## Results (1-50 of 112 matches)

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Label Polynomial Discriminant Galois group Class group
12.12.46769161084392848.1 $x^{12} - 5 x^{11} - 6 x^{10} + 56 x^{9} - 30 x^{8} - 162 x^{7} + 157 x^{6} + 158 x^{5} - 176 x^{4} - 66 x^{3} + 64 x^{2} + 12 x - 4$ $2^{4}\cdot 17^{9}\cdot 157^{2}$ $C_3\wr C_4$ (as 12T131) trivial
12.12.54191813450093072.1 $x^{12} - 3 x^{11} - 12 x^{10} + 47 x^{9} - x^{8} - 134 x^{7} + 102 x^{6} + 88 x^{5} - 118 x^{4} + 18 x^{3} + 21 x^{2} - 9 x + 1$ $2^{4}\cdot 13^{4}\cdot 17^{9}$ $C_3^2:C_{12}$ (as 12T73) trivial
12.12.683...097.1 $x^{12} - x^{11} - 28 x^{10} + 31 x^{9} + 232 x^{8} - 249 x^{7} - 742 x^{6} + 716 x^{5} + 925 x^{4} - 785 x^{3} - 388 x^{2} + 288 x + 13$ $7^{8}\cdot 17^{9}$ $C_{12}$ (as 12T1) trivial
12.12.308...577.1 $x^{12} - x^{11} - 29 x^{10} + 20 x^{9} + 283 x^{8} - 117 x^{7} - 1027 x^{6} + 249 x^{5} + 1081 x^{4} - 241 x^{3} - 279 x^{2} + 120 x - 13$ $17^{9}\cdot 127^{4}$ $C_3\times (C_3 : C_4)$ (as 12T19) trivial
12.12.967...337.1 $x^{12} - x^{11} - 36 x^{10} + 27 x^{9} + 394 x^{8} - 223 x^{7} - 1578 x^{6} + 448 x^{5} + 2307 x^{4} + 161 x^{3} - 806 x^{2} - 130 x + 13$ $13^{8}\cdot 17^{9}$ $C_{12}$ (as 12T1) trivial
12.12.201...377.1 $x^{12} - x^{11} - 44 x^{10} + 63 x^{9} + 574 x^{8} - 851 x^{7} - 2964 x^{6} + 4032 x^{5} + 6247 x^{4} - 6815 x^{3} - 4744 x^{2} + 2450 x + 1291$ $17^{9}\cdot 19^{8}$ $C_{12}$ (as 12T1) trivial
12.0.280...312.1 $x^{12} - 4 x^{11} + 49 x^{10} - 146 x^{9} + 1077 x^{8} - 2500 x^{7} + 13557 x^{6} - 23654 x^{5} + 102443 x^{4} - 124444 x^{3} + 459241 x^{2} - 307164 x + 924937$ $2^{12}\cdot 7^{8}\cdot 17^{9}$ $C_{12}$ (as 12T1) $[2, 482]$
12.2.962...904.1 $x^{12} - 4 x^{11} + 5 x^{10} - 16 x^{9} + 139 x^{8} - 620 x^{7} + 9067 x^{6} + 12152 x^{5} + 29456 x^{4} + 238584 x^{3} - 142428 x^{2} - 88432 x - 936752$ $-\,2^{15}\cdot 17^{9}\cdot 19^{5}$ $D_{12}$ (as 12T12) $[2]$
12.12.145...792.1 $x^{12} - 2 x^{11} - 40 x^{10} + 72 x^{9} + 482 x^{8} - 782 x^{7} - 1792 x^{6} + 2008 x^{5} + 2704 x^{4} - 1192 x^{3} - 1376 x^{2} + 184 x + 208$ $2^{10}\cdot 13^{2}\cdot 17^{9}\cdot 29^{4}$ $A_5^2:C_4$ (as 12T278) $[2]$
12.12.163...953.1 $x^{12} - x^{11} - 75 x^{10} + 58 x^{9} + 1982 x^{8} - 987 x^{7} - 22024 x^{6} + 6367 x^{5} + 89299 x^{4} - 25629 x^{3} - 66876 x^{2} - 18568 x - 883$ $13^{10}\cdot 17^{9}$ $C_{12}$ (as 12T1) $[2]$
