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Label Polynomial Discriminant Galois group Class group Regulator
20.0.328...569.1 $x^{20} - x^{19} + x^{17} - x^{16} + x^{14} - x^{13} + x^{11} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1$ $3^{10}\cdot 11^{18}$ $C_2\times C_{10}$ (as 20T3) trivial $62791.3897584$
20.0.582...056.1 $x^{20} - x^{18} + x^{16} - x^{14} + x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1$ $2^{20}\cdot 11^{18}$ $C_2\times C_{10}$ (as 20T3) trivial $140601.245383$
20.0.542...625.1 $x^{20} - x^{19} + 2 x^{18} - 3 x^{17} + 5 x^{16} - 8 x^{15} + 13 x^{14} - 21 x^{13} + 34 x^{12} - 55 x^{11} + 89 x^{10} + 55 x^{9} + 34 x^{8} + 21 x^{7} + 13 x^{6} + 8 x^{5} + 5 x^{4} + 3 x^{3} + 2 x^{2} + x + 1$ $5^{10}\cdot 11^{18}$ $C_2\times C_{10}$ (as 20T3) $[2]$ $140644.599182$
20.0.157...769.2 $x^{20} - x^{19} - x^{18} + 3 x^{17} - x^{16} - 5 x^{15} + 7 x^{14} + 3 x^{13} - 17 x^{12} + 11 x^{11} + 23 x^{10} + 22 x^{9} - 68 x^{8} + 24 x^{7} + 112 x^{6} - 160 x^{5} - 64 x^{4} + 384 x^{3} - 256 x^{2} - 512 x + 1024$ $7^{10}\cdot 11^{18}$ $C_2\times C_{10}$ (as 20T3) $[5]$ $707570.081247$
20.0.284...064.1 $x^{20} - 9 x^{18} + 53 x^{16} - 182 x^{14} + 454 x^{12} - 711 x^{10} + 796 x^{8} - 469 x^{6} + 190 x^{4} - 15 x^{2} + 1$ $2^{20}\cdot 3^{10}\cdot 11^{16}$ $C_2\times C_{10}$ (as 20T3) trivial $873105.021385$
20.0.596...344.5 $x^{20} - 2 x^{18} + 4 x^{16} - 8 x^{14} + 16 x^{12} - 32 x^{10} + 64 x^{8} - 128 x^{6} + 256 x^{4} - 512 x^{2} + 1024$ $2^{30}\cdot 11^{18}$ $C_2\times C_{10}$ (as 20T3) $[5]$ $794615.004358$
20.0.596...344.6 $x^{20} + 2 x^{18} + 4 x^{16} + 8 x^{14} + 16 x^{12} + 32 x^{10} + 64 x^{8} + 128 x^{6} + 256 x^{4} + 512 x^{2} + 1024$ $2^{30}\cdot 11^{18}$ $C_2\times C_{10}$ (as 20T3) $[11]$ $530208.250733$
20.0.264...625.1 $x^{20} - x^{19} + 14 x^{18} - 3 x^{17} + 131 x^{16} - 23 x^{15} + 547 x^{14} + 141 x^{13} + 1496 x^{12} + 223 x^{11} + 1987 x^{10} + 109 x^{9} + 1892 x^{8} - 114 x^{7} + 860 x^{6} - 175 x^{5} + 293 x^{4} - 40 x^{3} + 27 x^{2} + 3 x + 1$ $3^{10}\cdot 5^{10}\cdot 11^{16}$ $C_2\times C_{10}$ (as 20T3) $[11]$ $140644.599182$
20.0.343...625.1 $x^{20} + 10 x^{18} + 65 x^{16} - x^{15} + 250 x^{14} - 15 x^{13} + 700 x^{12} - 75 x^{11} + 1252 x^{10} - 250 x^{9} + 1620 x^{8} - 375 x^{7} + 1200 x^{6} - 374 x^{5} + 600 x^{4} - 115 x^{3} + 50 x^{2} + 5 x + 1$ $3^{10}\cdot 5^{34}$ $C_2\times C_{10}$ (as 20T3) $[11]$ $161406.837641$
