| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Narrow class group |
Unit group torsion |
Unit group rank |
Regulator |
Unit signature rank |
Max $p$ |
| 12.12.210...013.1 |
$x^{12} - x^{11} - 25 x^{10} + 25 x^{9} + 235 x^{8} - 235 x^{7} - 1013 x^{6} + 1013 x^{5} + 1899 x^{4} - 1899 x^{3} - 1013 x^{2} + 1013 x - 181$ |
$12$ |
(12, 0) |
$7^{6}\cdot 13^{11}$ |
$2$ |
$27.7756198526$ |
$27.775619852565686$ |
|
✓ |
✓ |
$C_{12}$ (as 12T1) |
trivial |
$[2]$ |
$2$ |
$11$ |
$41755.5171383$ |
$11$ |
$13$ |
| 12.12.989...125.1 |
$x^{12} - 3 x^{11} - 36 x^{10} + 106 x^{9} + 393 x^{8} - 1164 x^{7} - 1350 x^{6} + 4794 x^{5} + 441 x^{4} - 6643 x^{3} + 1926 x^{2} + 2865 x - 1349$ |
$12$ |
(12, 0) |
$3^{16}\cdot 5^{9}\cdot 7^{6}$ |
$3$ |
$38.2770267991$ |
$38.27702679912765$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
trivial |
$[2]$ |
$2$ |
$11$ |
$413348.51768$ |
$11$ |
$7$ |
| 12.4.164...704.1 |
$x^{12} - 7 x^{9} + x^{6} + 7 x^{3} + 2$ |
$12$ |
(4, 4) |
$2^{8}\cdot 3^{12}\cdot 7^{6}\cdot 101^{3}$ |
$4$ |
$39.942687444991925$ |
$216.36542738199515$ |
|
|
? |
$C_3^3:(S_3\times S_4)$ (as 12T258) |
trivial |
$[2]$ |
$2$ |
$7$ |
$337806.5910992553$ |
$3$ |
$101$ |
| 12.0.890...125.1 |
$x^{12} + 48 x^{10} - x^{9} + 774 x^{8} - 201 x^{7} + 5648 x^{6} - 4347 x^{5} + 22095 x^{4} - 26489 x^{3} + 72414 x^{2} - 18912 x + 156241$ |
$12$ |
(0, 6) |
$3^{18}\cdot 5^{9}\cdot 7^{6}$ |
$3$ |
$45.9682960173$ |
$45.968296017334616$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[2, 194]$ |
$[2, 194]$ |
$2$ |
$5$ |
$201.000834787$ |
$0$ |
$7$ |
| 12.0.153...477.1 |
$x^{12} - x^{11} + 66 x^{10} - 66 x^{9} + 1691 x^{8} - 1691 x^{7} + 21191 x^{6} - 21191 x^{5} + 134941 x^{4} - 134941 x^{3} + 419316 x^{2} - 419316 x + 622441$ |
$12$ |
(0, 6) |
$3^{6}\cdot 7^{6}\cdot 13^{11}$ |
$3$ |
$48.1087847964$ |
$48.10878479636254$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[2, 2, 146]$ |
$[2, 2, 146]$ |
$2$ |
$5$ |
$120.784031363$ |
$0$ |
$13$ |
| 12.12.187...125.1 |
$x^{12} - x^{11} - 45 x^{10} + 15 x^{9} + 661 x^{8} - 70 x^{7} - 3836 x^{6} + 660 x^{5} + 7876 x^{4} - 3890 x^{3} - 1930 x^{2} + 1489 x - 229$ |
$12$ |
(12, 0) |
$5^{9}\cdot 7^{6}\cdot 13^{8}$ |
$3$ |
$48.9108741572$ |
$48.91087415715005$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
trivial |
$[2, 2, 2]$ |
$2$ |
$11$ |
$1464478.29313$ |
$9$ |
$13$ |
| 12.0.863...248.1 |
$x^{12} + 91 x^{10} + 3185 x^{8} + 53508 x^{6} + 436982 x^{4} + 1529437 x^{2} + 1529437$ |
$12$ |
(0, 6) |
