Number field search results

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

Results (1-50 of 7190 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
12.0.295...000.1	$x^{12} - 4 x^{11} + 28 x^{10} - 76 x^{9} + 359 x^{8} - 772 x^{7} + 2662 x^{6} - 4216 x^{5} + 11540 x^{4} - 13284 x^{3} + 37260 x^{2} - 26468 x + 52681$	$12$	[0,6]	$2^{18}\cdot 5^{9}\cdot 7^{8}$	$3$	$34.6075767003$	$34.607576700316336$	✓	✓	?	$C_{12}$ (as 12T1)	$[146]$	$2$	$5$	$104.882003477$
12.0.374...000.1	$x^{12} + 33 x^{10} + 388 x^{8} + 2140 x^{6} + 5894 x^{4} + 7762 x^{2} + 3881$	$12$	[0,6]	$2^{12}\cdot 5^{6}\cdot 3881^{3}$	$3$	$35.2980658135$	$4211.514990116358$	✓		?	$S_4^2:C_2^2$ (as 12T235)	$[120]$	$2$	$5$	$144.815481876$
12.0.454...409.1	$x^{12} - x^{11} + 13 x^{10} - 23 x^{9} + 58 x^{8} - 162 x^{7} + 250 x^{6} - 399 x^{5} + 603 x^{4} - 825 x^{3} + 1227 x^{2} - 702 x + 984$	$12$	[0,6]	$3^{12}\cdot 11^{6}\cdot 13^{6}$	$3$	$35.874782229304195$	$62.13694553162394$				$C_6\times S_3$ (as 12T18)	$[140]$	$2$	$5$	$9806.65520035209$
12.0.497...449.3	$x^{12} - x^{11} + 44 x^{10} - 31 x^{9} + 691 x^{8} - 288 x^{7} + 4745 x^{6} - 300 x^{5} + 13879 x^{4} + 9649 x^{3} + 10628 x^{2} + 20959 x + 41581$	$12$	[0,6]	$3^{6}\cdot 7^{10}\cdot 17^{6}$	$3$	$36.1437703965$	$36.14377039654553$	✓	✓	?	$C_6\times C_2$ (as 12T2)	$[130]$	$2$	$5$	$140.798796005$
12.0.535...408.1	$x^{12} + 39 x^{10} + 585 x^{8} + 4212 x^{6} + 14742 x^{4} + 22113 x^{2} + 9477$	$12$	[0,6]	$2^{12}\cdot 3^{6}\cdot 13^{11}$	$3$	$36.3668229853$	$36.36682298534298$	✓	✓	?	$C_{12}$ (as 12T1)	$[2, 2, 26]$	$2$	$5$	$120.784031363$
12.0.648...969.1	$x^{12} - 4 x^{11} + 25 x^{10} - 68 x^{9} + 325 x^{8} - 686 x^{7} + 2604 x^{6} - 4075 x^{5} + 13689 x^{4} - 14393 x^{3} + 44782 x^{2} - 23610 x + 73319$	$12$	[0,6]	$13^{10}\cdot 19^{6}$	$2$	$36.954125331$	$36.95412533099223$	✓	✓	?	$C_6\times C_2$ (as 12T2)	$[117]$	$2$	$5$	$120.784031363$
12.0.748...200.1	$x^{12} + 20 x^{10} - 12 x^{9} + 171 x^{8} - 204 x^{7} + 1058 x^{6} - 1272 x^{5} + 4424 x^{4} - 4024 x^{3} + 8100 x^{2} - 5128 x + 9569$	$12$	[0,6]	$2^{18}\cdot 5^{2}\cdot 11^{2}\cdot 2113^{3}$	$4$	$37.396444739072344$	$964.2198919333701$	✓		?	$S_4^2:C_2^2$ (as 12T235)	$[2, 54]$	$2$	$5$	$248.23759908744555$