20.0.505...936.1 $x^{20} + 25 x^{16} + 184 x^{12} + 403 x^{8} + 155 x^{4} + 1$ $2^{40}\cdot 11^{16}$ $C_2\times C_{10}$ (as 20T3) $[5]$ $530208.250733$
20.0.344...744.1 $x^{20} + 21 x^{18} + 188 x^{16} + 934 x^{14} + 2806 x^{12} + 5202 x^{10} + 5809 x^{8} + 3629 x^{6} + 1090 x^{4} + 120 x^{2} + 1$ $2^{20}\cdot 3^{10}\cdot 11^{18}$ $C_2\times C_{10}$ (as 20T3) $[22]$ $125582.779517$
20.20.344...744.1 $x^{20} - 19 x^{18} + 152 x^{16} - 666 x^{14} + 1742 x^{12} - 2782 x^{10} + 2665 x^{8} - 1443 x^{6} + 390 x^{4} - 40 x^{2} + 1$ $2^{20}\cdot 3^{10}\cdot 11^{18}$ $C_2\times C_{10}$ (as 20T3) trivial $171724264.493$
20.0.344...744.2 $x^{20} + 11 x^{18} + 77 x^{16} + 330 x^{14} + 1034 x^{12} + 2189 x^{10} + 3388 x^{8} + 3267 x^{6} + 2178 x^{4} + 605 x^{2} + 121$ $2^{20}\cdot 3^{10}\cdot 11^{18}$ $C_2\times C_{10}$ (as 20T3) $[22]$ $281202.490766$
20.0.344...744.3 $x^{20} + 3 x^{18} + 9 x^{16} + 27 x^{14} + 81 x^{12} + 243 x^{10} + 729 x^{8} + 2187 x^{6} + 6561 x^{4} + 19683 x^{2} + 59049$ $2^{20}\cdot 3^{10}\cdot 11^{18}$ $C_2\times C_{10}$ (as 20T3) $[22]$ $1746210.04277$
20.0.470...000.1 $x^{20} + 27 x^{18} + 277 x^{16} + 1386 x^{14} + 3694 x^{12} + 5493 x^{10} + 4588 x^{8} + 2079 x^{6} + 470 x^{4} + 45 x^{2} + 1$ $2^{20}\cdot 5^{10}\cdot 11^{16}$ $C_2\times C_{10}$ (as 20T3) $[31]$ $140644.599182$
20.0.610...000.1 $x^{20} + 20 x^{18} + 170 x^{16} + 800 x^{14} + 2275 x^{12} + 4003 x^{10} + 4280 x^{8} + 2605 x^{6} + 775 x^{4} + 75 x^{2} + 1$ $2^{20}\cdot 5^{34}$ $C_2\times C_{10}$ (as 20T3) $[55]$ $161406.837641$
20.0.766...361.1 $x^{20} - x^{19} - 13 x^{18} + 104 x^{16} + 43 x^{15} - 734 x^{14} - 9 x^{13} + 3770 x^{12} + 355 x^{11} - 11777 x^{10} - 7082 x^{9} + 29156 x^{8} + 6480 x^{7} - 42976 x^{6} + 18272 x^{5} + 39296 x^{4} - 9856 x^{3} - 4608 x^{2} - 1536 x + 1024$ $3^{10}\cdot 7^{10}\cdot 11^{16}$ $C_2\times C_{10}$ (as 20T3) $[5]$ $2934029.89978$
20.0.766...369.1 $x^{20} - x^{19} + 4 x^{18} - 7 x^{17} + 19 x^{16} - 40 x^{15} + 97 x^{14} - 217 x^{13} + 508 x^{12} - 1159 x^{11} + 2683 x^{10} + 3477 x^{9} + 4572 x^{8} + 5859 x^{7} + 7857 x^{6} + 9720 x^{5} + 13851 x^{4} + 15309 x^{3} + 26244 x^{2} + 19683 x + 59049$ $11^{18}\cdot 13^{10}$ $C_2\times C_{10}$ (as 20T3) $[25]$ $2015201.7242$
20.0.291...536.2 $x^{20} - 18 x^{18} + 212 x^{16} - 1456 x^{14} + 7264 x^{12} - 22752 x^{10} + 50944 x^{8} - 60032 x^{6} + 48640 x^{4} - 7680 x^{2} + 1024$ $2^{30}\cdot 3^{10}\cdot 11^{16}$ $C_2\times C_{10}$ (as 20T3) $[5]$ $5268231.17547$