$2^{12}\cdot 7^{6}\cdot 13^{11}$ |
$3$ |
$55.5512397051$ |
$55.55123970513137$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[10, 130]$ |
$[10, 130]$ |
$2$ |
$5$ |
$120.784031363$ |
$0$ |
$13$ |
| 12.12.329...125.1 |
$x^{12} - x^{11} - 116 x^{10} + 116 x^{9} + 5149 x^{8} - 5149 x^{7} - 108575 x^{6} + 108575 x^{5} + 1085527 x^{4} - 1085527 x^{3} - 4287932 x^{2} + 4287932 x + 2620801$ |
$12$ |
(12, 0) |
$5^{6}\cdot 7^{6}\cdot 13^{11}$ |
$3$ |
$62.1081741075$ |
$62.108174107529564$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
$[2]$ |
$[2, 2, 2, 2]$ |
$2$ |
$11$ |
$2806966.20094$ |
$9$ |
$13$ |
| 12.12.316...125.1 |
$x^{12} - x^{11} - 120 x^{10} + 115 x^{9} + 4421 x^{8} - 4345 x^{7} - 64586 x^{6} + 60605 x^{5} + 372921 x^{4} - 296155 x^{3} - 701195 x^{2} + 386279 x - 49139$ |
$12$ |
(12, 0) |
$5^{9}\cdot 7^{6}\cdot 13^{10}$ |
$3$ |
$75.0002394905$ |
$75.00023949049753$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
$[2]$ |
$[2, 2, 2, 2]$ |
$2$ |
$11$ |
$14353015.8996$ |
$9$ |
$13$ |
| 12.0.405...000.1 |
$x^{12} + 93 x^{10} - 4 x^{9} + 3834 x^{8} + 36 x^{7} + 86663 x^{6} + 3672 x^{5} + 1136355 x^{4} + 125824 x^{3} + 8904264 x^{2} + 1547082 x + 31597721$ |
$12$ |
(0, 6) |
$2^{12}\cdot 3^{16}\cdot 5^{9}\cdot 7^{6}$ |
$4$ |
$76.5540535983$ |
$76.5540535982553$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[2, 2306]$ |
$[2, 2306]$ |
$2$ |
$5$ |
$201.000834787$ |
$0$ |
$7$ |
| 12.12.537...517.1 |
$x^{12} - 3 x^{11} - 81 x^{10} + 103 x^{9} + 2343 x^{8} + 264 x^{7} - 27030 x^{6} - 29388 x^{5} + 92934 x^{4} + 167050 x^{3} + 39348 x^{2} - 30711 x - 5113$ |
$12$ |
(12, 0) |
$3^{16}\cdot 7^{6}\cdot 13^{9}$ |
$3$ |
$78.3733132754$ |
$78.37331327541092$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
trivial |
$[2]$ |
$2$ |
$11$ |
$45900078.591$ |
$11$ |
$13$ |
| 12.0.552...872.1 |
$x^{12} + 182 x^{10} + 12740 x^{8} + 428064 x^{6} + 6991712 x^{4} + 48941984 x^{2} + 97883968$ |
$12$ |
(0, 6) |
$2^{18}\cdot 7^{6}\cdot 13^{11}$ |
$3$ |
$78.5613165976$ |
$78.56131659763557$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[38, 190]$ |
$[38, 190]$ |
$2$ |
$5$ |
$120.784031363$ |
$0$ |
$13$ |
| 12.12.552...872.1 |
$x^{12} - 182 x^{10} + 12740 x^{8} - 428064 x^{6} + 6991712 x^{4} - 48941984 x^{2} + 97883968$ |
$12$ |
(12, 0) |
$2^{18}\cdot 7^{6}\cdot 13^{11}$ |
$3$ |
$78.5613165976$ |
$78.56131659763557$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
$[10]$ |
$[2, 10]$ |
$2$ |
$11$ |
$2313184.68583$ |
$11$ |
$13$ |