12.0.794...856.1	$x^{12} - x^{11} + 3 x^{10} - 3 x^{9} + 8 x^{8} - 10 x^{7} + 22 x^{6} - 20 x^{5} + 32 x^{4} - 24 x^{3} + 48 x^{2} - 32 x + 64$	$12$	[0,6]	$2^{10}\cdot 1409\cdot 2346271^{2}$	$3$	$37.5835045744$	$204895.73021468052$	✓			$C_2^6.S_6$ (as 12T293)	$[101]$	$2$	$5$	$12728.3565312$
12.0.882...000.4	$x^{12} - 2 x^{11} + 21 x^{10} - 32 x^{9} + 279 x^{8} - 358 x^{7} + 2390 x^{6} - 2390 x^{5} + 13837 x^{4} - 9964 x^{3} + 50382 x^{2} - 20104 x + 90481$	$12$	[0,6]	$2^{12}\cdot 5^{6}\cdot 13^{10}$	$3$	$37.9141326098$	$37.914132609839655$	✓	✓	?	$C_6\times C_2$ (as 12T2)	$[4, 4, 8]$	$2$	$5$	$120.784031363$
12.0.912...856.1	$x^{12} + x^{10} + x^{8} + 9 x^{6} + 4 x^{4} + 16 x^{2} + 64$	$12$	[0,6]	$2^{20}\cdot 3^{2}\cdot 37^{2}\cdot 163^{4}$	$4$	$38.0189125559$	$904.873312397114$	✓			$C_2^2\wr S_3$ (as 12T139)	$[126]$	$2$	$5$	$16752.8331285$
12.0.968...001.1	$x^{12} - 4 x^{11} + 23 x^{10} - 64 x^{9} + 312 x^{8} - 632 x^{7} + 2493 x^{6} - 3780 x^{5} + 13720 x^{4} - 11802 x^{3} + 50834 x^{2} - 14525 x + 89971$	$12$	[0,6]	$3^{6}\cdot 7^{10}\cdot 19^{6}$	$3$	$38.2107704489$	$38.21077044890832$	✓	✓	?	$C_6\times C_2$ (as 12T2)	$[168]$	$2$	$5$	$140.798796005$
12.0.103...637.2	$x^{12} - x^{11} + x^{10} - 27 x^{9} + 27 x^{8} - 183 x^{7} + 326 x^{6} + 649 x^{5} + 131 x^{4} - 573 x^{3} + 1782 x^{2} - 2133 x + 4941$	$12$	[0,6]	$7^{8}\cdot 13^{11}$	$2$	$38.4161141302$	$38.416114130176354$	✓	✓		$C_{12}$ (as 12T1)	$[111]$	$2$	$5$	$17569.0378451$
12.0.125...576.1	$x^{12} - 6 x^{11} + 7 x^{10} + 20 x^{9} + 15 x^{8} - 246 x^{7} + 345 x^{6} - 24 x^{5} + 680 x^{4} - 1680 x^{3} + 3992 x^{2} - 3104 x + 8416$	$12$	[0,6]	$2^{22}\cdot 7^{6}\cdot 71^{4}$	$3$	$39.04122729464601$	$89.17398723843182$	✓			$S_3 \times C_2^2$ (as 12T10)	$[2, 78]$	$2$	$5$	$2363.3126941248165$
12.0.131...000.2	$x^{12} + 55 x^{10} + 1177 x^{8} + 12263 x^{6} + 63001 x^{4} + 137703 x^{2} + 63001$	$12$	[0,6]	$2^{12}\cdot 3^{6}\cdot 5^{6}\cdot 7^{10}$	$4$	$39.2034232971$	$39.20342329707507$	✓	✓	?	$C_6\times C_2$ (as 12T2)	$[2, 52]$	$4$	$5$	$1378.58167933$
