x^{9} + 70 x^{8} - 92 x^{7} + 108 x^{6} - 92 x^{5} + 70 x^{4} - 35 x^{3} + 15 x^{2} - 5 x + 1$	$12$	[0,6]	$2^{11}\cdot 17^{11}$	$2$	$25.3428628892$	$90.3116962480322$			?	$S_4^2:C_4$ (as 12T238)	$[2]$	$2$	$5$	$2362.1314195$
12.2.280755374552129536.1	$x^{12} - 3 x^{11} + 2 x^{10} + 4 x^{9} + 2 x^{8} - 28 x^{7} + 28 x^{6} + 11 x^{5} - 15 x^{4} + 64 x^{3} - 100 x^{2} + 54 x + 18$	$12$	[2,5]	$-\,2^{13}\cdot 17^{11}$	$2$	$28.4464017887$	$107.39931174612445$			?	$S_4^2:D_4$ (as 12T260)	$[2]$	$2$	$6$	$23296.9609907$
12.6.280755374552129536.1	$x^{12} - 5 x^{11} - 2 x^{10} + 50 x^{9} - 83 x^{8} - 75 x^{7} + 380 x^{6} - 330 x^{5} - 100 x^{4} + 356 x^{3} - 240 x^{2} + 80 x - 16$	$12$	[6,3]	$-\,2^{13}\cdot 17^{11}$	$2$	$28.4464017887$	$47.84095458188848$				$S_3^2:C_4$ (as 12T80)	$[2]$	$2$	$8$	$69919.1497116$
12.2.112...144.1	$x^{12} - 3 x^{11} - 15 x^{10} + 21 x^{9} + 104 x^{8} + 108 x^{7} - 244 x^{6} - 516 x^{5} - 168 x^{4} + 744 x^{3} + 784 x^{2} - 48 x - 832$	$12$	[2,5]	$-\,2^{15}\cdot 17^{11}$	$2$	$31.9300064187$	$53.69965587306223$				$D_6\wr C_2$ (as 12T125)	$[2]$	$2$	$6$	$128617.729182$
12.2.112...144.2	$x^{12} + 17 x^{10} + 119 x^{8} + 459 x^{6} + 884 x^{4} + 136 x^{2} - 544$	$12$	[2,5]	$-\,2^{15}\cdot 17^{11}$	$2$	$31.9300064187$	$101.37145155686015$				$S_4^2:C_4$ (as 12T238)	$[2]$	$2$	$6$	$192984.280825$
12.2.112...144.3	$x^{12} - 17 x^{8} - 119 x^{6} + 374 x^{4} - 612 x^{2} - 136$	$12$	[2,5]	$-\,2^{15}\cdot 17^{11}$	$2$	$31.9300064187$	$69.63983780733449$				$S_4^2:D_4$ (as 12T260)	$[2]$	$2$	$6$	$57518.3147705$
12.2.112...144.4	$x^{12} + 17 x^{10} + 102 x^{8} + 238 x^{6} + 289 x^{4} - 255 x^{2} - 136$	$12$	[2,5]	$-\,2^{15}\cdot 17^{11}$	$2$	$31.9300064187$	$53.69965587306223$				$D_6\wr C_2$ (as 12T125)	$[2]$	$2$	$6$	$57352.8535259$
12.2.112...144.5	$x^{12} - 4 x^{11} + 13 x^{10} - 22 x^{9} + 8 x^{8} + 32 x^{7} - 88 x^{6} + 64 x^{5} + 32 x^{4} - 176 x^{3} + 208 x^{2} - 128 x + 64$	$12$	[2,5]	$-\,2^{15}\cdot 17^{11}$	$2$	$31.9300064187$	$56.89280357730381$				$S_4^2:C_4$ (as 12T238)	$[2, 2]$	$2$	$6$	$52217.0172233$
12.0.112...144.1	$x^{12} - 5 x^{11} + 15 x^{10} - 18 x^{9} + 19 x^{8} - 7 x^{7} + 6 x^{6} - 7 x^{5} + 19 x^{4} - 18 x^{3} + 15 x^{2} - 5 x + 1$	$12$	[0,6]	$2^{15}\cdot 17^{11}$	$2$	$31.9300064187$	$60.275825724785875$			?	$D_6\wr C_2$ (as 12T125)	$[6]$	$2$	$5$	$7531.86927297$
