## Results (1-50 of at least 1000)

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Label Polynomial Discriminant Galois group Class group
12.0.45399026464443729.1 $x^{12} - 6 x^{11} + 11 x^{10} - 66 x^{8} + 198 x^{7} - 231 x^{6} + 66 x^{5} + 770 x^{4} - 1452 x^{3} + 2332 x^{2} - 1623 x + 1147$ $3^{6}\cdot 7^{4}\cdot 11^{10}$ $C_6\times S_3$ (as 12T18) trivial
12.0.696...056.20 $x^{12} + 6 x^{10} + 59 x^{8} - 132 x^{7} + 394 x^{6} - 660 x^{5} + 1203 x^{4} - 1716 x^{3} + 1216 x^{2} - 440 x + 100$ $2^{28}\cdot 11^{10}$ $S_3^2:C_2^2$ (as 12T77) trivial
12.0.100...889.1 $x^{12} - 11 x^{6} + 121$ $3^{18}\cdot 11^{10}$ $C_6\times S_3$ (as 12T18) trivial
12.0.116...624.1 $x^{12} - x^{11} - 36 x^{10} - 3 x^{9} + 548 x^{8} + 583 x^{7} - 3701 x^{6} - 7854 x^{5} + 5604 x^{4} + 35190 x^{3} + 53928 x^{2} + 48060 x + 21708$ $2^{8}\cdot 3^{6}\cdot 7^{4}\cdot 11^{10}$ $C_3\times S_3^2$ (as 12T70) $[3, 3]$
12.0.109...329.1 $x^{12} - 2 x^{11} + 17 x^{10} + x^{9} + 72 x^{8} - 49 x^{7} + 564 x^{6} - 1026 x^{5} - 92 x^{4} - 1371 x^{3} + 7787 x^{2} - 7768 x + 2293$ $3^{6}\cdot 7^{8}\cdot 11^{10}$ $C_6\times S_3$ (as 12T18) $[18]$
12.8.111...896.1 $x^{12} - 4 x^{11} - 4 x^{10} + 28 x^{9} - 83 x^{8} + 440 x^{7} - 768 x^{6} - 792 x^{5} + 3565 x^{4} - 4012 x^{3} + 2492 x^{2} - 876 x + 113$ $2^{32}\cdot 11^{10}$ $S_3^2:C_2^2$ (as 12T77) trivial
12.4.111...896.8 $x^{12} - 22 x^{8} + 132 x^{6} + 121 x^{4} - 1452 x^{2} + 484$ $2^{32}\cdot 11^{10}$ $S_4^2:C_2^2$ (as 12T236) trivial
12.0.185...984.1 $x^{12} + 22 x^{10} + 297 x^{8} + 1947 x^{6} + 8228 x^{4} + 605 x^{2} + 121$ $2^{12}\cdot 3^{6}\cdot 7^{4}\cdot 11^{10}$ $C_6\times S_3$ (as 12T18) $[2]$
12.2.222...792.7 $x^{12} - 16 x^{10} + 202 x^{8} - 88 x^{7} - 1432 x^{6} + 528 x^{5} + 5383 x^{4} - 2112 x^{3} - 8772 x^{2} + 7128 x - 2386$ $-\,2^{33}\cdot 11^{10}$ $S_3^2:C_2^2$ (as 12T78) trivial
12.4.445...584.10 $x^{12} - 22 x^{10} + 143 x^{8} - 308 x^{6} - 121 x^{4} + 1210 x^{2} + 121$ $2^{34}\cdot 11^{10}$ $S_4^2:C_2^2$ (as 12T236) trivial
12.4.445...584.13 $x^{12} - 22 x^{8} - 132 x^{6} + 121 x^{4} + 1452 x^{2} + 484$ $2^{34}\cdot 11^{10}$ $S_4^2:C_2^2$ (as 12T236) trivial
12.4.445...584.16 $x^{12} + 22 x^{10} + 121 x^{8} - 264 x^{6} - 2904 x^{4} + 1936$ $2^{34}\cdot 11^{10}$ $S_4^2:C_2^2$ (as 12T236) trivial
12.0.709...625.1 $x^{12} - 2 x^{11} - 22 x^{10} + 132 x^{9} + 682 x^{8} - 583 x^{7} - 5346 x^{6} + 8910 x^{5} + 101024 x^{4} + 282106 x^{3} + 410091 x^{2} + 319097 x + 105571$ $3^{6}\cdot 5^{6}\cdot 7^{4}\cdot 11^{10}$ $C_6\times S_3$ (as 12T18) $[4]$
12.0.813...009.1 $x^{12} + 33 x^{6} + 1089$ $3^{22}\cdot 11^{10}$ $C_6\times S_3$ (as 12T18) $[3]$