12.12.244...937.1 $x^{12} - x^{11} - 100 x^{10} + 96 x^{9} + 3746 x^{8} - 3362 x^{7} - 65339 x^{6} + 51584 x^{5} + 525352 x^{4} - 322117 x^{3} - 1551355 x^{2} + 579413 x + 104959$ $3^{6}\cdot 7^{10}\cdot 17^{9}$ $C_{12}$ (as 12T1) $[2]$
12.12.411...928.1 $x^{12} - 45 x^{10} - 30 x^{9} + 702 x^{8} + 936 x^{7} - 4035 x^{6} - 8694 x^{5} + 2385 x^{4} + 20528 x^{3} + 21816 x^{2} + 9696 x + 1616$ $2^{6}\cdot 3^{12}\cdot 17^{9}\cdot 101^{2}$ $C_3^2\wr C_2.D_4$ (as 12T211) trivial
12.2.990...088.1 $x^{12} - 4 x^{11} + 16 x^{10} - 38 x^{9} - 47 x^{8} - 450 x^{7} + 3162 x^{6} - 4200 x^{5} + 8768 x^{4} - 11648 x^{3} + 6272 x^{2} - 2560 x - 4096$ $-\,2^{10}\cdot 13^{8}\cdot 17^{9}$ $D_{12}$ (as 12T12) $[6]$
12.12.101...177.1 $x^{12} - x^{11} - 60 x^{10} + 75 x^{9} + 1123 x^{8} - 1414 x^{7} - 8469 x^{6} + 9673 x^{5} + 24708 x^{4} - 23467 x^{3} - 16187 x^{2} + 15038 x - 2636$ $17^{9}\cdot 31^{8}$ $C_{12}$ (as 12T1) trivial
12.0.179...968.1 $x^{12} - 4 x^{11} + 100 x^{10} - 316 x^{9} + 4307 x^{8} - 10660 x^{7} + 101974 x^{6} - 189064 x^{5} + 1400852 x^{4} - 1767732 x^{3} + 10735044 x^{2} - 7114100 x + 35851369$ $2^{18}\cdot 7^{8}\cdot 17^{9}$ $C_{12}$ (as 12T1) $[2, 1082]$
12.12.179...968.1 $x^{12} - 4 x^{11} - 104 x^{10} + 364 x^{9} + 4239 x^{8} - 12292 x^{7} - 86658 x^{6} + 191056 x^{5} + 934304 x^{4} - 1352932 x^{3} - 4997300 x^{2} + 3448884 x + 10118401$ $2^{18}\cdot 7^{8}\cdot 17^{9}$ $C_{12}$ (as 12T1) $[2]$
12.0.396...352.1 $x^{12} - 4 x^{11} + 41 x^{10} - 130 x^{9} + 945 x^{8} - 2044 x^{7} + 12317 x^{6} - 19586 x^{5} + 105551 x^{4} - 77288 x^{3} + 634081 x^{2} - 13652 x + 1704149$ $2^{12}\cdot 13^{8}\cdot 17^{9}$ $C_{12}$ (as 12T1) $[6, 222]$
12.0.396...352.2 $x^{12} - 2 x^{11} - 30 x^{10} - 26 x^{9} + 761 x^{8} - 336 x^{7} - 1632 x^{6} + 4656 x^{5} + 1424 x^{4} - 5824 x^{3} + 11904 x^{2} + 5120 x + 4096$ $2^{12}\cdot 13^{8}\cdot 17^{9}$ $D_{12}$ (as 12T12) $[3, 24]$
12.12.416...737.1 $x^{12} - x^{11} - 68 x^{10} + 3 x^{9} + 1528 x^{8} + 1135 x^{7} - 12600 x^{6} - 17100 x^{5} + 25453 x^{4} + 41563 x^{3} - 10018 x^{2} - 22360 x - 2789$ $17^{9}\cdot 37^{8}$ $C_{12}$ (as 12T1) trivial
12.0.523...625.1 $x^{12} - x^{11} + 138 x^{10} - 142 x^{9} + 7554 x^{8} - 8122 x^{7} + 212169 x^{6} - 183798 x^{5} + 3278536 x^{4} - 1074435 x^{3} + 27959931 x^{2} + 6161227 x + 136845241$ $5^{6}\cdot 7^{10}\cdot 17^{9}$ $C_{12}$ (as 12T1) $[2, 8066]$