12.4.112...144.1	$x^{12} + 68 x^{6} - 663 x^{4} - 272 x^{2} + 34$	$12$	[4,4]	$2^{15}\cdot 17^{11}$	$2$	$31.9300064187$	$113.78560715460762$				$S_4^2:D_4$ (as 12T260)	$[2]$	$2$	$7$	$96240.6144719$
12.4.112...144.2	$x^{12} - 4 x^{11} + 13 x^{10} - 22 x^{9} + 42 x^{8} - 2 x^{7} - 3 x^{6} - 4 x^{5} - 308 x^{4} - 6 x^{3} - 234 x^{2} - 162 x + 81$	$12$	[4,4]	$2^{15}\cdot 17^{11}$	$2$	$31.9300064187$	$69.63983780733449$			?	$S_4^2:C_4$ (as 12T238)	$[2]$	$2$	$7$	$37665.0870587$
12.0.112...144.2	$x^{12} - 3 x^{11} + 2 x^{10} + 21 x^{9} - 32 x^{8} - 45 x^{7} + 351 x^{6} - 584 x^{5} + 648 x^{4} - 412 x^{3} + 988 x^{2} - 1272 x + 1208$	$12$	[0,6]	$2^{15}\cdot 17^{11}$	$2$	$31.9300064187$	$37.971390815226314$				$S_3^2:C_4$ (as 12T80)	$[2]$	$2$	$5$	$9164.81984036$
12.0.403...817.1	$x^{12} - 2 x^{11} + 16 x^{10} - 24 x^{9} + 111 x^{8} - 101 x^{7} + 566 x^{6} - 314 x^{5} + 1256 x^{4} - 1635 x^{3} + 851 x^{2} - 2345 x + 1789$	$12$	[0,6]	$7^{6}\cdot 17^{11}$	$2$	$35.51898373246793$	$35.51898373246793$			?	$S_3 \times C_4$ (as 12T11)	$[2]$	$2$	$5$	$7218.657057374844$
12.6.449...576.1	$x^{12} - 34 x^{8} + 34 x^{6} + 136 x^{4} + 136 x^{2} - 544$	$12$	[6,3]	$-\,2^{17}\cdot 17^{11}$	$2$	$35.8402204073$	$80.45857442045158$				$S_4^2:C_4$ (as 12T238)	$[2]$	$2$	$8$	$289099.334914$
12.2.449...576.1	$x^{12} + 17 x^{10} + 85 x^{8} + 17 x^{6} - 986 x^{4} - 2686 x^{2} - 2176$	$12$	[2,5]	$-\,2^{17}\cdot 17^{11}$	$2$	$35.8402204073$	$110.54635179425756$				$S_4^2:C_4$ (as 12T238)	$[2]$	$2$	$6$	$173507.065365$
12.6.449...576.2	$x^{12} - 17 x^{10} + 68 x^{8} - 34 x^{6} + 374 x^{4} - 136$	$12$	[6,3]	$-\,2^{17}\cdot 17^{11}$	$2$	$35.8402204073$	$56.89280357730381$				$S_4^2:C_4$ (as 12T238)	$[2]$	$2$	$8$	$289137.665015$
12.2.449...576.2	$x^{12} + 17 x^{8} + 238 x^{6} - 68 x^{4} - 2040 x^{2} - 2176$	$12$	[2,5]	$-\,2^{17}\cdot 17^{11}$	$2$	$35.8402204073$	$47.84095458188848$				$S_3^2:C_4$ (as 12T80)	$[2]$	$2$	$6$	$416597.997169$
12.6.449...576.3	$x^{12} - 17 x^{10} + 85 x^{8} - 119 x^{6} - 102 x^{4} + 340 x^{2} - 136$	$12$	[6,3]	$-\,2^{17}\cdot 17^{11}$	$2$	$35.8402204073$	$95.68190916377696$				$S_4^2:C_4$ (as 12T238)	$[2]$	$2$	$8$	$426965.637378$
12.2.449...576.3	$x^{12} + 17 x^{10} + 102 x^{8} + 153 x^{6} - 476 x^{4} - 1496 x^{2} - 544$	$12$	[2,5]	$-\,2^{17}\cdot 17^{11}$	$2$	$35.8402204073$	$107.39931174612445$				$S_4^2:D_4$ (as 12T260)	$[2]$	$2$	$6$	$147713.135061$