12.0.131...000.3	$x^{12} - 2 x^{11} + 19 x^{10} - 26 x^{9} + 260 x^{8} - 364 x^{7} + 2388 x^{6} - 2590 x^{5} + 14491 x^{4} - 13666 x^{3} + 62305 x^{2} - 40136 x + 118441$	$12$	[0,6]	$2^{12}\cdot 3^{6}\cdot 5^{6}\cdot 7^{10}$	$4$	$39.2034232971$	$39.20342329707507$	✓	✓	?	$C_6\times C_2$ (as 12T2)	$[2, 156]$	$2$	$5$	$140.798796005$
12.0.131...000.5	$x^{12} - 6 x^{11} + 51 x^{10} - 200 x^{9} + 978 x^{8} - 2778 x^{7} + 9197 x^{6} - 18642 x^{5} + 45309 x^{4} - 62422 x^{3} + 108054 x^{2} - 79542 x + 163549$	$12$	[0,6]	$2^{12}\cdot 3^{6}\cdot 5^{6}\cdot 7^{10}$	$4$	$39.2034232971$	$39.20342329707507$	✓	✓	?	$C_6\times C_2$ (as 12T2)	$[4, 52]$	$2$	$5$	$104.882003477$
12.0.131...000.6	$x^{12} + 35 x^{10} + 875 x^{8} + 10500 x^{6} + 91875 x^{4} + 306250 x^{2} + 765625$	$12$	[0,6]	$2^{12}\cdot 3^{6}\cdot 5^{6}\cdot 7^{10}$	$4$	$39.2034232971$	$39.20342329707507$	✓	✓	?	$C_6\times C_2$ (as 12T2)	$[2, 52]$	$6$	$5$	$2122.0586041$
12.0.131...000.7	$x^{12} + 15 x^{10} + 225 x^{8} + 3375 x^{6} + 50625 x^{4} + 759375 x^{2} + 11390625$	$12$	[0,6]	$2^{12}\cdot 3^{6}\cdot 5^{6}\cdot 7^{10}$	$4$	$39.2034232971$	$39.20342329707507$	✓	✓	?	$C_6\times C_2$ (as 12T2)	$[2, 52]$	$14$	$5$	$3031.01301368$
12.0.131...000.9	$x^{12} - 2 x^{11} - x^{10} - 2 x^{9} + 100 x^{8} - 204 x^{7} + 20 x^{6} - 390 x^{5} + 4243 x^{4} - 5206 x^{3} + 5381 x^{2} + 10088 x + 28561$	$12$	[0,6]	$2^{12}\cdot 3^{6}\cdot 5^{6}\cdot 7^{10}$	$4$	$39.2034232971$	$39.20342329707507$	✓	✓	?	$C_6\times C_2$ (as 12T2)	$[2, 52]$	$2$	$5$	$553.066702068$
12.0.131...000.10	$x^{12} - 6 x^{11} + 25 x^{10} - 70 x^{9} + 257 x^{8} - 674 x^{7} + 1805 x^{6} - 3284 x^{5} + 8459 x^{4} - 12124 x^{3} + 24313 x^{2} - 18702 x + 48721$	$12$	[0,6]	$2^{12}\cdot 3^{6}\cdot 5^{6}\cdot 7^{10}$	$4$	$39.2034232971$	$39.20342329707507$	✓	✓	?	$C_6\times C_2$ (as 12T2)	$[2, 52]$	$2$	$5$	$246.505463083$
12.0.133...625.1	$x^{12} - 4 x^{11} + 27 x^{10} - 68 x^{9} + 396 x^{8} - 934 x^{7} + 4774 x^{6} - 9889 x^{5} + 37692 x^{4} - 54863 x^{3} + 153377 x^{2} - 115667 x + 250879$	$12$	[0,6]	$5^{6}\cdot 7^{8}\cdot 23^{6}$	$3$	$39.2416819483$	$39.24168194830305$	✓	✓	?	$C_6\times C_2$ (as 12T2)	$[3, 117]$	$2$	$5$	$104.882003477$