20.0.291...536.4 $x^{20} + 18 x^{18} + 212 x^{16} + 1456 x^{14} + 7264 x^{12} + 22752 x^{10} + 50944 x^{8} + 60032 x^{6} + 48640 x^{4} + 7680 x^{2} + 1024$ $2^{30}\cdot 3^{10}\cdot 11^{16}$ $C_2\times C_{10}$ (as 20T3) $[5, 5]$ $530208.250733$
20.0.320...625.1 $x^{20} - x^{19} + 19 x^{18} - 15 x^{17} + 148 x^{16} - 88 x^{15} + 618 x^{14} - 266 x^{13} + 1534 x^{12} - 470 x^{11} + 2342 x^{10} - 263 x^{9} + 1906 x^{8} + 1335 x^{7} + 479 x^{6} + 2937 x^{5} - 134 x^{4} + 3709 x^{3} - 1963 x^{2} - 1928 x + 9901$ $3^{10}\cdot 5^{10}\cdot 11^{18}$ $C_2\times C_{10}$ (as 20T3) $[44]$ $125582.779517$
20.20.320...625.1 $x^{20} - x^{19} - 31 x^{18} + 30 x^{17} + 368 x^{16} - 338 x^{15} - 2132 x^{14} + 1794 x^{13} + 6524 x^{12} - 4730 x^{11} - 11153 x^{10} + 6622 x^{9} + 10781 x^{8} - 4995 x^{7} - 5641 x^{6} + 1922 x^{5} + 1391 x^{4} - 316 x^{3} - 108 x^{2} + 12 x + 1$ $3^{10}\cdot 5^{10}\cdot 11^{18}$ $C_2\times C_{10}$ (as 20T3) trivial $527561758.587$
20.0.320...625.2 $x^{20} - x^{19} - 11 x^{18} + 12 x^{17} + 76 x^{16} - 88 x^{15} - 318 x^{14} + 406 x^{13} + 946 x^{12} - 1352 x^{11} - 1783 x^{10} + 3334 x^{9} + 1837 x^{8} - 9549 x^{7} + 4445 x^{6} + 13860 x^{5} - 16127 x^{4} + 17590 x^{3} - 2068 x^{2} - 37412 x + 39601$ $3^{10}\cdot 5^{10}\cdot 11^{18}$ $C_2\times C_{10}$ (as 20T3) $[4]$ $5362955.97373$
20.0.320...625.3 $x^{20} - x^{19} - 3 x^{18} + 7 x^{17} + 5 x^{16} - 33 x^{15} + 13 x^{14} + 119 x^{13} - 171 x^{12} - 305 x^{11} + 989 x^{10} - 1220 x^{9} - 2736 x^{8} + 7616 x^{7} + 3328 x^{6} - 33792 x^{5} + 20480 x^{4} + 114688 x^{3} - 196608 x^{2} - 262144 x + 1048576$ $3^{10}\cdot 5^{10}\cdot 11^{18}$ $C_2\times C_{10}$ (as 20T3) $[2, 22]$ $2681477.98686$
20.20.611...256.1 $x^{20} - 20 x^{18} + 169 x^{16} - 784 x^{14} + 2172 x^{12} - 3664 x^{10} + 3683 x^{8} - 2072 x^{6} + 575 x^{4} - 60 x^{2} + 1$ $2^{40}\cdot 11^{18}$ $C_2\times C_{10}$ (as 20T3) trivial $659839531.614$
20.0.611...256.3 $x^{20} + 20 x^{18} + 169 x^{16} + 784 x^{14} + 2172 x^{12} + 3664 x^{10} + 3683 x^{8} + 2072 x^{6} + 575 x^{4} + 60 x^{2} + 1$ $2^{40}\cdot 11^{18}$ $C_2\times C_{10}$ (as 20T3) $[110]$ $140601.245383$
20.0.611...256.4 $x^{20} + 33 x^{16} + 352 x^{12} + 1331 x^{8} + 1331 x^{4} + 121$ $2^{40}\cdot 11^{18}$ $C_2\times C_{10}$ (as 20T3) $[22]$ $794615.004358$
