| 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 |
| 12.4.7556814453125.1 |
$x^{12} - 2 x^{11} - 5 x^{10} + 9 x^{9} + 10 x^{8} - 14 x^{7} - 3 x^{6} + 2 x^{5} - 6 x^{4} + 6 x^{3} - 2 x^{2} + 4 x + 1$ |
$12$ |
[4,4] |
$5^{9}\cdot 7^{2}\cdot 281^{2}$ |
$3$ |
$11.8357258363$ |
$148.29608409769435$ |
|
|
? |
$S_4^2:C_4$ (as 12T237) |
trivial |
$[2]$ |
$2$ |
$7$ |
$46.1267786085$ |
| 12.4.11278142578125.1 |
$x^{12} - x^{11} - 4 x^{10} + 7 x^{9} - 11 x^{7} + 7 x^{6} + 8 x^{5} - 6 x^{4} + 2 x^{3} + 17 x^{2} + 10 x + 1$ |
$12$ |
[4,4] |
$3^{6}\cdot 5^{9}\cdot 89^{2}$ |
$3$ |
$12.2373241781$ |
$54.63653310709071$ |
|
|
? |
$S_3^2:C_4$ (as 12T79) |
trivial |
$[2]$ |
$2$ |
$7$ |
$60.3421704761$ |
| 12.8.51942673828125.1 |
$x^{12} - 2 x^{11} - 6 x^{10} + 11 x^{9} + 15 x^{8} - 17 x^{7} - 27 x^{6} + 4 x^{5} + 29 x^{4} + 4 x^{3} - 12 x^{2} + 1$ |
$12$ |
[8,2] |
$3^{6}\cdot 5^{9}\cdot 191^{2}$ |
$3$ |
$13.8982576497$ |
$80.03958242980093$ |
|
|
? |
$S_3^2:C_4$ (as 12T79) |
trivial |
$[2]$ |
$2$ |
$9$ |
$245.622566038$ |
| 12.2.55916310546875.1 |
$x^{12} - 4 x^{11} + 8 x^{10} - 9 x^{9} - 2 x^{8} + 2 x^{7} + 29 x^{6} - 39 x^{5} + x^{4} + 2 x^{3} + 8 x^{2} + 3 x - 9$ |
$12$ |
[2,5] |
$-\,5^{9}\cdot 31^{5}$ |
$2$ |
$13.9838967604$ |
$18.616942190179014$ |
|
|
|
$D_{12}$ (as 12T12) |
trivial |
$[2]$ |
$2$ |
$6$ |
$133.406775563$ |
| 12.2.80525500000000.1 |
$x^{12} - 3 x^{11} + 3 x^{10} + 8 x^{9} - 9 x^{8} - x^{7} + 14 x^{6} + 3 x^{5} + 3 x^{4} + 24 x^{3} + 23 x^{2} + 9 x + 1$ |
$12$ |
[2,5] |
$-\,2^{8}\cdot 5^{9}\cdot 11^{5}$ |
$3$ |
$14.4154361172$ |
$17.603965534028475$ |
|
|
|
$D_{12}$ (as 12T12) |
trivial |
$[2]$ |
$2$ |
$6$ |
$165.101772087$ |
| 12.8.264764548828125.1 |
$x^{12} - 3 x^{11} - 3 x^{10} + 13 x^{9} + 3 x^{8} - 16 x^{7} - 19 x^{6} + 23 x^{5} + 41 x^{4} - 61 x^{3} - 3 x^{2} + 44 x - 19$ |
$12$ |
[8,2] |
$3^{2}\cdot 5^{9}\cdot 3881^{2}$ |
$3$ |
$15.9186042579$ |
$360.7945361423178$ |
|
|
? |
$S_4^2:C_4$ (as 12T237) |
trivial |
$[2]$ |
$2$ |
$9$ |
$628.571652529$ |
| 12.8.326521931640625.1 |
$x^{12} - 3 x^{11} - 2 x^{10} + 7 x^{9} - 3 x^{8} + 24 x^{7} - 18 x^{6} - 19 x^{5} + 22 x^{4} - 21 x^{3} + 20 x^{2} - 8 x + 1$ |
$12$ |
[8,2] |
$5^{9}\cdot 7^{8}\cdot 29$ |
$3$ |
$16.199167513483026$ |
$65.8908629733479$ |
|
|
? |
$C_2\wr C_6$ (as 12T134) |
trivial |
$[2]$ |
$2$ |
$9$ |
$659.3786067574857$ |
| 12.12.551709470703125.1 |
$x^{12} - x^{11} - 12 x^{10} + 11 x^{9} + 54 x^{8} - 43 x^{7} - 113 x^{6} + 71 x^{5} + 110 x^{4} - 46 x^{3} - 40 x^{2} + 8 x + 1$ |
$12$ |
[12,0] |
$5^{9}\cdot 7^{10}$ |
$2$ |
$16.9229421535$ |
$16.9229421535458$ |
|
✓ |
✓ |
$C_{12}$ (as 12T1) |
trivial |
$[2]$ |
$2$ |