12.0.727...097.1 $x^{12} - x^{11} + 52 x^{10} + 112 x^{9} + 1234 x^{8} + 1884 x^{7} - 6287 x^{6} - 70 x^{5} + 136036 x^{4} - 166513 x^{3} + 131837 x^{2} - 272169 x + 1944923$ $17^{9}\cdot 19^{10}$ $C_{12}$ (as 12T1) $[10, 130]$
12.12.138...697.1 $x^{12} - x^{11} - 76 x^{10} + 19 x^{9} + 1915 x^{8} + 834 x^{7} - 18925 x^{6} - 17455 x^{5} + 60172 x^{4} + 61645 x^{3} - 50203 x^{2} - 64242 x - 12836$ $17^{9}\cdot 43^{8}$ $C_{12}$ (as 12T1) trivial
12.0.146...408.1 $x^{12} - 4 x^{11} + 34 x^{10} - 192 x^{9} + 2255 x^{8} - 8416 x^{7} + 20394 x^{6} - 2272 x^{5} + 143792 x^{4} - 271424 x^{3} + 129376 x^{2} + 327680 x + 1048576$ $2^{18}\cdot 17^{9}\cdot 19^{6}$ $D_{12}$ (as 12T12) $[4, 8]$
12.12.329...473.1 $x^{12} - x^{11} - 181 x^{10} + 235 x^{9} + 12574 x^{8} - 17946 x^{7} - 425827 x^{6} + 594152 x^{5} + 7336816 x^{4} - 8706536 x^{3} - 60135100 x^{2} + 44656755 x + 183393769$ $7^{8}\cdot 13^{6}\cdot 17^{9}$ $C_{12}$ (as 12T1) $[2]$
12.0.778...625.1 $x^{12} - x^{11} + 176 x^{10} - 241 x^{9} + 13764 x^{8} - 20921 x^{7} + 610782 x^{6} - 868596 x^{5} + 16022269 x^{4} - 17677113 x^{3} + 231278288 x^{2} - 141901568 x + 1423267621$ $3^{6}\cdot 5^{6}\cdot 7^{8}\cdot 17^{9}$ $C_{12}$ (as 12T1) $[2, 7466]$
12.0.824...192.1 $x^{12} - 4 x^{11} + 33 x^{10} - 74 x^{9} + 741 x^{8} - 2188 x^{7} + 12781 x^{6} - 23894 x^{5} + 116843 x^{4} - 253700 x^{3} + 1179577 x^{2} - 1888296 x + 3771709$ $2^{12}\cdot 17^{9}\cdot 19^{8}$ $C_{12}$ (as 12T1) $[6, 654]$
12.12.227...657.1 $x^{12} - x^{11} - 100 x^{10} + 99 x^{9} + 3340 x^{8} - 2877 x^{7} - 46644 x^{6} + 33812 x^{5} + 266073 x^{4} - 180321 x^{3} - 517506 x^{2} + 369428 x + 16999$ $17^{9}\cdot 61^{8}$ $C_{12}$ (as 12T1) trivial
12.12.253...528.1 $x^{12} - 4 x^{11} - 112 x^{10} + 380 x^{9} + 4719 x^{8} - 13468 x^{7} - 92386 x^{6} + 222256 x^{5} + 848264 x^{4} - 1642580 x^{3} - 3278996 x^{2} + 3844396 x + 4689281$ $2^{18}\cdot 13^{8}\cdot 17^{9}$ $C_{12}$ (as 12T1) $[2]$
12.0.253...528.1 $x^{12} - 4 x^{11} + 92 x^{10} - 300 x^{9} + 3971 x^{8} - 9660 x^{7} + 97334 x^{6} - 167928 x^{5} + 1444284 x^{4} - 1443204 x^{3} + 12846660 x^{2} - 4211292 x + 52322057$ $2^{18}\cdot 13^{8}\cdot 17^{9}$ $C_{12}$ (as 12T1) $[26, 338]$
12.12.294...937.1 $x^{12} - 3 x^{11} - 99 x^{10} + 136 x^{9} + 3552 x^{8} - 84 x^{7} - 54369 x^{6} - 53109 x^{5} + 303915 x^{4} + 504060 x^{3} - 257076 x^{2} - 788400 x - 333136$ $3^{16}\cdot 7^{8}\cdot 17^{9}$ $C_{12}$ (as 12T1) $[3]$