20.0.112...969.1 $x^{20} - x^{19} + 5 x^{18} - 9 x^{17} + 29 x^{16} - 65 x^{15} + 181 x^{14} - 441 x^{13} + 1165 x^{12} - 2929 x^{11} + 7589 x^{10} + 11716 x^{9} + 18640 x^{8} + 28224 x^{7} + 46336 x^{6} + 66560 x^{5} + 118784 x^{4} + 147456 x^{3} + 327680 x^{2} + 262144 x + 1048576$ $11^{18}\cdot 17^{10}$ $C_2\times C_{10}$ (as 20T3) $[41]$ $3338983.62101$
20.0.136...264.1 $x^{20} - 27 x^{18} + 352 x^{16} - 2709 x^{14} + 13339 x^{12} - 42123 x^{10} + 84004 x^{8} - 96768 x^{6} + 59840 x^{4} - 11520 x^{2} + 1024$ $2^{20}\cdot 7^{10}\cdot 11^{16}$ $C_2\times C_{10}$ (as 20T3) $[5]$ $4006867.75615$
20.0.340...281.2 $x^{20} - x^{19} - 4 x^{18} + 9 x^{17} + 11 x^{16} - 56 x^{15} + x^{14} + 279 x^{13} - 284 x^{12} - 1111 x^{11} + 2531 x^{10} - 5555 x^{9} - 7100 x^{8} + 34875 x^{7} + 625 x^{6} - 175000 x^{5} + 171875 x^{4} + 703125 x^{3} - 1562500 x^{2} - 1953125 x + 9765625$ $11^{18}\cdot 19^{10}$ $C_2\times C_{10}$ (as 20T3) $[55]$ $8845130.03478$
20.0.412...809.1 $x^{20} - x^{19} - x^{18} - 34 x^{17} + 29 x^{16} + 25 x^{15} + 371 x^{14} - 237 x^{13} - 232 x^{12} - 1510 x^{11} + 811 x^{10} + 1383 x^{9} + 1792 x^{8} - 1064 x^{7} - 2903 x^{6} + 1617 x^{5} + 2774 x^{4} - 960 x^{3} - 1175 x^{2} - 500 x + 625$ $3^{10}\cdot 31^{18}$ $C_2\times C_{10}$ (as 20T3) $[15]$ $6483708.43992$
20.0.569...000.1 $x^{20} + 17 x^{18} + 124 x^{16} + 502 x^{14} + 1230 x^{12} + 1858 x^{10} + 1721 x^{8} + 833 x^{6} + 554 x^{4} - 1560 x^{2} + 7921$ $2^{20}\cdot 5^{10}\cdot 11^{18}$ $C_2\times C_{10}$ (as 20T3) $[124]$ $281202.490766$
20.20.569...000.1 $x^{20} - 33 x^{18} + 429 x^{16} - 2838 x^{14} + 10450 x^{12} - 22407 x^{10} + 28556 x^{8} - 21417 x^{6} + 8954 x^{4} - 1815 x^{2} + 121$ $2^{20}\cdot 5^{10}\cdot 11^{18}$ $C_2\times C_{10}$ (as 20T3) trivial $2463631598.95$
20.0.569...000.2 $x^{20} - 23 x^{18} + 232 x^{16} - 1354 x^{14} + 5094 x^{12} - 13102 x^{10} + 24113 x^{8} - 33551 x^{6} + 38270 x^{4} - 39480 x^{2} + 39601$ $2^{20}\cdot 5^{10}\cdot 11^{18}$ $C_2\times C_{10}$ (as 20T3) $[4]$ $11184526.8933$
20.0.569...000.3 $x^{20} - 5 x^{18} + 25 x^{16} - 125 x^{14} + 625 x^{12} - 3125 x^{10} + 15625 x^{8} - 78125 x^{6} + 390625 x^{4} - 1953125 x^{2} + 9765625$ $2^{20}\cdot 5^{10}\cdot 11^{18}$ $C_2\times C_{10}$ (as 20T3) $[2, 62]$ $5592263.44664$