| 12.0.136...125.1 |
$x^{12} - x^{11} + 60 x^{10} - 20 x^{9} + 1851 x^{8} + 910 x^{7} + 34804 x^{6} + 25020 x^{5} + 400191 x^{4} + 234775 x^{3} + 2982520 x^{2} + 1874059 x + 11467171$ |
$12$ |
(0, 6) |
$3^{6}\cdot 5^{9}\cdot 7^{6}\cdot 13^{8}$ |
$4$ |
$84.7161190828$ |
$84.71611908279147$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[2, 2, 2, 674]$ |
$[2, 2, 2, 674]$ |
$2$ |
$5$ |
$615.54450504$ |
$0$ |
$13$ |
| 12.12.195...125.1 |
$x^{12} - x^{11} - 69 x^{10} + 63 x^{9} + 1498 x^{8} - 1333 x^{7} - 11510 x^{6} + 7257 x^{5} + 32026 x^{4} - 16721 x^{3} - 31351 x^{2} + 14560 x + 5441$ |
$12$ |
(12, 0) |
$5^{9}\cdot 7^{6}\cdot 31^{8}$ |
$3$ |
$87.3006852202$ |
$87.30068522019472$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
trivial |
$[2]$ |
$2$ |
$11$ |
$37110834.0693$ |
$11$ |
$31$ |
| 12.12.364...000.1 |
$x^{12} - 210 x^{10} + 15435 x^{8} - 514500 x^{6} + 8103375 x^{4} - 56723625 x^{2} + 132355125$ |
$12$ |
(12, 0) |
$2^{12}\cdot 3^{18}\cdot 5^{9}\cdot 7^{6}$ |
$4$ |
$91.9365920347$ |
$91.93659203466923$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
$[2, 2]$ |
$[2, 2, 2]$ |
$2$ |
$11$ |
$10795763.9489$ |
$11$ |
$7$ |
| 12.0.373...293.1 |
$x^{12} - x^{11} + 248 x^{10} - 248 x^{9} + 23713 x^{8} - 23713 x^{7} + 1093717 x^{6} - 1093717 x^{5} + 24812139 x^{4} - 24812139 x^{3} + 250137148 x^{2} - 250137148 x + 861733601$ |
$12$ |
(0, 6) |
$7^{6}\cdot 11^{6}\cdot 13^{11}$ |
$3$ |
$92.1213093705$ |
$92.12130937050695$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[2, 16930]$ |
$[2, 16930]$ |
$2$ |
$5$ |
$120.784031363$ |
$0$ |
$13$ |
| 12.0.483...653.1 |
$x^{12} + 126 x^{10} - 139 x^{9} + 4491 x^{8} - 8943 x^{7} + 75688 x^{6} - 47997 x^{5} + 394032 x^{4} + 292656 x^{3} + 819162 x^{2} + 931563 x + 3255981$ |
$12$ |
(0, 6) |
$3^{18}\cdot 7^{6}\cdot 13^{9}$ |
$3$ |
$94.121408212$ |
$94.12140821202699$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[2, 2, 962]$ |
$[2, 2, 962]$ |
$2$ |
$5$ |
$1744.53950676$ |
$0$ |
$13$ |
| 12.0.600...713.1 |
$x^{12} - 3 x^{11} + 75 x^{10} - 132 x^{9} + 2661 x^{8} - 2733 x^{7} + 59179 x^{6} - 38283 x^{5} + 863829 x^{4} - 375395 x^{3} + 7241259 x^{2} - 1697166 x + 26129611$ |
$12$ |
(0, 6) |
$3^{16}\cdot 7^{6}\cdot 17^{9}$ |
$3$ |
$95.8401277638$ |
$95.84012776376548$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[2, 2, 818]$ |
$[2, 2, 818]$ |
$2$ |
$5$ |
$1868.05183797$ |
$0$ |
$17$ |
| 12.12.629...792.1 |
$x^{12} - 273 x^{10} + 28665 x^{8} - 1444716 x^{6} + 35395542 x^{4} - 371653191 x^{2} + 1114959573$ |