12.0.136...896.2	$x^{12} - 6 x^{11} + 5 x^{10} + 22 x^{9} + 51 x^{8} - 246 x^{7} - 5 x^{6} - 42 x^{5} + 1413 x^{4} + 394 x^{3} + 4775 x^{2} + 2038 x + 8206$	$12$	[0,6]	$2^{12}\cdot 3^{6}\cdot 7^{6}\cdot 79^{4}$	$4$	$39.32620210364847$	$81.4616474176652$	✓			$S_3 \times C_2^2$ (as 12T10)	$[110]$	$2$	$5$	$1749.1252305329158$
12.0.141...672.1	$x^{12} - x^{11} + 3 x^{10} - x^{9} + 4 x^{8} + 10 x^{6} + 16 x^{4} - 8 x^{3} + 48 x^{2} - 32 x + 64$	$12$	[0,6]	$2^{8}\cdot 3^{2}\cdot 113\cdot 7364131^{2}$	$4$	$39.4291118055$	$125902.37696600525$	✓			$C_2^6.S_6$ (as 12T293)	$[102]$	$2$	$5$	$17136.9252865$
12.0.148...432.1	$x^{12} - x^{11} + 4 x^{10} - 3 x^{9} + 12 x^{8} - 6 x^{7} + 23 x^{6} - 12 x^{5} + 48 x^{4} - 24 x^{3} + 64 x^{2} - 32 x + 64$	$12$	[0,6]	$2^{4}\cdot 12113\cdot 8762773^{2}$	$3$	$39.6023753083$	$517169.97465374257$	✓		?	$C_2^6.S_6$ (as 12T293)	$[105]$	$2$	$5$	$4054.86971924$
12.0.151...192.1	$x^{12} - 2 x^{11} + 4 x^{10} - 5 x^{9} + 6 x^{8} - 5 x^{7} + 11 x^{6} - 10 x^{5} + 24 x^{4} - 40 x^{3} + 64 x^{2} - 64 x + 64$	$12$	[0,6]	$2^{4}\cdot 3^{2}\cdot 1549^{2}\cdot 2657\cdot 4057^{2}$	$5$	$39.6526522627$	$447625.2875028398$	✓			$C_2^6.S_6$ (as 12T293)	$[128]$	$2$	$5$	$11135.8577933$
12.0.154...888.1	$x^{12} - 2 x^{11} + 6 x^{10} - 9 x^{9} + 20 x^{8} - 25 x^{7} + 45 x^{6} - 50 x^{5} + 80 x^{4} - 72 x^{3} + 96 x^{2} - 64 x + 64$	$12$	[0,6]	$2^{4}\cdot 3^{2}\cdot 1657\cdot 8055869^{2}$	$4$	$39.7337128865$	$317661.6175509948$	✓		?	$C_2^6.S_6$ (as 12T293)	$[104]$	$2$	$5$	$4195.70224599$
12.0.169...968.1	$x^{12} - x^{11} + 4 x^{10} - 3 x^{9} + 10 x^{8} - 6 x^{7} + 23 x^{6} - 12 x^{5} + 40 x^{4} - 24 x^{3} + 64 x^{2} - 32 x + 64$	$12$	[0,6]	$2^{4}\cdot 19^{2}\cdot 10273\cdot 535229^{2}$	$4$	$40.0436489574$	$646435.5894379579$	✓			$C_2^6.S_6$ (as 12T293)	$[107]$	$2$	$5$	$5535.49045313$
12.0.172...000.2	$x^{12} - 2 x^{11} + 23 x^{10} - 42 x^{9} + 377 x^{8} - 430 x^{7} + 4372 x^{6} - 2306 x^{5} + 32791 x^{4} - 7712 x^{3} + 141770 x^{2} - 16004 x + 276121$	$12$	[0,6]	$2^{18}\cdot 3^{6}\cdot 5^{6}\cdot 7^{8}$	$4$	$40.0856856437$	$40.085685643740796$	✓	✓	?	$C_6\times C_2$ (as 12T2)	$[228]$	$2$	$5$	$104.882003477$