12.6.449...576.4	$x^{12} - 17 x^{10} + 119 x^{8} - 255 x^{6} - 170 x^{4} + 612 x^{2} - 34$	$12$	[6,3]	$-\,2^{17}\cdot 17^{11}$	$2$	$35.8402204073$	$80.45857442045158$				$S_4^2:C_4$ (as 12T238)	$[2]$	$2$	$8$	$737857.290597$
12.2.449...576.4	$x^{12} + 17 x^{10} + 34 x^{8} - 476 x^{6} - 1088 x^{4} - 544$	$12$	[2,5]	$-\,2^{17}\cdot 17^{11}$	$2$	$35.8402204073$	$69.63983780733449$				$S_4^2:D_4$ (as 12T260)	$[2]$	$2$	$6$	$108621.284464$
12.2.449...576.5	$x^{12} + 17 x^{10} + 102 x^{8} + 238 x^{6} + 68 x^{4} - 408 x^{2} - 136$	$12$	[2,5]	$-\,2^{17}\cdot 17^{11}$	$2$	$35.8402204073$	$113.78560715460762$				$S_4^2:C_4$ (as 12T238)	$[2]$	$2$	$6$	$168278.276356$
12.2.449...576.6	$x^{12} - 17 x^{8} + 119 x^{6} + 374 x^{4} + 612 x^{2} - 136$	$12$	[2,5]	$-\,2^{17}\cdot 17^{11}$	$2$	$35.8402204073$	$69.63983780733449$			?	$S_4^2:D_4$ (as 12T260)	$[2]$	$2$	$6$	$61007.8821044$
12.2.449...576.7	$x^{12} - 17 x^{10} + 119 x^{8} - 442 x^{6} + 833 x^{4} - 476 x^{2} - 34$	$12$	[2,5]	$-\,2^{17}\cdot 17^{11}$	$2$	$35.8402204073$	$122.30511559717738$				$S_4^2:D_4$ (as 12T260)	$[2]$	$2$	$6$	$161649.858539$
12.2.449...576.8	$x^{12} + 17 x^{8} - 85 x^{6} + 51 x^{4} + 34 x^{2} - 34$	$12$	[2,5]	$-\,2^{17}\cdot 17^{11}$	$2$	$35.8402204073$	$122.30511559717738$				$S_4^2:D_4$ (as 12T260)	$[2]$	$2$	$6$	$126690.654584$
12.2.449...576.9	$x^{12} - 34 x^{9} - 34 x^{8} - 34 x^{7} + 187 x^{6} + 170 x^{5} - 119 x^{4} - 986 x^{3} - 1071 x^{2} - 272 x + 544$	$12$	[2,5]	$-\,2^{17}\cdot 17^{11}$	$2$	$35.8402204073$	$69.63983780733449$				$S_4^2:D_4$ (as 12T260)	$[2]$	$2$	$6$	$112558.113937$
12.2.449...576.10	$x^{12} - x^{11} + 4 x^{10} - 20 x^{9} - 9 x^{8} + 25 x^{7} - 14 x^{6} - 322 x^{5} + 304 x^{4} - 1200 x^{3} + 880 x^{2} - 920 x + 608$	$12$	[2,5]	$-\,2^{17}\cdot 17^{11}$	$2$	$35.8402204073$	$122.30511559717738$				$S_4^2:D_4$ (as 12T260)	$[2]$	$2$	$6$	$128565.789094$
12.8.449...576.1	$x^{12} - 2 x^{11} - 18 x^{10} + 78 x^{9} - 127 x^{8} + 86 x^{7} + 158 x^{6} - 450 x^{5} + 168 x^{4} + 184 x^{3} - 50 x^{2} - 16 x + 4$	$12$	[8,2]	$2^{17}\cdot 17^{11}$	$2$	$35.8402204073$	$60.275825724785875$				$D_6\wr C_2$ (as 12T125)	$[2]$	$2$	$9$	$678751.076549$