12.12.294...937.2 $x^{12} - 3 x^{11} - 99 x^{10} + 108 x^{9} + 3615 x^{8} + 1617 x^{7} - 55041 x^{6} - 87213 x^{5} + 268551 x^{4} + 688433 x^{3} + 130815 x^{2} - 469788 x - 108289$ $3^{16}\cdot 7^{8}\cdot 17^{9}$ $C_{12}$ (as 12T1) $[3]$
12.0.321...457.1 $x^{12} - x^{11} + 227 x^{10} - 309 x^{9} + 22502 x^{8} - 33994 x^{7} + 1245613 x^{6} - 1770344 x^{5} + 40287440 x^{4} - 44781080 x^{3} + 712437652 x^{2} - 444508317 x + 5341899473$ $7^{8}\cdot 17^{9}\cdot 19^{6}$ $C_{12}$ (as 12T1) $[2, 19058]$
12.12.481...577.1 $x^{12} - x^{11} - 108 x^{10} + 47 x^{9} + 3970 x^{8} + 593 x^{7} - 60752 x^{6} - 35744 x^{5} + 357779 x^{4} + 243701 x^{3} - 684328 x^{2} - 409666 x + 55127$ $17^{9}\cdot 67^{8}$ $C_{12}$ (as 12T1) trivial
12.12.593...433.1 $x^{12} - x^{11} - 338 x^{10} + 334 x^{9} + 43730 x^{8} - 42394 x^{7} - 2726655 x^{6} + 2288070 x^{5} + 83876760 x^{4} - 44603207 x^{3} - 1136572641 x^{2} + 122837871 x + 4028583637$ $7^{10}\cdot 11^{6}\cdot 17^{9}$ $C_{12}$ (as 12T1) $[2]$
12.0.669...488.1 $x^{12} + 221 x^{10} + 15470 x^{8} + 409513 x^{6} + 4884100 x^{4} + 26569504 x^{2} + 53139008$ $2^{12}\cdot 13^{10}\cdot 17^{9}$ $C_{12}$ (as 12T1) $[2, 2, 2, 2308]$
12.0.100...952.1 $x^{12} + 357 x^{10} + 49266 x^{8} + 3331881 x^{6} + 114704100 x^{4} + 1871970912 x^{2} + 11231825472$ $2^{12}\cdot 3^{6}\cdot 7^{10}\cdot 17^{9}$ $C_{12}$ (as 12T1) $[2, 2, 4, 4996]$
12.12.154...581.1 $x^{12} - x^{11} - 194 x^{10} + 194 x^{9} + 12403 x^{8} - 13703 x^{7} - 305057 x^{6} + 332682 x^{5} + 2890746 x^{4} - 2743521 x^{3} - 8936524 x^{2} + 4919524 x + 8816575$ $3^{6}\cdot 13^{11}\cdot 17^{9}$ $C_{12}$ (as 12T1) $[2, 4]$
12.12.154...581.2 $x^{12} - x^{11} - 194 x^{10} + 194 x^{9} + 12403 x^{8} - 5747 x^{7} - 328925 x^{6} - 140700 x^{5} + 3663804 x^{4} + 4850481 x^{3} - 11223874 x^{2} - 24361208 x - 11400947$ $3^{6}\cdot 13^{11}\cdot 17^{9}$ $C_{12}$ (as 12T1) $[2, 4]$
12.2.426...688.1 $x^{12} - 4 x^{11} - 42 x^{10} + 244 x^{9} + 358 x^{8} - 4976 x^{7} + 3556 x^{6} + 61336 x^{5} - 169959 x^{4} + 17108 x^{3} + 437158 x^{2} - 492972 x + 440928$ $-\,2^{10}\cdot 17^{9}\cdot 37^{8}$ $D_{12}$ (as 12T12) $[2, 78]$
12.0.256...753.1 $x^{12} - x^{11} + 118 x^{10} + 358 x^{9} + 11849 x^{8} + 29743 x^{7} + 302976 x^{6} + 208604 x^{5} + 6247104 x^{4} + 1390928 x^{3} + 56729344 x^{2} - 7913664 x + 183584512$ $17^{9}\cdot 43^{10}$ $C_{12}$ (as 12T1) $[2, 429106]$
