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 |
16.0.10251562500000000.1 |
$x^{16} - 4 x^{15} + 6 x^{14} + 9 x^{13} - 52 x^{12} + 91 x^{11} - 36 x^{10} - 163 x^{9} + 403 x^{8} - 489 x^{7} + 356 x^{6} - 143 x^{5} + 13 x^{4} + 12 x^{3} - x^{2} - 3 x + 1$ |
$16$ |
[0,8] |
$2^{8}\cdot 3^{8}\cdot 5^{14}$ |
$3$ |
$10.0155402124$ |
$14.164112802887677$ |
|
|
? |
$(C_8:C_2):C_2$ (as 16T16) |
trivial |
$30$ |
$7$ |
$224.827155954$ |
16.0.32400000000000000.1 |
$x^{16} - 2 x^{15} + 2 x^{14} + 4 x^{13} + x^{12} - 12 x^{11} + 15 x^{10} + 32 x^{9} - 21 x^{8} + 6 x^{7} + 20 x^{6} - 34 x^{5} - 4 x^{4} + 22 x^{3} - 2 x^{2} - 4 x + 1$ |
$16$ |
[0,8] |
$2^{16}\cdot 3^{4}\cdot 5^{14}$ |
$3$ |
$10.7623983632$ |
$14.164112802887677$ |
|
|
? |
$(C_8:C_2):C_2$ (as 16T16) |
trivial |
$20$ |
$7$ |
$357.4244052$ |
16.0.96148443603515625.1 |
$x^{16} - 5 x^{15} + 19 x^{14} - 50 x^{13} + 112 x^{12} - 205 x^{11} + 337 x^{10} - 470 x^{9} + 600 x^{8} - 655 x^{7} + 673 x^{6} - 550 x^{5} + 472 x^{4} - 260 x^{3} + 186 x^{2} - 55 x + 31$ |
$16$ |
[0,8] |
$3^{8}\cdot 5^{14}\cdot 7^{4}$ |
$3$ |
$11.5195069512$ |
$18.737360009153413$ |
|
|
? |
$(C_8:C_2):C_2$ (as 16T16) |
trivial |
$30$ |
$7$ |
$733.048403988$ |
16.0.164025000000000000.1 |
$x^{16} - 5 x^{15} + 19 x^{14} - 50 x^{13} + 107 x^{12} - 180 x^{11} + 237 x^{10} - 225 x^{9} + 150 x^{8} - 25 x^{7} + 13 x^{6} + 40 x^{5} + 37 x^{4} + 35 x^{3} + 21 x^{2} + 5 x + 1$ |
$16$ |
[0,8] |
$2^{12}\cdot 3^{8}\cdot 5^{14}$ |
$3$ |
$11.9105516812$ |
$20.031080424826147$ |
|
|
? |
$(C_8:C_2):C_2$ (as 16T16) |
trivial |
$30$ |
$7$ |
$1005.23975626$ |
16.0.960400000000000000.1 |
$x^{16} - 2 x^{15} + 8 x^{14} - 24 x^{13} + 70 x^{12} - 194 x^{11} + 423 x^{10} - 722 x^{9} + 1006 x^{8} - 1150 x^{7} + 1075 x^{6} - 840 x^{5} + 570 x^{4} - 330 x^{3} + 145 x^{2} - 40 x + 5$ |
$16$ |
[0,8] |
$2^{16}\cdot 5^{14}\cdot 7^{4}$ |
$3$ |
$13.3015808784$ |
$21.636039690375302$ |
|
|
? |
$(C_8:C_2):C_2$ (as 16T16) |
trivial |
$20$ |
$7$ |
$2187.29813817$ |
16.0.262...000.1 |
$x^{16} - 10 x^{14} + 50 x^{12} - 145 x^{10} + 270 x^{8} - 300 x^{6} + 150 x^{4} - 25 x^{2} + 25$ |
$16$ |
[0,8] |
$2^{16}\cdot 3^{8}\cdot 5^{14}$ |
$3$ |
$14.1641128029$ |
$20.031080424826147$ |
|
|
? |
$(C_8:C_2):C_2$ (as 16T16) |
trivial |
$30$ |
$7$ |
$4605.01634619$ |
16.8.262...000.1 |
$x^{16} - 8 x^{15} + 29 x^{14} - 58 x^{13} + 48 x^{12} + 62 x^{11} - 234 x^{10} + 306 x^{9} - 172 x^{8} - 68 x^{7} + 239 x^{6} - 314 x^{5} + 313 x^{4} - 206 x^{3} + 76 x^{2} - 14 x + 1$ |
$16$ |
[8,4] |
$2^{16}\cdot 3^{8}\cdot 5^{14}$ |
$3$ |
$14.1641128029$ |