12.0.184...625.1	$x^{12} - 3 x^{11} + 17 x^{10} - 20 x^{9} + 125 x^{8} - 153 x^{7} + 479 x^{6} + 219 x^{5} + 1285 x^{4} + 1925 x^{3} + 3582 x^{2} + 4459 x + 4889$	$12$	[0,6]	$5^{10}\cdot 11^{3}\cdot 23^{2}\cdot 139^{3}$	$4$	$40.32102040737776$	$717.0388127560874$	✓		?	$S_4^2:C_2^2$ (as 12T235)	$[2, 54]$	$2$	$5$	$650.2654122260483$
12.0.192...976.2	$x^{12} - 6 x^{11} + 11 x^{10} + 29 x^{8} - 182 x^{7} + 293 x^{6} - 176 x^{5} + 796 x^{4} - 1544 x^{3} + 1858 x^{2} - 1080 x + 4792$	$12$	[0,6]	$2^{22}\cdot 7^{6}\cdot 79^{4}$	$3$	$40.45569897876693$	$94.06380813043877$	✓			$S_3 \times C_2^2$ (as 12T10)	$[2, 66]$	$2$	$5$	$2677.892123307377$
12.0.204...761.1	$x^{12} - 4 x^{11} + 31 x^{10} - 88 x^{9} + 480 x^{8} - 1046 x^{7} + 4500 x^{6} - 7261 x^{5} + 27052 x^{4} - 29227 x^{3} + 99169 x^{2} - 53803 x + 177113$	$12$	[0,6]	$13^{10}\cdot 23^{6}$	$2$	$40.6583776028$	$40.65837760277681$	✓	✓	?	$C_6\times C_2$ (as 12T2)	$[252]$	$2$	$5$	$120.784031363$
12.0.213...625.2	$x^{12} - 4 x^{11} + 43 x^{10} - 112 x^{9} + 748 x^{8} - 1200 x^{7} + 6649 x^{6} - 4588 x^{5} + 36700 x^{4} - 9786 x^{3} + 141674 x^{2} - 70165 x + 271181$	$12$	[0,6]	$5^{6}\cdot 7^{10}\cdot 13^{6}$	$3$	$40.8042166701$	$40.80421667009982$	✓	✓	?	$C_6\times C_2$ (as 12T2)	$[4, 4, 20]$	$2$	$5$	$104.882003477$
12.0.220...000.1	$x^{12} + 18 x^{10} - 4 x^{9} + 234 x^{8} + 36 x^{7} + 1738 x^{6} + 72 x^{5} + 8355 x^{4} + 3624 x^{3} + 40764 x^{2} + 21732 x + 70471$	$12$	[0,6]	$2^{18}\cdot 3^{16}\cdot 5^{9}$	$3$	$40.9198628762$	$40.91986287620002$	✓	✓	?	$C_{12}$ (as 12T1)	$[218]$	$2$	$5$	$201.000834787$
12.0.224...952.1	$x^{12} + 3 x^{10} + 8 x^{8} - 2 x^{7} + 18 x^{6} - 4 x^{5} + 32 x^{4} + 48 x^{2} + 64$	$12$	[0,6]	$2^{12}\cdot 2017\cdot 1647931^{2}$	$3$	$40.9806325661$	$172764.01457624164$	✓			$C_2^6.S_6$ (as 12T293)	$[144]$	$2$	$5$	$13956.5070278$
12.0.225...625.1	$x^{12} - 4 x^{11} - x^{10} + 10 x^{9} + 103 x^{8} - 172 x^{7} + 707 x^{6} - 250 x^{5} + 4471 x^{4} - 2724 x^{3} + 17649 x^{2} - 7080 x + 35495$	$12$	[0,6]	$5^{6}\cdot 11^{6}\cdot 13^{8}$	$3$	$41.0024914087$	$41.00249140869786$	✓	✓		$C_6\times C_2$ (as 12T2)	$[2, 2, 42]$	$2$	$5$	$615.54450504$