12.0.813...009.2 $x^{12} - 99 x^{6} + 9801$ $3^{22}\cdot 11^{10}$ $C_6\times S_3$ (as 12T18) trivial
12.6.891...168.1 $x^{12} - 4 x^{11} + 6 x^{10} - 20 x^{9} - 21 x^{8} + 80 x^{7} - 392 x^{6} + 128 x^{5} + 1653 x^{4} + 652 x^{3} - 1090 x^{2} + 268 x - 17$ $-\,2^{35}\cdot 11^{10}$ $S_3^2:C_2^2$ (as 12T78) trivial
12.4.178...336.10 $x^{12} + 22 x^{10} + 143 x^{8} + 308 x^{6} - 121 x^{4} - 1210 x^{2} + 121$ $2^{36}\cdot 11^{10}$ $S_4^2:C_2^2$ (as 12T236) trivial
12.4.178...336.16 $x^{12} - 22 x^{10} + 121 x^{8} + 264 x^{6} - 2904 x^{4} + 1936$ $2^{36}\cdot 11^{10}$ $S_4^2:C_2^2$ (as 12T236) trivial
12.0.257...584.1 $x^{12} - 44 x^{6} + 1936$ $2^{8}\cdot 3^{18}\cdot 11^{10}$ $C_6\times S_3$ (as 12T18) $[3, 3, 3]$
12.0.257...584.2 $x^{12} - 176 x^{6} + 30976$ $2^{8}\cdot 3^{18}\cdot 11^{10}$ $C_6\times S_3$ (as 12T18) $[3, 3]$
12.6.356...672.1 $x^{12} - 352 x^{6} - 242 x^{4} + 5808 x^{2} - 3872$ $-\,2^{37}\cdot 11^{10}$ $S_4^2:C_2^2$ (as 12T235) trivial
12.6.356...672.2 $x^{12} - 44 x^{8} - 352 x^{6} + 484 x^{4} + 7744 x^{2} - 3872$ $-\,2^{37}\cdot 11^{10}$ $S_4^2:C_2^2$ (as 12T235) trivial
12.2.356...672.7 $x^{12} - 44 x^{8} + 352 x^{6} + 484 x^{4} - 7744 x^{2} - 3872$ $-\,2^{37}\cdot 11^{10}$ $S_4^2:C_2^2$ (as 12T235) trivial
12.2.356...672.12 $x^{12} + 22 x^{10} + 121 x^{8} + 176 x^{6} + 968 x^{4} - 5808 x^{2} - 968$ $-\,2^{37}\cdot 11^{10}$ $S_4^2:C_2^2$ (as 12T235) trivial
12.2.356...672.19 $x^{12} + 22 x^{10} + 209 x^{8} + 1056 x^{6} + 2662 x^{4} + 2420 x^{2} - 242$ $-\,2^{37}\cdot 11^{10}$ $S_4^2:C_2^2$ (as 12T235) $[3]$
12.2.356...672.36 $x^{12} - 2 x^{11} - 37 x^{10} + 80 x^{9} + 526 x^{8} - 1576 x^{7} - 2180 x^{6} + 14048 x^{5} - 19260 x^{4} + 5000 x^{3} + 4212 x^{2} + 3456 x + 3128$ $-\,2^{37}\cdot 11^{10}$ $S_4^2:C_2^2$ (as 12T235) trivial
12.0.119...976.2 $x^{12} - 44 x^{10} + 1188 x^{8} - 15576 x^{6} + 131648 x^{4} - 19360 x^{2} + 7744$ $2^{18}\cdot 3^{6}\cdot 7^{4}\cdot 11^{10}$ $C_6\times S_3$ (as 12T18) $[2]$
12.0.119...976.3 $x^{12} + 44 x^{10} + 1188 x^{8} + 15576 x^{6} + 131648 x^{4} + 19360 x^{2} + 7744$ $2^{18}\cdot 3^{6}\cdot 7^{4}\cdot 11^{10}$ $C_6\times S_3$ (as 12T18) $[12]$
12.6.142...688.1 $x^{12} - 242 x^{8} - 704 x^{6} + 11616 x^{4} - 15488$ $-\,2^{39}\cdot 11^{10}$ $S_4^2:C_2^2$ (as 12T235) trivial
12.2.142...688.1 $x^{12} - 242 x^{8} + 704 x^{6} + 11616 x^{4} - 15488$ $-\,2^{39}\cdot 11^{10}$ $S_4^2:C_2^2$ (as 12T235) $[2]$
12.6.142...688.2 $x^{12} - 22 x^{10} + 121 x^{8} - 176 x^{6} + 968 x^{4} + 5808 x^{2} - 968$ $-\,2^{39}\cdot 11^{10}$ $S_4^2:C_2^2$ (as 12T235) trivial
12.2.142...688.2 $x^{12} + 352 x^{6} - 242 x^{4} - 5808 x^{2} - 3872$ $-\,2^{39}\cdot 11^{10}$ $S_4^2:C_2^2$ (as 12T235) trivial