$14.164112802887677$ |
|
|
? |
$(C_8:C_2):C_2$ (as 16T16) |
trivial |
$2$ |
$11$ |
$1176.18765647$ |
16.0.285...625.1 |
$x^{16} - 5 x^{15} + 16 x^{14} - 25 x^{13} + 27 x^{12} - 35 x^{11} + 48 x^{10} - 90 x^{9} + 165 x^{8} - 195 x^{7} + 247 x^{6} - 190 x^{5} + 157 x^{4} - 80 x^{3} + 39 x^{2} - 10 x + 1$ |
$16$ |
[0,8] |
$3^{4}\cdot 5^{14}\cdot 7^{8}$ |
$3$ |
$14.2373147899$ |
$18.737360009153413$ |
|
|
? |
$(C_8:C_2):C_2$ (as 16T16) |
trivial |
$10$ |
$7$ |
$2117.22006174$ |
16.0.829...000.1 |
$x^{16} - 6 x^{15} + 9 x^{14} + 4 x^{13} + 11 x^{12} - 58 x^{11} - 29 x^{10} + 32 x^{9} + 162 x^{8} + 98 x^{7} - 54 x^{6} - 182 x^{5} - 119 x^{4} + 6 x^{3} + 69 x^{2} + 46 x + 11$ |
$16$ |
[0,8] |
$2^{24}\cdot 3^{4}\cdot 5^{14}$ |
$3$ |
$15.2203297289$ |
$20.031080424826147$ |
|
|
? |
$(C_8:C_2):C_2$ (as 16T16) |
trivial |
$10$ |
$7$ |
$3884.1943821$ |
16.0.829...000.2 |
$x^{16} - 2 x^{15} + 12 x^{14} - 6 x^{13} + 26 x^{12} + 68 x^{11} - 30 x^{10} + 222 x^{9} + 199 x^{8} - 224 x^{7} + 1210 x^{6} - 994 x^{5} + 1546 x^{4} - 698 x^{3} + 778 x^{2} - 184 x + 181$ |
$16$ |
[0,8] |
$2^{24}\cdot 3^{4}\cdot 5^{14}$ |
$3$ |
$15.2203297289$ |
$20.031080424826147$ |
|
|
? |
$(C_8:C_2):C_2$ (as 16T16) |
$[2]$ |
$20$ |
$7$ |
$3660.4680193$ |
16.0.900...000.1 |
$x^{16} - x^{15} - 4 x^{14} + 6 x^{13} + 3 x^{12} - 26 x^{11} + 24 x^{10} + 93 x^{9} - 212 x^{8} + 54 x^{7} + 316 x^{6} - 497 x^{5} + 373 x^{4} - 227 x^{3} + 154 x^{2} - 67 x + 11$ |
$16$ |
[0,8] |
$2^{8}\cdot 5^{14}\cdot 7^{8}$ |
$3$ |
$15.2989903831$ |
$21.636039690375302$ |
|
|
? |
$(C_8:C_2):C_2$ (as 16T16) |
trivial |
$10$ |
$7$ |
$3973.7989882$ |
16.8.230...625.1 |
$x^{16} - 6 x^{15} + 8 x^{14} + 13 x^{13} - 39 x^{12} + 29 x^{11} + 15 x^{10} - 81 x^{9} + 89 x^{8} + 38 x^{7} - 100 x^{6} + 2 x^{5} + 46 x^{4} + x^{3} - 23 x^{2} + 7 x + 1$ |
$16$ |
[8,4] |
$3^{8}\cdot 5^{14}\cdot 7^{8}$ |
$3$ |
$18.7373600092$ |
$18.737360009153413$ |
|
|
? |
$(C_8:C_2):C_2$ (as 16T16) |
trivial |
$2$ |
$11$ |
$17701.471457$ |
16.8.671...000.1 |
$x^{16} - 8 x^{15} + 22 x^{14} - 14 x^{13} - 79 x^{12} + 232 x^{11} - 105 x^{10} - 502 x^{9} + 679 x^{8} + 344 x^{7} - 1165 x^{6} + 464 x^{5} + 526 x^{4} - 562 x^{3} + 193 x^{2} - 26 x + 1$ |
$16$ |
[8,4] |
$2^{24}\cdot 3^{8}\cdot 5^{14}$ |
$3$ |
$20.0310804248$ |
$20.031080424826147$ |
|
|
? |
$(C_8:C_2):C_2$ (as 16T16) |
trivial |
$2$ |
$11$ |
$33307.3689353$ |
16.8.671...000.2 |
$x^{16} - 2 x^{15} - 6 x^{14} - 2 x^{13} + 23 x^{12} + 48 x^{11} - 34 x^{10} + 34 x^{9} - 12 x^{8} - 232 x^{7} - 356 x^{6} + 44 x^{5} + 378 x^{4} + 216 x^{3} + 66 x^{2} + 14 x + 1$ |