$12$ |
(12, 0) |
$2^{12}\cdot 3^{6}\cdot 7^{6}\cdot 13^{11}$ |
$4$ |
$96.2175695927$ |
$96.21756959272508$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
$[2, 2]$ |
$[2, 2, 2, 2]$ |
$2$ |
$11$ |
$13423777.933$ |
$10$ |
$13$ |
| 12.0.767...000.1 |
$x^{12} - 4 x^{11} + 95 x^{10} - 310 x^{9} + 4086 x^{8} - 9940 x^{7} + 95129 x^{6} - 167270 x^{5} + 1290821 x^{4} - 1290920 x^{3} + 10911490 x^{2} - 2712134 x + 42149801$ |
$12$ |
(0, 6) |
$2^{12}\cdot 5^{9}\cdot 7^{6}\cdot 13^{8}$ |
$4$ |
$97.8217483143$ |
$97.8217483143001$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[2, 2, 2, 2402]$ |
$[2, 2, 2, 2402]$ |
$2$ |
$5$ |
$615.54450504$ |
$0$ |
$13$ |
| 12.12.807...125.1 |
$x^{12} - x^{11} - 77 x^{10} - 9 x^{9} + 1939 x^{8} + 1192 x^{7} - 18668 x^{6} - 8224 x^{5} + 78090 x^{4} + 3434 x^{3} - 110290 x^{2} + 15653 x + 23111$ |
$12$ |
(12, 0) |
$5^{9}\cdot 7^{6}\cdot 37^{8}$ |
$3$ |
$98.2300441638$ |
$98.23004416381879$ |
|
✓ |
|
$C_{12}$ (as 12T1) |
trivial |
$[2]$ |
$2$ |
$11$ |
$167516541.331$ |
$11$ |
$37$ |
| 12.0.240...125.1 |
$x^{12} - x^{11} + 339 x^{10} - 339 x^{9} + 44279 x^{8} - 44279 x^{7} + 2786135 x^{6} - 2786135 x^{5} + 85955767 x^{4} - 85955767 x^{3} + 1167160983 x^{2} - 1167160983 x + 5183066071$ |
$12$ |
(0, 6) |
$3^{6}\cdot 5^{6}\cdot 7^{6}\cdot 13^{11}$ |
$4$ |
$107.57451312$ |
$107.57451311957502$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[2, 2, 2, 2, 4, 1588]$ |
$[2, 2, 2, 2, 4, 1588]$ |
$2$ |
$5$ |
$120.784031363$ |
$0$ |
$13$ |
| 12.0.259...000.1 |
$x^{12} + 198 x^{10} - 4 x^{9} + 16434 x^{8} + 36 x^{7} + 721738 x^{6} + 16272 x^{5} + 17720895 x^{4} + 980664 x^{3} + 239556504 x^{2} + 20795892 x + 1409004451$ |
$12$ |
(0, 6) |
$2^{18}\cdot 3^{16}\cdot 5^{9}\cdot 7^{6}$ |
$4$ |
$108.263780853$ |
$108.26378085328948$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[2, 31330]$ |
$[2, 31330]$ |
$2$ |
$5$ |
$201.000834787$ |
$0$ |
$7$ |
| 12.12.259...000.1 |
$x^{12} - 222 x^{10} - 4 x^{9} + 18954 x^{8} + 36 x^{7} - 792502 x^{6} + 18792 x^{5} + 16906515 x^{4} - 945176 x^{3} - 170001876 x^{2} + 14201892 x + 594583991$ |
$12$ |
(12, 0) |
$2^{18}\cdot 3^{16}\cdot 5^{9}\cdot 7^{6}$ |
$4$ |
$108.263780853$ |
$108.26378085328948$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
$[2]$ |
$[2, 2]$ |
$2$ |
$11$ |
$74290561.6871$ |
$11$ |
$7$ |
| 12.12.268...125.1 |
$x^{12} - x^{11} - 85 x^{10} + 7 x^{9} + 2362 x^{8} + 867 x^{7} - 25542 x^{6} - 9023 x^{5} + 119662 x^{4} + 19979 x^{3} - 204203 x^{2} + 13476 x + 1661$ |