20.0.927...681.1 $x^{20} - x^{19} + 22 x^{18} - 21 x^{17} + 307 x^{16} - 286 x^{15} + 2619 x^{14} - 2333 x^{13} + 16258 x^{12} - 13925 x^{11} + 67715 x^{10} - 53723 x^{9} + 202840 x^{8} - 146169 x^{7} + 361505 x^{6} - 203544 x^{5} + 399607 x^{4} - 237335 x^{3} + 147488 x^{2} - 28073 x + 4489$ $3^{10}\cdot 7^{10}\cdot 11^{18}$ $C_2\times C_{10}$ (as 20T3) $[66]$ $1415140.16249$
20.20.927...681.1 $x^{20} - x^{19} - 38 x^{18} + 33 x^{17} + 613 x^{16} - 448 x^{15} - 5463 x^{14} + 3223 x^{13} + 29302 x^{12} - 13187 x^{11} - 96559 x^{10} + 30691 x^{9} + 191218 x^{8} - 39237 x^{7} - 212737 x^{6} + 28344 x^{5} + 116035 x^{4} - 15587 x^{3} - 23758 x^{2} + 4783 x + 331$ $3^{10}\cdot 7^{10}\cdot 11^{18}$ $C_2\times C_{10}$ (as 20T3) trivial $2904089575.06$
20.0.927...681.3 $x^{20} - 8 x^{19} + 27 x^{18} - 52 x^{17} + 132 x^{16} - 452 x^{15} + 1108 x^{14} - 1974 x^{13} + 4254 x^{12} - 9042 x^{11} + 17084 x^{10} - 27764 x^{9} + 50255 x^{8} - 71930 x^{7} + 123807 x^{6} - 139074 x^{5} + 238062 x^{4} - 158880 x^{3} + 351000 x^{2} - 96318 x + 278653$ $3^{10}\cdot 7^{10}\cdot 11^{18}$ $C_2\times C_{10}$ (as 20T3) $[330]$ $125582.779517$
20.0.927...681.4 $x^{20} - x^{19} + 6 x^{18} - 11 x^{17} + 41 x^{16} - 96 x^{15} + 301 x^{14} - 781 x^{13} + 2286 x^{12} - 6191 x^{11} + 17621 x^{10} + 30955 x^{9} + 57150 x^{8} + 97625 x^{7} + 188125 x^{6} + 300000 x^{5} + 640625 x^{4} + 859375 x^{3} + 2343750 x^{2} + 1953125 x + 9765625$ $3^{10}\cdot 7^{10}\cdot 11^{18}$ $C_2\times C_{10}$ (as 20T3) $[66]$ $5868059.79956$
20.0.126...625.3 $x^{20} - 8 x^{19} + 21 x^{18} - 57 x^{16} - 166 x^{15} + 1385 x^{14} - 3815 x^{13} + 8065 x^{12} - 16253 x^{11} + 38496 x^{10} - 88398 x^{9} + 203504 x^{8} - 392889 x^{7} + 695944 x^{6} - 1005043 x^{5} + 1343738 x^{4} - 1372952 x^{3} + 1330894 x^{2} - 768615 x + 512579$ $5^{10}\cdot 7^{10}\cdot 11^{16}$ $C_2\times C_{10}$ (as 20T3) $[5, 55]$ $140644.599182$
20.0.164...625.1 $x^{20} + 30 x^{18} + 435 x^{16} - 11 x^{15} + 3750 x^{14} - 265 x^{13} + 20825 x^{12} - 2735 x^{11} + 74975 x^{10} - 15000 x^{9} + 173240 x^{8} - 42800 x^{7} + 238320 x^{6} - 63648 x^{5} + 172800 x^{4} - 28800 x^{3} + 32000 x^{2} + 2560 x + 1024$ $5^{34}\cdot 7^{10}$ $C_2\times C_{10}$ (as 20T3) $[4, 4, 4, 4]$ $161406.837641$
20.0.230...169.1 $x^{20} - x^{19} - 5 x^{18} + 11 x^{17} + 19 x^{16} - 85 x^{15} - 29 x^{14} + 539 x^{13} - 365 x^{12} - 2869 x^{11} + 5059 x^{10} - 17214 x^{9} - 13140 x^{8} + 116424 x^{7} - 37584 x^{6} - 660960 x^{5} + 886464 x^{4} + 3079296 x^{3} - 8398080 x^{2} - 10077696 x + 60466176$ $11^{18}\cdot 23^{10}$ $C_2\times C_{10}$ (as 20T3) $[2, 2, 2, 6]$ $13106437.7678$