12.0.236...864.1	$x^{12} - 2 x^{11} + 39 x^{10} - 56 x^{9} + 583 x^{8} - 722 x^{7} + 4385 x^{6} - 5892 x^{5} + 17236 x^{4} - 21784 x^{3} + 42740 x^{2} - 24752 x + 26272$	$12$	[0,6]	$2^{12}\cdot 23^{6}\cdot 79^{4}$	$3$	$41.1562955629$	$85.25256594378845$	✓			$S_3 \times C_2^2$ (as 12T10)	$[2, 54]$	$4$	$5$	$33271.26880089057$
12.0.240...536.1	$x^{12} - 2 x^{11} - 7 x^{10} + 28 x^{9} + 32 x^{8} - 224 x^{7} + 760 x^{6} - 1482 x^{5} + 3225 x^{4} - 4194 x^{3} + 7551 x^{2} - 5130 x + 6291$	$12$	[0,6]	$2^{18}\cdot 3^{6}\cdot 31^{2}\cdot 107^{4}$	$4$	$41.22181998341178$	$282.14889686121404$	✓			$C_2^2\times S_4$ (as 12T48)	$[154]$	$2$	$5$	$1710.0656712556267$
12.0.244...625.1	$x^{12} - x^{11} + 34 x^{10} - 65 x^{9} + 534 x^{8} - 1104 x^{7} + 4605 x^{6} - 8677 x^{5} + 22434 x^{4} - 32854 x^{3} + 51069 x^{2} - 41724 x + 23029$	$12$	[0,6]	$3^{2}\cdot 5^{6}\cdot 19^{2}\cdot 7841^{3}$	$4$	$41.27847791367259$	$1494.8862833005057$	✓		?	$S_4^2:C_2^2$ (as 12T235)	$[2, 82]$	$2$	$5$	$227.7146795199663$
12.0.257...488.1	$x^{12} - 2 x^{11} + 3 x^{10} - 2 x^{9} + 2 x^{8} + 4 x^{7} - 6 x^{6} + 8 x^{5} + 8 x^{4} - 16 x^{3} + 48 x^{2} - 64 x + 64$	$12$	[0,6]	$2^{12}\cdot 3^{2}\cdot 313\cdot 1493447^{2}$	$4$	$41.4518453032$	$105918.71347405991$	✓			$C_2^6.S_6$ (as 12T293)	$[110]$	$2$	$5$	$35133.5231798$
12.0.263...624.1	$x^{12} - 2 x^{11} + 27 x^{10} - 42 x^{9} + 419 x^{8} - 538 x^{7} + 4136 x^{6} - 4132 x^{5} + 26950 x^{4} - 19172 x^{3} + 108501 x^{2} - 42258 x + 211303$	$12$	[0,6]	$2^{18}\cdot 3^{6}\cdot 13^{10}$	$3$	$41.5328513573$	$41.53285135730279$	✓	✓	?	$C_6\times C_2$ (as 12T2)	$[2, 182]$	$2$	$5$	$120.784031363$
12.0.263...624.7	$x^{12} + 14 x^{10} + 8 x^{8} - 888 x^{6} - 384 x^{4} + 10624 x^{2} + 40000$	$12$	[0,6]	$2^{18}\cdot 3^{6}\cdot 13^{10}$	$3$	$41.5328513573$	$41.53285135730279$	✓	✓		$C_6\times C_2$ (as 12T2)	$[104]$	$2$	$5$	$4543.27035708$
12.0.268...137.1	$x^{12} + 3 x^{10} - x^{9} + 7 x^{8} - 5 x^{7} + 17 x^{6} - 10 x^{5} + 28 x^{4} - 8 x^{3} + 48 x^{2} + 64$	$12$	[0,6]	$79^{2}\cdot 6833\cdot 793627^{2}$	$3$	$41.5998284198$	$654526.8596390832$	✓			$C_2^6.S_6$ (as 12T293)	$[141]$	$2$	$5$	$8806.66665203$
12.0.279...376.3	$x^{12} + 15 x^{10} + 169 x^{8} + 1527 x^{6} + 8625 x^{4} + 26083 x^{2} + 32761$	$12$	[0,6]	$2^{12}\cdot 7^{10}\cdot 17^{6}$	$3$	$41.7352311359$	$41.735231135947174$	✓	✓	?	$C_6\times C_2$ (as 12T2)	$[3, 60]$	$2$	$5$	$246.505463083$