$12$ |
(12, 0) |
$5^{9}\cdot 7^{6}\cdot 43^{8}$ |
$3$ |
$108.581414174$ |
$108.58141417376535$ |
|
✓ |
|
$C_{12}$ (as 12T1) |
trivial |
$[2]$ |
$2$ |
$11$ |
$453618701.983$ |
$11$ |
$43$ |
| 12.12.508...397.1 |
$x^{12} - x^{11} - 389 x^{10} + 389 x^{9} + 58111 x^{8} - 58111 x^{7} - 4153889 x^{6} + 4153889 x^{5} + 143266111 x^{4} - 143266111 x^{3} - 2068033889 x^{2} + 2068033889 x + 7408966111$ |
$12$ |
(12, 0) |
$7^{6}\cdot 13^{11}\cdot 17^{6}$ |
$3$ |
$114.521814469$ |
$114.52181446913116$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
$[2, 4]$ |
$[2, 2, 4]$ |
$2$ |
$11$ |
$27949318.0699$ |
$11$ |
$17$ |
| 12.12.511...989.1 |
$x^{12} - x^{11} - 119 x^{10} + 111 x^{9} + 3765 x^{8} - 441 x^{7} - 40423 x^{6} - 11147 x^{5} + 166214 x^{4} + 82434 x^{3} - 218376 x^{2} - 159894 x - 19683$ |
$12$ |
(12, 0) |
$7^{6}\cdot 61^{11}$ |
$2$ |
$114.578034707$ |
$114.57803470701889$ |
|
✓ |
|
$C_{12}$ (as 12T1) |
$[5]$ |
$[10]$ |
$2$ |
$11$ |
$4054993494.0$ |
$11$ |
$61$ |
| 12.12.540...417.1 |
$x^{12} - 192 x^{10} - 86 x^{9} + 13518 x^{8} + 10038 x^{7} - 427924 x^{6} - 356058 x^{5} + 5983365 x^{4} + 3873152 x^{3} - 30810276 x^{2} - 9405162 x + 12747043$ |
$12$ |
(12, 0) |
$3^{18}\cdot 7^{6}\cdot 17^{9}$ |
$3$ |
$115.09795122$ |
$115.09795122029558$ |
|
✓ |
|
$C_{12}$ (as 12T1) |
$[2]$ |
$[2, 2, 2, 2]$ |
$2$ |
$11$ |
$371738754.767$ |
$9$ |
$17$ |
| 12.12.907...373.1 |
$x^{12} - 3 x^{11} - 147 x^{10} + 181 x^{9} + 6048 x^{8} - 8823 x^{7} - 97200 x^{6} + 207711 x^{5} + 486144 x^{4} - 1597571 x^{3} + 529779 x^{2} + 1662600 x - 1223767$ |
$12$ |
(12, 0) |
$3^{16}\cdot 7^{6}\cdot 13^{11}$ |
$3$ |
$120.178127392$ |
$120.17812739215435$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
$[3]$ |
$[6]$ |
$2$ |
$11$ |
$204157817.642$ |
$11$ |
$13$ |
| 12.0.991...453.1 |
$x^{12} - x^{11} + 430 x^{10} - 430 x^{9} + 71215 x^{8} - 71215 x^{7} + 5677387 x^{6} - 5677387 x^{5} + 221515009 x^{4} - 221515009 x^{3} + 3782835772 x^{2} - 3782835772 x + 20571919369$ |
$12$ |
(0, 6) |
$7^{6}\cdot 13^{11}\cdot 19^{6}$ |
$3$ |
$121.071120032$ |
$121.07112003153593$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[2, 50866]$ |
$[2, 50866]$ |
$2$ |
$5$ |
$120.784031363$ |
$0$ |
$19$ |
| 12.0.113...713.1 |
$x^{12} - x^{11} + 66 x^{10} - 109 x^{9} + 2468 x^{8} - 3963 x^{7} + 59792 x^{6} - 70408 x^{5} + 956959 x^{4} - 604359 x^{3} + 8687928 x^{2} - 2044686 x + 33557129$ |
$12$ |
(0, 6) |
$7^{6}\cdot 13^{8}\cdot 17^{9}$ |
