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 |
20.4.175...000.1 |
$x^{20} - 13 x^{18} + 63 x^{16} - 166 x^{14} + 305 x^{12} - 351 x^{10} + 293 x^{8} - 158 x^{6} + 71 x^{4} - 25 x^{2} + 5$ |
$20$ |
[4,8] |
$2^{28}\cdot 5^{15}\cdot 11^{8}$ |
$3$ |
$23.0264279186$ |
$60.087432229036395$ |
|
|
? |
$C_{10}:F_5$ (as 20T49) |
trivial |
$2$ |
$11$ |
$1431459.05224$ |
20.4.253...000.1 |
$x^{20} - 3 x^{19} - 11 x^{18} + 33 x^{17} + 66 x^{16} - 183 x^{15} - 277 x^{14} + 579 x^{13} + 874 x^{12} - 865 x^{11} - 1801 x^{10} - 11 x^{9} + 1956 x^{8} + 2795 x^{7} + 2635 x^{6} + 1273 x^{5} + 44 x^{4} - 155 x^{3} - 25 x^{2} + 5 x + 1$ |
$20$ |
[4,8] |
$2^{16}\cdot 3^{10}\cdot 5^{15}\cdot 11^{8}$ |
$4$ |
$26.3129294441$ |
$68.66355347467841$ |
|
|
? |
$C_{10}:F_5$ (as 20T49) |
trivial |
$2$ |
$11$ |
$2156441.45048$ |
20.0.781...000.1 |
$x^{20} - 15 x^{18} + 105 x^{16} - 4 x^{15} - 400 x^{14} + 20 x^{13} + 1025 x^{12} + 60 x^{11} - 1754 x^{10} - 200 x^{9} + 2080 x^{8} + 200 x^{7} - 1210 x^{6} + 516 x^{5} + 225 x^{4} - 710 x^{3} + 400 x^{2} - 80 x + 16$ |
$20$ |
[0,10] |
$2^{24}\cdot 5^{31}$ |
$2$ |
$27.8380942914$ |
$38.982178030461924$ |
|
|
? |
$C_{10}:F_5$ (as 20T49) |
trivial |
$10$ |
$9$ |
$14787405.0482$ |
20.0.781...000.2 |
$x^{20} - 10 x^{18} + 80 x^{16} - 20 x^{15} - 350 x^{14} + 150 x^{13} + 1025 x^{12} - 500 x^{11} - 1860 x^{10} + 750 x^{9} + 1925 x^{8} - 750 x^{7} - 1275 x^{6} + 850 x^{5} + 1625 x^{4} + 1000 x^{3} + 1000 x^{2} + 1000 x + 400$ |
$20$ |
[0,10] |
$2^{24}\cdot 5^{31}$ |
$2$ |
$27.8380942914$ |
$38.982178030461924$ |
|
|
? |
$C_{10}:F_5$ (as 20T49) |
trivial |
$10$ |
$9$ |
$11302864.7053$ |
20.0.179...000.1 |
$x^{20} + 8 x^{18} + 44 x^{16} + 192 x^{14} + 696 x^{12} + 2050 x^{10} + 4560 x^{8} + 7400 x^{6} + 7700 x^{4} + 4000 x^{2} + 500$ |
$20$ |
[0,10] |
$2^{38}\cdot 5^{15}\cdot 11^{8}$ |
$3$ |
$32.56428665554607$ |
$84.97646158647748$ |
|
|
? |
$C_{10}:F_5$ (as 20T49) |
$[2]$ |
$2$ |
$9$ |
$5024343.372652114$ |
20.0.518...125.1 |
$x^{20} + 90 x^{18} + 2955 x^{16} + 42350 x^{14} + 252865 x^{12} + 666510 x^{10} + 804650 x^{8} + 495425 x^{6} + 162450 x^{4} + 27075 x^{2} + 1805$ |
$20$ |
[0,10] |
$3^{8}\cdot 5^{31}\cdot 19^{8}$ |
$3$ |
$61.059528869$ |
$251.70081117843628$ |
✓ |
|
|
$C_{10}:F_5$ (as 20T49) |
$[109]$ |
$10$ |
$9$ |
$307931905.969$ |
20.0.378...125.1 |
$x^{20} - 5 x^{19} + 37 x^{18} - 107 x^{17} + 467 x^{16} - 1170 x^{15} + 4619 x^{14} - 7039 x^{13} + 36318 x^{12} - 62610 x^{11} + 238424 x^{10} - 298521 x^{9} + 1250475 x^{8} - 464666 x^{7} + 3262784 x^{6} + 2705304 x^{5} + 4160432 x^{4} + 4720352 x^{3} + 6042880 x^{2} + 1184384 x + 92416$ |
$20$ |
[0,10] |
$3^{16}\cdot 5^{15}\cdot 7^{8}\cdot 29^{8}$ |
$4$ |
$67.4408324294$ |
$315.05902548913$ |
✓ |
|
|
$C_{10}:F_5$ (as 20T49) |
$[95]$ |
$10$ |
$9$ |
$631632012.968$ |
20.20.340...125.1 |
$x^{20} - 6 x^{19} - 53 x^{18} + 348 x^{17} + 1098 x^{16} - 8142 x^{15} - 11667 x^{14} + 100758 x^{13} + 71988 x^{12} - 730512 x^{11} - 273903 x^{10} + 3212694 x^{9} + 616446 x^{8} - 8513820 x^{7} - 526425 x^{6} + 13024230 x^{5} - 747660 x^{4} - 10277550 x^{3} + 1728925 x^{2} + 3018000 x - 707225$ |
$20$ |
[20,0] |
$3^{18}\cdot 5^{15}\cdot 7^{8}\cdot 29^{8}$ |
$4$ |
$75.2722759506$ |
$351.6446795369566$ |
|
|
|
$C_{10}:F_5$ (as 20T49) |
trivial |
$2$ |
$19$ |
$8111181538130$ |
20.0.167...125.1 |
$x^{20} - x^{19} + 14 x^{18} + 18 x^{17} + 276 x^{16} + 549 x^{15} + 3660 x^{14} + 11661 x^{13} + 46692 x^{12} + 154466 x^{11} + 619795 x^{10} + 1778500 x^{9} + 4629726 x^{8} + 11244435 x^{7} + 22807710 x^{6} + 38372595 x^{5} + 58254132 x^{4} + 62926140 x^{3} + 60818846 x^{2} + 32304409 x + 19702831$ |
$20$ |
[0,10] |
$3^{18}\cdot 5^{15}\cdot 7^{10}\cdot 29^{8}$ |
$4$ |
$91.44181795157638$ |
$351.6446795369566$ |
✓ |
|
|
$C_{10}:F_5$ (as 20T49) |
$[2, 410]$ |
$2$ |
$9$ |
$631632012.9676874$ |
20.20.461...000.1 |
$x^{20} - 75 x^{18} + 2250 x^{16} - 120 x^{15} - 34875 x^{14} + 6600 x^{13} + 300375 x^{12} - 127800 x^{11} - 1431615 x^{10} + 1080000 x^{9} + 3435750 x^{8} - 3948750 x^{7} - 2860875 x^{6} + 5261850 x^{5} - 421875 x^{4} - 2079000 x^{3} + 877500 x^{2} - 54000 x - 3600$ |
$20$ |
[20,0] |
$2^{16}\cdot 3^{18}\cdot 5^{39}$ |
$3$ |
$107.950494038$ |
$160.42270464920298$ |
|
|
? |
$C_{10}:F_5$ (as 20T49) |
trivial |
$2$ |
$19$ |
$128509830940000$ |