12.4.449...576.1	$x^{12} - 4 x^{11} - 4 x^{10} + 12 x^{9} + 59 x^{8} - 172 x^{7} - 20 x^{6} + 540 x^{5} - 189 x^{4} - 1400 x^{3} + 1432 x^{2} + 688 x - 1007$	$12$	[4,4]	$2^{17}\cdot 17^{11}$	$2$	$35.8402204073$	$113.78560715460762$			?	$S_4^2:D_4$ (as 12T260)	$[2]$	$2$	$7$	$101687.346638$
12.0.449...576.1	$x^{12} - x^{11} + 4 x^{10} - 3 x^{9} + 59 x^{8} + 8 x^{7} + 207 x^{6} + 103 x^{5} + 406 x^{4} + 143 x^{3} + 489 x^{2} - 70 x + 98$	$12$	[0,6]	$2^{17}\cdot 17^{11}$	$2$	$35.8402204073$	$95.68190916377696$			?	$S_4^2:D_4$ (as 12T260)	$[2, 2]$	$2$	$5$	$16124.0322786$
12.0.449...576.2	$x^{12} + 17 x^{8} + 51 x^{6} - 34 x^{4} - 34 x^{2} + 136$	$12$	[0,6]	$2^{17}\cdot 17^{11}$	$2$	$35.8402204073$	$117.11977994207535$			?	$S_4^2:C_4$ (as 12T238)	$[2]$	$2$	$5$	$21067.9935344$
12.4.449...576.2	$x^{12} - 3 x^{11} + 2 x^{10} - 13 x^{9} + 36 x^{8} - 45 x^{7} + 79 x^{6} - 142 x^{5} + 70 x^{4} - 4 x^{3} + 206 x^{2} - 150 x - 50$	$12$	[4,4]	$2^{17}\cdot 17^{11}$	$2$	$35.8402204073$	$85.24289022322928$				$S_4^2:D_4$ (as 12T260)	$[2]$	$2$	$7$	$65986.6167804$
12.4.449...576.3	$x^{12} - 3 x^{11} + 2 x^{10} - 13 x^{9} + 19 x^{8} + 40 x^{7} - 108 x^{6} - 40 x^{5} + 240 x^{4} + 64 x^{3} - 32 x^{2} - 48 x - 16$	$12$	[4,4]	$2^{17}\cdot 17^{11}$	$2$	$35.8402204073$	$85.24289022322928$				$S_4^2:D_4$ (as 12T260)	$[2]$	$2$	$7$	$187300.206044$
12.0.449...576.3	$x^{12} + 17 x^{10} + 119 x^{8} + 459 x^{6} + 952 x^{4} + 1020 x^{2} + 136$	$12$	[0,6]	$2^{17}\cdot 17^{11}$	$2$	$35.8402204073$	$69.63983780733449$			?	$S_4^2:C_4$ (as 12T238)	$[2]$	$2$	$5$	$28881.2210464$
12.4.449...576.4	$x^{12} - 4 x^{11} + 13 x^{10} - 22 x^{9} - 9 x^{8} - 36 x^{7} + 116 x^{6} - 174 x^{5} + 134 x^{4} - 176 x^{3} + 106 x^{2} + 8 x - 4$	$12$	[4,4]	$2^{17}\cdot 17^{11}$	$2$	$35.8402204073$	$65.73125404566245$			?	$S_4^2:D_4$ (as 12T260)	$[2]$	$2$	$7$	$86961.9671975$
12.0.449...576.4	$x^{12} - 2 x^{11} - x^{10} + 10 x^{9} + 43 x^{8} - 152 x^{7} + 294 x^{6} - 348 x^{5} + 712 x^{4} - 768 x^{3} + 868 x^{2} - 288 x + 752$	$12$	[0,6]	$2^{17}\cdot 17^{11}$	$2$	$35.8402204073$	$60.275825724785875$				$D_6\wr C_2$ (as 12T125)	$[2]$	$2$	$5$	$30270.5942168$
12.4.449...576.5	$x^{12} - 17 x^{10} + 85 x^{8} - 85 x^{6} - 136 x^{4} + 102 x^{2} + 34$	$12$	[4,4]	$2^{17}\cdot 17^{11}$	$2$	$35.8402204073$	$65.73125404566245$				$S_4^2:D_4$ (as 12T260)	$[2]$	$2$	$7$	$188428.575509$