$3$ |
$122.465740426$ |
$122.46574042594001$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[4562]$ |
$[4562]$ |
$2$ |
$5$ |
$3407.79685773$ |
$0$ |
$17$ |
| 12.0.134...000.1 |
$x^{12} + 455 x^{10} + 79625 x^{8} + 6688500 x^{6} + 273113750 x^{4} + 4779490625 x^{2} + 23897453125$ |
$12$ |
(0, 6) |
$2^{12}\cdot 5^{6}\cdot 7^{6}\cdot 13^{11}$ |
$4$ |
$124.216348215$ |
$124.21634821505913$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[2, 2, 2, 2, 11290]$ |
$[2, 2, 2, 2, 11290]$ |
$2$ |
$5$ |
$120.784031363$ |
$0$ |
$13$ |
| 12.0.175...125.1 |
$x^{12} - 3 x^{11} + 279 x^{10} - 831 x^{9} + 32505 x^{8} - 91308 x^{7} + 2005158 x^{6} - 4813584 x^{5} + 68420724 x^{4} - 119458244 x^{3} + 1226604198 x^{2} - 1176569685 x + 9174406301$ |
$12$ |
(0, 6) |
$3^{16}\cdot 5^{9}\cdot 7^{6}\cdot 11^{6}$ |
$4$ |
$126.950535983$ |
$126.95053598308475$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[2, 2, 28564]$ |
$[2, 2, 28564]$ |
$2$ |
$5$ |
$201.000834787$ |
$0$ |
$11$ |
| 12.0.230...125.1 |
$x^{12} - x^{11} + 335 x^{10} - 340 x^{9} + 32176 x^{8} - 37105 x^{7} + 1189849 x^{6} - 1265720 x^{5} + 20941196 x^{4} - 8812845 x^{3} + 183520115 x^{2} + 36616109 x + 788284771$ |
$12$ |
(0, 6) |
$3^{6}\cdot 5^{9}\cdot 7^{6}\cdot 13^{10}$ |
$4$ |
$129.904225377$ |
$129.90422537737544$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[2, 2, 2, 18, 666]$ |
$[2, 2, 2, 18, 666]$ |
$2$ |
$5$ |
$615.54450504$ |
$0$ |
$13$ |
| 12.0.233...000.1 |
$x^{12} + 420 x^{10} + 61740 x^{8} + 4116000 x^{6} + 129654000 x^{4} + 1815156000 x^{2} + 8470728000$ |
$12$ |
(0, 6) |
$2^{18}\cdot 3^{18}\cdot 5^{9}\cdot 7^{6}$ |
$4$ |
$130.017975334$ |
$130.01797533379147$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[2, 2, 31090]$ |
$[2, 2, 31090]$ |
$2$ |
$5$ |
$201.000834787$ |
$0$ |
$7$ |
| 12.12.233...000.1 |
$x^{12} - 420 x^{10} + 61740 x^{8} - 4116000 x^{6} + 129654000 x^{4} - 1815156000 x^{2} + 8470728000$ |
$12$ |
(12, 0) |
$2^{18}\cdot 3^{18}\cdot 5^{9}\cdot 7^{6}$ |
$4$ |
$130.017975334$ |
$130.01797533379147$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
$[2, 2]$ |
$[2, 2, 2]$ |
$2$ |
$11$ |
$209356404.388$ |
$11$ |
$7$ |
| 12.0.312...557.1 |
$x^{12} - x^{11} + 521 x^{10} - 521 x^{9} + 104521 x^{8} - 104521 x^{7} + 10088521 x^{6} - 10088521 x^{5} + 476008521 x^{4} - 476008521 x^{3} + 9794408521 x^{2} - 9794408521 x + 63042408521$ |
$12$ |
(0, 6) |
$7^{6}\cdot 13^{11}\cdot 23^{6}$ |
$3$ |
$133.207193268$ |