20.20.352...856.1 $x^{20} - 2 x^{19} - 39 x^{18} + 76 x^{17} + 590 x^{16} - 1104 x^{15} - 4374 x^{14} + 7644 x^{13} + 16726 x^{12} - 25808 x^{11} - 33034 x^{10} + 40262 x^{9} + 33501 x^{8} - 26542 x^{7} - 16067 x^{6} + 6736 x^{5} + 3516 x^{4} - 450 x^{3} - 292 x^{2} - 20 x + 1$ $2^{30}\cdot 3^{10}\cdot 11^{18}$ $C_2\times C_{10}$ (as 20T3) trivial $4400553067.16$
20.0.352...856.2 $x^{20} + 38 x^{18} + 608 x^{16} + 5328 x^{14} + 27872 x^{12} + 89024 x^{10} + 170560 x^{8} + 184704 x^{6} + 99840 x^{4} + 20480 x^{2} + 1024$ $2^{30}\cdot 3^{10}\cdot 11^{18}$ $C_2\times C_{10}$ (as 20T3) $[5, 110]$ $125582.779517$
20.20.352...856.2 $x^{20} - 38 x^{18} + 608 x^{16} - 5328 x^{14} + 27872 x^{12} - 89024 x^{10} + 170560 x^{8} - 184704 x^{6} + 99840 x^{4} - 20480 x^{2} + 1024$ $2^{30}\cdot 3^{10}\cdot 11^{18}$ $C_2\times C_{10}$ (as 20T3) trivial $5855953195.46$
20.0.352...856.4 $x^{20} - 22 x^{18} + 308 x^{16} - 2640 x^{14} + 16544 x^{12} - 70048 x^{10} + 216832 x^{8} - 418176 x^{6} + 557568 x^{4} - 309760 x^{2} + 123904$ $2^{30}\cdot 3^{10}\cdot 11^{18}$ $C_2\times C_{10}$ (as 20T3) $[22]$ $11866284.7339$
20.0.352...856.5 $x^{20} + 22 x^{18} + 308 x^{16} + 2640 x^{14} + 16544 x^{12} + 70048 x^{10} + 216832 x^{8} + 418176 x^{6} + 557568 x^{4} + 309760 x^{2} + 123904$ $2^{30}\cdot 3^{10}\cdot 11^{18}$ $C_2\times C_{10}$ (as 20T3) $[124]$ $1589230.00872$
20.0.352...856.7 $x^{20} - 2 x^{19} + x^{18} + 4 x^{17} + 66 x^{16} - 144 x^{15} + 266 x^{14} - 100 x^{13} + 1822 x^{12} - 3344 x^{11} + 10198 x^{10} - 10362 x^{9} + 36517 x^{8} - 42190 x^{7} + 138157 x^{6} - 145432 x^{5} + 383064 x^{4} - 352162 x^{3} + 765484 x^{2} - 438908 x + 652081$ $2^{30}\cdot 3^{10}\cdot 11^{18}$ $C_2\times C_{10}$ (as 20T3) $[2, 310]$ $125582.779517$
20.0.352...856.8 $x^{20} - 6 x^{18} + 36 x^{16} - 216 x^{14} + 1296 x^{12} - 7776 x^{10} + 46656 x^{8} - 279936 x^{6} + 1679616 x^{4} - 10077696 x^{2} + 60466176$ $2^{30}\cdot 3^{10}\cdot 11^{18}$ $C_2\times C_{10}$ (as 20T3) $[5, 10]$ $11866284.7339$
20.0.352...856.9 $x^{20} + 6 x^{18} + 36 x^{16} + 216 x^{14} + 1296 x^{12} + 7776 x^{10} + 46656 x^{8} + 279936 x^{6} + 1679616 x^{4} + 10077696 x^{2} + 60466176$ $2^{30}\cdot 3^{10}\cdot 11^{18}$ $C_2\times C_{10}$ (as 20T3) $[124]$ $10536462.3509$
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