12.0.449...576.5	$x^{12} - 4 x^{11} + 13 x^{10} - 22 x^{9} - 9 x^{8} + 66 x^{7} - 20 x^{6} - 106 x^{5} + 253 x^{4} - 176 x^{3} + 106 x^{2} - 264 x + 234$	$12$	[0,6]	$2^{17}\cdot 17^{11}$	$2$	$35.8402204073$	$69.63983780733449$			?	$S_4^2:C_4$ (as 12T238)	$[2, 2]$	$2$	$5$	$22408.4289326$
12.4.449...576.6	$x^{12} - 17 x^{10} + 170 x^{8} - 969 x^{6} + 2788 x^{4} - 3162 x^{2} + 136$	$12$	[4,4]	$2^{17}\cdot 17^{11}$	$2$	$35.8402204073$				?	$S_4^2:C_4$ (as 12T238)	$[2]$	$2$	$7$	$73222.1861898$
12.4.449...576.7	$x^{12} - 17 x^{10} + 119 x^{8} - 459 x^{6} + 952 x^{4} - 1020 x^{2} + 136$	$12$	[4,4]	$2^{17}\cdot 17^{11}$	$2$	$35.8402204073$	$69.63983780733449$			?	$S_4^2:C_4$ (as 12T238)	$[2]$	$2$	$7$	$71140.579375$
12.4.449...576.8	$x^{12} + 34 x^{8} - 136 x^{6} - 51 x^{4} + 272 x^{2} + 136$	$12$	[4,4]	$2^{17}\cdot 17^{11}$	$2$	$35.8402204073$	$118.8233263691419$				$S_4^2:D_4$ (as 12T260)	$[2]$	$2$	$7$	$204871.710251$
12.4.449...576.9	$x^{12} - 17 x^{10} + 119 x^{8} - 442 x^{6} + 935 x^{4} - 1088 x^{2} + 544$	$12$	[4,4]	$2^{17}\cdot 17^{11}$	$2$	$35.8402204073$				?	$S_4^2:C_4$ (as 12T238)	$[2]$	$2$	$7$	$71461.2964582$
12.4.449...576.10	$x^{12} - 17 x^{10} + 85 x^{8} - 306 x^{6} + 748 x^{4} - 1003 x^{2} + 544$	$12$	[4,4]	$2^{17}\cdot 17^{11}$	$2$	$35.8402204073$	$53.69965587306223$			?	$S_3^2:C_4$ (as 12T80)	$[2]$	$2$	$7$	$131794.878234$
12.4.449...576.11	$x^{12} + 17 x^{10} + 51 x^{8} - 221 x^{6} - 408 x^{4} + 204 x^{2} + 544$	$12$	[4,4]	$2^{17}\cdot 17^{11}$	$2$	$35.8402204073$	$65.73125404566245$				$S_4^2:D_4$ (as 12T260)	$[2]$	$2$	$7$	$126704.356288$
12.0.133...625.1	$x^{12} - 6 x^{11} + 25 x^{10} - 70 x^{9} + 151 x^{8} - 250 x^{7} + 347 x^{6} - 394 x^{5} + 393 x^{4} - 314 x^{3} + 212 x^{2} - 95 x + 33$	$12$	[0,6]	$5^{8}\cdot 17^{11}$	$2$	$39.254686577190164$	$39.254686577190164$			?	$A_5:C_4$ (as 12T124)	$[4]$	$2$	$5$	$27801.4421457893$
12.6.179...304.1	$x^{12} - 6 x^{11} - 9 x^{10} + 66 x^{9} + 100 x^{8} - 250 x^{7} - 520 x^{6} + 218 x^{5} + 733 x^{4} - 620 x^{3} - 2015 x^{2} - 1472 x - 358$	$12$	[6,3]	$-\,2^{19}\cdot 17^{11}$	$2$	$40.2292872102$	$65.73125404566245$				$S_4^2:C_4$ (as 12T238)	$[2]$	$2$	$8$	$389304.384241$
12.2.179...304.1	$x^{12} - 34 x^{8} - 153 x^{6} - 561 x^{4} - 1071 x^{2} - 2176$	$12$	[2,5]	$-\,2^{19}\cdot 17^{11}$	$2$	$40.2292872102$	$102.84593327285764$			?	$S_4^2:D_4$ (as 12T260)	$[2]$	$2$	$6$	$111433.616757$

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