$133.20719326848513$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[2, 2, 47890]$ |
$[2, 2, 47890]$ |
$2$ |
$5$ |
$120.784031363$ |
$0$ |
$23$ |
| 12.12.402...688.1 |
$x^{12} - 546 x^{10} + 114660 x^{8} - 11557728 x^{6} + 566328672 x^{4} - 11892902112 x^{2} + 71357412672$ |
$12$ |
(12, 0) |
$2^{18}\cdot 3^{6}\cdot 7^{6}\cdot 13^{11}$ |
$4$ |
$136.072191857$ |
$136.07219185660892$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
$[2, 2]$ |
$[2, 2, 2, 2]$ |
$2$ |
$11$ |
$135584001.874$ |
$10$ |
$13$ |
| 12.0.402...688.1 |
$x^{12} + 546 x^{10} + 114660 x^{8} + 11557728 x^{6} + 566328672 x^{4} + 11892902112 x^{2} + 71357412672$ |
$12$ |
(0, 6) |
$2^{18}\cdot 3^{6}\cdot 7^{6}\cdot 13^{11}$ |
$4$ |
$136.072191857$ |
$136.07219185660892$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[2, 2, 4, 22664]$ |
$[2, 2, 4, 22664]$ |
$2$ |
$5$ |
$120.784031363$ |
$0$ |
$13$ |
| 12.12.440...125.1 |
$x^{12} - x^{11} - 109 x^{10} + 87 x^{9} + 3895 x^{8} - 2916 x^{7} - 54548 x^{6} + 34528 x^{5} + 328494 x^{4} - 126798 x^{3} - 857098 x^{2} + 97405 x + 720071$ |
$12$ |
(12, 0) |
$5^{9}\cdot 7^{6}\cdot 61^{8}$ |
$3$ |
$137.087044443$ |
$137.08704444287918$ |
|
✓ |
|
$C_{12}$ (as 12T1) |
$[13]$ |
$[26]$ |
$2$ |
$11$ |
$102325460.015$ |
$11$ |
$61$ |
| 12.12.477...125.1 |
$x^{12} - 3 x^{11} - 351 x^{10} + 1051 x^{9} + 47643 x^{8} - 135984 x^{7} - 3183480 x^{6} + 8060604 x^{5} + 110156256 x^{4} - 219107728 x^{3} - 1866768084 x^{2} + 2189145765 x + 12060450271$ |
$12$ |
(12, 0) |
$3^{16}\cdot 5^{9}\cdot 7^{6}\cdot 13^{6}$ |
$4$ |
$138.009782797$ |
$138.009782796564$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
$[2]$ |
$[2, 2]$ |
$2$ |
$11$ |
$227673592.327$ |
$11$ |
$13$ |
| 12.0.491...000.1 |
$x^{12} - 4 x^{11} + 200 x^{10} - 660 x^{9} + 16931 x^{8} - 43260 x^{7} + 758414 x^{6} - 1412640 x^{5} + 19054056 x^{4} - 21995940 x^{3} + 268525140 x^{2} - 120274404 x + 1673373521$ |
$12$ |
(0, 6) |
$2^{18}\cdot 5^{9}\cdot 7^{6}\cdot 13^{8}$ |
$4$ |
$138.340843161$ |
$138.34084316113064$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[2, 2, 2, 19930]$ |
$[2, 2, 2, 19930]$ |
$2$ |
$5$ |
$615.54450504$ |
$0$ |
$13$ |
| 12.12.491...000.1 |
$x^{12} - 4 x^{11} - 220 x^{10} + 740 x^{9} + 18471 x^{8} - 51100 x^{7} - 751066 x^{6} + 1628440 x^{5} + 15350636 x^{4} - 23965460 x^{3} - 144223700 x^{2} + 132979156 x + 445705961$ |
$12$ |
(12, 0) |
$2^{18}\cdot 5^{9}\cdot 7^{6}\cdot 13^{8}$ |
$4$ |
$138.340843161$ |
$138.34084316113064$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