$16$ |
[8,4] |
$2^{24}\cdot 3^{8}\cdot 5^{14}$ |
$3$ |
$20.0310804248$ |
$20.031080424826147$ |
|
|
? |
$(C_8:C_2):C_2$ (as 16T16) |
trivial |
$2$ |
$11$ |
$24091.2329353$ |
16.0.149...896.26 |
$x^{16} - 8 x^{12} + 32 x^{8} - 72 x^{4} + 81$ |
$16$ |
[0,8] |
$2^{64}\cdot 3^{4}$ |
$2$ |
$21.057184207239878$ |
$27.712812921102035$ |
|
|
? |
$(C_8:C_2):C_2$ (as 16T16) |
trivial |
$16$ |
$7$ |
$134624.5258758725$ |
16.0.149...896.46 |
$x^{16} - 16 x^{12} + 128 x^{8} - 576 x^{4} + 1296$ |
$16$ |
[0,8] |
$2^{64}\cdot 3^{4}$ |
$2$ |
$21.057184207239878$ |
$27.712812921102035$ |
|
|
? |
$(C_8:C_2):C_2$ (as 16T16) |
trivial |
$16$ |
$7$ |
$122671.83674323976$ |
16.8.230...000.1 |
$x^{16} - 8 x^{15} + 24 x^{14} - 28 x^{13} - 37 x^{12} + 172 x^{11} - 194 x^{10} - 104 x^{9} + 503 x^{8} - 388 x^{7} - 321 x^{6} + 666 x^{5} - 57 x^{4} - 386 x^{3} + 91 x^{2} + 66 x - 19$ |
$16$ |
[8,4] |
$2^{16}\cdot 5^{14}\cdot 7^{8}$ |
$3$ |
$21.6360396904$ |
$21.636039690375302$ |
|
|
? |
$(C_8:C_2):C_2$ (as 16T16) |
trivial |
$2$ |
$11$ |
$52483.3993487$ |
16.0.630...000.1 |
$x^{16} + 19 x^{14} - 20 x^{13} + 142 x^{12} - 260 x^{11} + 617 x^{10} - 1100 x^{9} + 1585 x^{8} - 1750 x^{7} + 1398 x^{6} - 600 x^{5} + 202 x^{4} - 680 x^{3} + 1256 x^{2} - 750 x + 181$ |
$16$ |
[0,8] |
$2^{16}\cdot 3^{8}\cdot 5^{14}\cdot 7^{4}$ |
$4$ |
$23.0390139024$ |
$37.474720018306826$ |
✓ |
|
? |
$(C_8:C_2):C_2$ (as 16T16) |
$[2, 2]$ |
$2$ |
$7$ |
$3121.7160225$ |
16.0.302...144.14 |
$x^{16} - 24 x^{14} + 244 x^{12} - 1248 x^{10} + 3086 x^{8} - 2496 x^{6} + 872 x^{4} - 96 x^{2} + 4$ |
$16$ |
[0,8] |
$2^{62}\cdot 3^{8}$ |
$2$ |
$25.412761497225222$ |
$27.712812921102035$ |
|
|
|
$(C_8:C_2):C_2$ (as 16T16) |
trivial |
$6$ |
$7$ |
$308067.0434259548$ |
16.0.302...144.91 |
$x^{16} - 16 x^{14} + 104 x^{12} - 352 x^{10} + 660 x^{8} - 672 x^{6} + 336 x^{4} - 64 x^{2} + 196$ |
$16$ |
[0,8] |
$2^{62}\cdot 3^{8}$ |
$2$ |
$25.412761497225222$ |
$27.712812921102035$ |
|
|
|
$(C_8:C_2):C_2$ (as 16T16) |
trivial |
$6$ |
$7$ |
$280715.1951789658$ |
16.0.590...000.1 |
$x^{16} - 4 x^{15} + 13 x^{14} - 18 x^{13} + 16 x^{12} - 9 x^{11} - 120 x^{10} + 136 x^{9} + 189 x^{8} - 228 x^{7} + 165 x^{6} + 283 x^{5} - 49 x^{4} + 659 x^{3} + 1222 x^{2} + 708 x + 631$ |
$16$ |
[0,8] |
$2^{8}\cdot 3^{8}\cdot 5^{14}\cdot 7^{8}$ |
$4$ |
$26.498628648$ |
$37.474720018306826$ |
✓ |
|
? |
$(C_8:C_2):C_2$ (as 16T16) |
$[2, 2]$ |
$2$ |
$7$ |
$14409.2792961$ |
16.8.121...576.5 |
$x^{16} - 48 x^{12} - 32 x^{10} + 196 x^{8} + 192 x^{6} - 104 x^{4} - 112 x^{2} + 1$ |
$16$ |
[8,4] |
$2^{64}\cdot 3^{8}$ |