12.12.297...312.1 $x^{12} - 323 x^{10} + 30362 x^{8} - 862087 x^{6} + 10432900 x^{4} - 56754976 x^{2} + 113509952$ $2^{12}\cdot 17^{9}\cdot 19^{10}$ $C_{12}$ (as 12T1) $[2, 2]$
12.12.640...928.1 $x^{12} - 714 x^{10} + 197064 x^{8} - 26655048 x^{6} + 1835265600 x^{4} - 59903069184 x^{2} + 718836830208$ $2^{18}\cdot 3^{6}\cdot 7^{10}\cdot 17^{9}$ $C_{12}$ (as 12T1) $[2, 2, 4]$
12.0.640...928.1 $x^{12} + 714 x^{10} + 197064 x^{8} + 26655048 x^{6} + 1835265600 x^{4} + 59903069184 x^{2} + 718836830208$ $2^{18}\cdot 3^{6}\cdot 7^{10}\cdot 17^{9}$ $C_{12}$ (as 12T1) $[2, 2, 2, 134660]$
12.12.802...857.2 $x^{12} - x^{11} - 188 x^{10} - 213 x^{9} + 12715 x^{8} + 39298 x^{7} - 324717 x^{6} - 1733319 x^{5} + 680764 x^{4} + 20357101 x^{3} + 48082157 x^{2} + 40734254 x + 8274052$ $17^{9}\cdot 127^{8}$ $C_{12}$ (as 12T1) $[3]$
12.12.129...217.1 $x^{12} - 273 x^{10} - 266 x^{9} + 22995 x^{8} + 26796 x^{7} - 759367 x^{6} - 1041642 x^{5} + 10115364 x^{4} + 13933640 x^{3} - 50535072 x^{2} - 52157952 x + 75464704$ $3^{18}\cdot 7^{10}\cdot 17^{9}$ $C_{12}$ (as 12T1) $[6]$
12.12.129...217.2 $x^{12} - 273 x^{10} - 203 x^{9} + 22995 x^{8} + 16842 x^{7} - 733096 x^{6} - 283563 x^{5} + 8467347 x^{4} - 1448881 x^{3} - 20439468 x^{2} + 18954180 x - 4504472$ $3^{18}\cdot 7^{10}\cdot 17^{9}$ $C_{12}$ (as 12T1) $[6]$
12.0.120...952.1 $x^{12} - 33 x^{10} - 112 x^{9} + 1575 x^{8} + 7056 x^{7} - 3355 x^{6} - 165312 x^{5} - 167664 x^{4} + 2470720 x^{3} + 17419956 x^{2} + 42136416 x + 63660176$ $2^{12}\cdot 3^{16}\cdot 7^{8}\cdot 17^{9}$ $C_{12}$ (as 12T1) $[2, 2, 2, 2, 2, 2886]$
12.0.120...952.2 $x^{12} - 33 x^{10} - 140 x^{9} + 1575 x^{8} + 8820 x^{7} - 709 x^{6} - 206640 x^{5} - 346269 x^{4} + 3026660 x^{3} + 21758073 x^{2} + 55541430 x + 71323433$ $2^{12}\cdot 3^{16}\cdot 7^{8}\cdot 17^{9}$ $C_{12}$ (as 12T1) $[22, 4818]$
12.0.634...776.1 $x^{12} + 663 x^{10} + 145197 x^{8} + 12578436 x^{6} + 376744446 x^{4} + 3398916573 x^{2} + 1164012525$ $2^{12}\cdot 3^{6}\cdot 13^{11}\cdot 17^{9}$ $C_{12}$ (as 12T1) $[2, 2, 2, 45860]$
12.0.634...776.2 $x^{12} + 663 x^{10} + 145197 x^{8} + 13389948 x^{6} + 488733102 x^{4} + 4143884589 x^{2} + 1164012525$ $2^{12}\cdot 3^{6}\cdot 13^{11}\cdot 17^{9}$ $C_{12}$ (as 12T1) $[2, 2, 2, 992324]$
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