$[2]$ |
$[2, 2, 2, 2]$ |
$2$ |
$11$ |
$470247789.115$ |
$9$ |
$13$ |
| 12.0.816...357.2 |
$x^{12} + 117 x^{10} - 130 x^{9} + 3978 x^{8} + 3198 x^{7} + 36790 x^{6} + 127179 x^{5} + 185601 x^{4} + 966459 x^{3} + 3601026 x^{2} - 4045977 x + 14063127$ |
$12$ |
(0, 6) |
$3^{18}\cdot 7^{6}\cdot 13^{11}$ |
$3$ |
$144.326354389$ |
$144.3263543890876$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[2, 2, 1374]$ |
$[2, 2, 1374]$ |
$2$ |
$5$ |
$16557.8683169$ |
$0$ |
$13$ |
| 12.12.933...125.1 |
$x^{12} - x^{11} - 117 x^{10} + 35 x^{9} + 4561 x^{8} + 530 x^{7} - 71578 x^{6} - 23592 x^{5} + 494106 x^{4} + 230160 x^{3} - 1344720 x^{2} - 700035 x + 654595$ |
$12$ |
(12, 0) |
$5^{9}\cdot 7^{6}\cdot 67^{8}$ |
$3$ |
$145.935088245$ |
$145.93508824473827$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
trivial |
$[2, 2, 2]$ |
$2$ |
$11$ |
$1551159953.66$ |
$9$ |
$67$ |
| 12.12.125...173.1 |
$x^{12} - x^{11} - 662 x^{10} + 662 x^{9} + 168403 x^{8} - 168403 x^{7} - 20525153 x^{6} + 20525153 x^{5} + 1210741429 x^{4} - 1210741429 x^{3} - 30186556412 x^{2} + 30186556412 x + 198565185001$ |
$12$ |
(12, 0) |
$7^{6}\cdot 13^{11}\cdot 29^{6}$ |
$3$ |
$149.576290526$ |
$149.5762905263832$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
$[2, 2]$ |
$[2, 2, 4]$ |
$2$ |
$11$ |
$304406914.477$ |
$10$ |
$29$ |
| 12.0.219...632.1 |
$x^{12} + 261 x^{10} - 4 x^{9} + 25170 x^{8} + 36 x^{7} + 1020463 x^{6} - 20856 x^{5} + 14573331 x^{4} - 70512 x^{3} + 132597792 x^{2} + 32672106 x + 538607889$ |
$12$ |
(0, 6) |
$2^{12}\cdot 3^{16}\cdot 7^{6}\cdot 13^{9}$ |
$4$ |
$156.746626551$ |
$156.74662655082184$ |
✓ |
✓ |
|
$C_{12}$ (as 12T1) |
$[30, 14430]$ |
$[30, 14430]$ |
$2$ |
$5$ |
$1744.539506763238$ |
$0$ |
$13$ |
| 12.0.841...697.1 |
$x^{12} - x^{11} + 150 x^{10} - 171 x^{9} + 9726 x^{8} - 4556 x^{7} + 346803 x^{6} + 138223 x^{5} + 6995921 x^{4} + 7768425 x^{3} + 77264521 x^{2} + 85568226 x + 408841883$ |
$12$ |
(0, 6) |
$7^{6}\cdot 97^{11}$ |
$2$ |
$175.289718295$ |
$175.28971829540143$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[8138]$ |
$[8138]$ |
$2$ |
$5$ |
$20745.972038718897$ |
$0$ |
$97$ |
| 12.12.181...696.1 |
$x^{12} - 364 x^{10} + 47138 x^{8} - 2604056 x^{6} + 55683992 x^{4} - 251701632 x^{2} + 305887400$ |
$12$ |
(12, 0) |
$2^{33}\cdot 7^{6}\cdot 13^{11}$ |
$3$ |
$186.851353324$ |
$186.85135332377914$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
$[4]$ |
$[2, 4]$ |
$2$ |
$11$ |
$1247757812.8824928$ |
$11$ |
$13$ |