12.6.142...688.3 $x^{12} - 198 x^{8} + 1760 x^{6} - 6292 x^{4} + 7744 x^{2} - 968$ $-\,2^{39}\cdot 11^{10}$ $S_4^2:C_2^2$ (as 12T235) trivial
12.2.142...688.3 $x^{12} - 198 x^{8} - 1760 x^{6} - 6292 x^{4} - 7744 x^{2} - 968$ $-\,2^{39}\cdot 11^{10}$ $S_4^2:C_2^2$ (as 12T235) $[2]$
12.6.142...688.4 $x^{12} - 22 x^{10} + 209 x^{8} - 1056 x^{6} + 2662 x^{4} - 2420 x^{2} - 242$ $-\,2^{39}\cdot 11^{10}$ $S_4^2:C_2^2$ (as 12T235) trivial
12.6.142...688.5 $x^{12} - 22 x^{10} + 649 x^{8} - 5720 x^{6} + 14278 x^{4} + 1452 x^{2} - 242$ $-\,2^{39}\cdot 11^{10}$ $S_4^2:C_2^2$ (as 12T235) trivial
12.0.241...489.1 $x^{12} - 1034 x^{6} + 290521$ $3^{18}\cdot 7^{4}\cdot 11^{10}$ $C_6\times S_3$ (as 12T18) $[3, 3, 3]$
12.4.285...376.1 $x^{12} + 22 x^{10} - 55 x^{8} + 836 x^{6} + 2541 x^{4} - 18150 x^{2} + 121$ $2^{40}\cdot 11^{10}$ $S_4^2:C_2^2$ (as 12T236) trivial
12.0.285...376.1 $x^{12} + 22 x^{10} + 99 x^{8} + 616 x^{6} + 11616 x^{4} + 22264 x^{2} + 484$ $2^{40}\cdot 11^{10}$ $S_4^2:C_2^2$ (as 12T236) $[6]$
12.8.285...376.1 $x^{12} - 22 x^{10} + 99 x^{8} - 616 x^{6} + 11616 x^{4} - 22264 x^{2} + 484$ $2^{40}\cdot 11^{10}$ $S_4^2:C_2^2$ (as 12T236) trivial
12.4.285...376.2 $x^{12} - 22 x^{10} - 55 x^{8} - 836 x^{6} + 2541 x^{4} + 18150 x^{2} + 121$ $2^{40}\cdot 11^{10}$ $S_4^2:C_2^2$ (as 12T236) trivial
12.4.285...376.3 $x^{12} + 44 x^{10} + 616 x^{8} + 3168 x^{6} + 1452 x^{4} - 5808 x^{2} + 1936$ $2^{40}\cdot 11^{10}$ $S_4^2:C_2^2$ (as 12T236) trivial
12.4.285...376.4 $x^{12} - 44 x^{10} + 616 x^{8} - 3168 x^{6} + 1452 x^{4} + 5808 x^{2} + 1936$ $2^{40}\cdot 11^{10}$ $S_4^2:C_2^2$ (as 12T236) trivial
12.4.285...376.5 $x^{12} + 22 x^{10} + 231 x^{8} - 1408 x^{6} - 5808 x^{4} + 7744$ $2^{40}\cdot 11^{10}$ $S_4^2:C_2^2$ (as 12T236) trivial
12.4.285...376.6 $x^{12} - 22 x^{10} + 231 x^{8} + 1408 x^{6} - 5808 x^{4} + 7744$ $2^{40}\cdot 11^{10}$ $S_4^2:C_2^2$ (as 12T236) trivial
12.0.411...344.1 $x^{12} + 11 x^{6} + 121$ $2^{12}\cdot 3^{18}\cdot 11^{10}$ $C_6\times S_3$ (as 12T18) $[2]$
12.2.570...752.1 $x^{12} - 396 x^{8} - 5764 x^{6} - 36421 x^{4} - 109868 x^{2} - 128018$ $-\,2^{41}\cdot 11^{10}$ $S_4^2:C_2^2$ (as 12T235) $[3]$
12.6.570...752.1 $x^{12} - 22 x^{10} - 77 x^{8} + 1408 x^{6} + 6534 x^{4} - 29524 x^{2} - 128018$ $-\,2^{41}\cdot 11^{10}$ $S_4^2:C_2^2$ (as 12T235) trivial
12.6.570...752.2 $x^{12} - 396 x^{8} + 5764 x^{6} - 36421 x^{4} + 109868 x^{2} - 128018$ $-\,2^{41}\cdot 11^{10}$ $S_4^2:C_2^2$ (as 12T235) trivial
12.2.570...752.2 $x^{12} + 22 x^{10} - 77 x^{8} - 1408 x^{6} + 6534 x^{4} + 29524 x^{2} - 128018$ $-\,2^{41}\cdot 11^{10}$ $S_4^2:C_2^2$ (as 12T235) trivial
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