12.0.286...336.1	$x^{12} + 24 x^{10} + 210 x^{8} + 800 x^{6} + 1197 x^{4} + 360 x^{2} + 9$	$12$	[0,6]	$2^{24}\cdot 3^{16}\cdot 199^{2}$	$3$	$41.81805636856457$	$244.14520686135816$	✓			$C_2^2 \times A_4$ (as 12T25)	$[3, 36]$	$2$	$5$	$2461.219139761961$
12.0.292...625.1	$x^{12} - 6 x^{11} + 45 x^{10} - 150 x^{9} + 636 x^{8} - 1230 x^{7} + 3551 x^{6} - 2436 x^{5} + 14157 x^{4} - 6522 x^{3} + 61566 x^{2} - 50892 x + 94429$	$12$	[0,6]	$3^{18}\cdot 5^{6}\cdot 13^{6}$	$3$	$41.8927201313$	$41.892720131306824$	✓	✓	?	$C_6\times C_2$ (as 12T2)	$[152]$	$2$	$5$	$201.000834787$
12.0.295...000.1	$x^{12} + 43 x^{10} + 620 x^{8} + 3832 x^{6} + 11348 x^{4} + 15632 x^{2} + 7729$	$12$	[0,6]	$2^{12}\cdot 5^{6}\cdot 59^{3}\cdot 131^{3}$	$4$	$41.93202389971155$	$752.9953120666239$	✓		?	$S_4^2:C_2^2$ (as 12T235)	$[2, 2, 44]$	$2$	$5$	$237.59694420980654$
12.0.304...169.1	$x^{12} - 4 x^{11} + 29 x^{10} - 84 x^{9} + 461 x^{8} - 976 x^{7} + 4353 x^{6} - 6772 x^{5} + 27208 x^{4} - 25046 x^{3} + 110223 x^{2} - 37447 x + 213487$	$12$	[0,6]	$3^{6}\cdot 7^{10}\cdot 23^{6}$	$3$	$42.0409878326$	$42.04098783260326$	✓	✓	?	$C_6\times C_2$ (as 12T2)	$[234]$	$2$	$5$	$140.798796005$
12.0.307...568.1	$x^{12} - x^{11} + 3 x^{10} - 2 x^{9} + 9 x^{8} - 5 x^{7} + 17 x^{6} - 10 x^{5} + 36 x^{4} - 16 x^{3} + 48 x^{2} - 32 x + 64$	$12$	[0,6]	$2^{4}\cdot 59^{2}\cdot 7297\cdot 274867^{2}$	$4$	$42.0663143708$	$546067.2664999763$	✓			$C_2^6.S_6$ (as 12T293)	$[173]$	$2$	$5$	$8745.57935457$
12.0.316...625.1	$x^{12} + 9 x^{10} - 4 x^{9} + 183 x^{8} + 36 x^{7} + 2281 x^{6} + 1200 x^{5} + 17949 x^{4} + 5580 x^{3} + 77817 x^{2} + 5118 x + 156329$	$12$	[0,6]	$3^{16}\cdot 5^{6}\cdot 19^{6}$	$3$	$42.171929867$	$42.17192986702622$	✓	✓	?	$C_6\times C_2$ (as 12T2)	$[2, 2, 2, 2, 12]$	$2$	$5$	$201.000834787$
12.0.331...416.1	$x^{12} - x^{11} + 4 x^{10} - 5 x^{9} + 10 x^{8} - 16 x^{7} + 23 x^{6} - 32 x^{5} + 40 x^{4} - 40 x^{3} + 64 x^{2} - 32 x + 64$	$12$	[0,6]	$2^{6}\cdot 3^{2}\cdot 569\cdot 10050083^{2}$	$4$	$42.3307702109$	$370464.4833826854$	✓			$C_2^6.S_6$ (as 12T293)	$[120]$	$2$	$5$	$9386.37666609$