$2$ |
$27.712812921102035$ |
$27.712812921102035$ |
|
|
? |
$(C_8:C_2):C_2$ (as 16T16) |
trivial |
$2$ |
$11$ |
$586980.1171542035$ |
16.8.121...576.33 |
$x^{16} - 16 x^{14} - 48 x^{12} + 240 x^{10} - 84 x^{8} - 160 x^{6} + 32 x^{4} + 32 x^{2} + 4$ |
$16$ |
[8,4] |
$2^{64}\cdot 3^{8}$ |
$2$ |
$27.712812921102035$ |
$27.712812921102035$ |
|
|
? |
$(C_8:C_2):C_2$ (as 16T16) |
trivial |
$2$ |
$11$ |
$644173.284336215$ |
16.0.245...664.120 |
$x^{16} - 24 x^{14} + 252 x^{12} - 1440 x^{10} + 4734 x^{8} - 8640 x^{6} + 7992 x^{4} - 2592 x^{2} + 324$ |
$16$ |
[0,8] |
$2^{62}\cdot 3^{12}$ |
$2$ |
$33.44507500385779$ |
$36.47211291127644$ |
|
|
? |
$(C_8:C_2):C_2$ (as 16T16) |
trivial |
$6$ |
$7$ |
$994561.8165555086$ |
16.0.245...664.139 |
$x^{16} + 264 x^{12} + 1332 x^{8} + 1296 x^{4} + 324$ |
$16$ |
[0,8] |
$2^{62}\cdot 3^{12}$ |
$2$ |
$33.44507500385779$ |
$36.47211291127644$ |
|
|
? |
$(C_8:C_2):C_2$ (as 16T16) |
trivial |
$6$ |
$7$ |
$990835.7076394719$ |
16.8.980...656.64 |
$x^{16} - 72 x^{12} + 1332 x^{8} - 432 x^{6} - 4752 x^{4} - 2592 x^{2} + 81$ |
$16$ |
[8,4] |
$2^{64}\cdot 3^{12}$ |
$2$ |
$36.47211291127644$ |
$36.47211291127644$ |
|
|
? |
$(C_8:C_2):C_2$ (as 16T16) |
trivial |
$2$ |
$11$ |
$4758940.822095593$ |
16.8.980...656.99 |
$x^{16} - 264 x^{12} + 1332 x^{8} - 1296 x^{4} + 324$ |
$16$ |
[8,4] |
$2^{64}\cdot 3^{12}$ |
$2$ |
$36.47211291127644$ |
$36.47211291127644$ |
|
|
? |
$(C_8:C_2):C_2$ (as 16T16) |
trivial |
$2$ |
$11$ |
$4741111.531313534$ |
16.0.980...656.106 |
$x^{16} + 81$ |
$16$ |
[0,8] |
$2^{64}\cdot 3^{12}$ |
$2$ |
$36.47211291127644$ |
$36.47211291127644$ |
|
|
? |
$(C_8:C_2):C_2$ (as 16T16) |
$[2]$ |
$8$ |
$7$ |
$2275898.2164446316$ |
16.0.980...656.112 |
$x^{16} - 24 x^{12} + 288 x^{8} + 216 x^{4} + 81$ |
$16$ |
[0,8] |
$2^{64}\cdot 3^{12}$ |
$2$ |
$36.47211291127644$ |
$36.47211291127644$ |
|
|
? |
$(C_8:C_2):C_2$ (as 16T16) |
$[2]$ |
$8$ |
$7$ |
$2267371.60251765$ |
16.16.612...000.1 |
$x^{16} - 96 x^{14} + 2760 x^{12} - 31392 x^{10} + 173268 x^{8} - 509760 x^{6} + 810000 x^{4} - 648000 x^{2} + 202500$ |
$16$ |
[16,0] |
$2^{64}\cdot 3^{12}\cdot 5^{4}$ |
$3$ |
$54.5385295904$ |
$81.55412375266188$ |
|
|
? |
$(C_8:C_2):C_2$ (as 16T16) |
trivial |
$2$ |
$15$ |
$755590682.095$ |
16.16.957...000.1 |
$x^{16} - 48 x^{14} + 936 x^{12} - 9504 x^{10} + 53460 x^{8} - 163296 x^{6} + 244944 x^{4} - 139968 x^{2} + 324$ |
$16$ |
[16,0] |
$2^{62}\cdot 3^{12}\cdot 5^{8}$ |
$3$ |
$74.7854612212$ |
$81.55412375266188$ |
|
|
? |
$(C_8:C_2):C_2$ (as 16T16) |
trivial |
$2$ |
$15$ |
$8532023860.82$ |