$11$ |
$1656.08671936$ |
| 12.12.756680642578125.1 |
$x^{12} - 12 x^{10} - x^{9} + 54 x^{8} + 9 x^{7} - 112 x^{6} - 27 x^{5} + 105 x^{4} + 31 x^{3} - 36 x^{2} - 12 x + 1$ |
$12$ |
[12,0] |
$3^{18}\cdot 5^{9}$ |
$2$ |
$17.3743827793$ |
$17.374382779324037$ |
|
✓ |
✓ |
$C_{12}$ (as 12T1) |
trivial |
$[2]$ |
$2$ |
$11$ |
$2075.03148059$ |
| 12.2.839808000000000.1 |
$x^{12} - 2 x^{11} + 3 x^{10} - 8 x^{9} + 16 x^{8} - 34 x^{7} + 29 x^{6} - 8 x^{5} + 8 x^{4} - 14 x^{3} + 3 x^{2} - 4 x + 1$ |
$12$ |
[2,5] |
$-\,2^{16}\cdot 3^{8}\cdot 5^{9}$ |
$3$ |
$17.5259539923$ |
$43.49515732752436$ |
|
|
|
$(C_3^2\times S_3^2):C_4$ (as 12T209) |
trivial |
$[2]$ |
$2$ |
$6$ |
$744.690680414$ |
| 12.0.885780500000000.1 |
$x^{12} - x^{11} - 2 x^{10} + 11 x^{9} + 4 x^{8} - 43 x^{7} + 17 x^{6} + 66 x^{5} - 90 x^{4} - 6 x^{3} + 100 x^{2} - 72 x + 16$ |
$12$ |
[0,6] |
$2^{8}\cdot 5^{9}\cdot 11^{6}$ |
$3$ |
$17.603965534$ |
$17.603965534028475$ |
|
|
? |
$D_{12}$ (as 12T12) |
$[4]$ |
$[4]$ |
$2$ |
$5$ |
$343.095833247$ |
| 12.0.1733405626953125.1 |
$x^{12} - 4 x^{11} + 12 x^{10} - 14 x^{9} - 4 x^{8} + 37 x^{7} - 44 x^{6} - 54 x^{5} + 268 x^{4} - 428 x^{3} + 402 x^{2} - 252 x + 81$ |
$12$ |
[0,6] |
$5^{9}\cdot 31^{6}$ |
$2$ |
$18.6169421902$ |
$18.616942190179014$ |
|
|
|
$D_{12}$ (as 12T12) |
$[4]$ |
$[4]$ |
$2$ |
$5$ |
$277.230875502$ |
| 12.8.3192864500000000.1 |
$x^{12} - 5 x^{11} + 2 x^{10} + 18 x^{9} - 41 x^{8} + 52 x^{7} + 7 x^{6} - 114 x^{5} + 105 x^{4} - 2 x^{3} - 24 x^{2} + x + 1$ |
$12$ |
[8,2] |
$2^{8}\cdot 5^{9}\cdot 7^{2}\cdot 19^{4}$ |
$4$ |
$19.5891251427$ |
$99.99207658219244$ |
|
|
? |
$A_4^2:C_4$ (as 12T159) |
trivial |
$[2]$ |
$2$ |
$9$ |
$2293.41440984$ |
| 12.8.3531579275390625.1 |
$x^{12} - 7 x^{10} - 4 x^{9} + 14 x^{8} + 21 x^{7} - 2 x^{6} - 28 x^{5} - 20 x^{4} + 4 x^{3} + 14 x^{2} + 7 x + 1$ |
$12$ |
[8,2] |
$3^{6}\cdot 5^{9}\cdot 29\cdot 31^{2}\cdot 89$ |
$5$ |
$19.7544107603$ |
$1638.1851312400668$ |
|
|
✓ |
$S_3\wr C_4$ (as 12T264) |
trivial |
$[2]$ |
$2$ |
$9$ |
$2512.55345376$ |
| 12.12.4663778923828125.1 |
$x^{12} - x^{11} - 12 x^{10} + 9 x^{9} + 53 x^{8} - 27 x^{7} - 106 x^{6} + 34 x^{5} + 96 x^{4} - 17 x^{3} - 32 x^{2} + 2 x + 1$ |
$12$ |
[12,0] |
$3^{6}\cdot 5^{9}\cdot 29\cdot 179\cdot 631$ |
$5$ |
$20.2175331069$ |
$10481.617922149297$ |
|
|
✓ |
$S_3\wr C_4$ (as 12T264) |
trivial |
$[2]$ |
$2$ |
$11$ |
$5490.17233206$ |
| 12.12.4961330525390625.1 |
$x^{12} - 5 x^{11} - x^{10} + 34 x^{9} - 19 x^{8} - 83 x^{7} + 50 x^{6} + 92 x^{5} - 37 x^{4} - 47 x^{3} + 6 x^{2} + 9 x + 1$ |
$12$ |
[12,0] |
$3^{6}\cdot 5^{9}\cdot 3484501$ |
$3$ |
$20.3220031059$ |
$10810.814796072955$ |
|
|
✓ |
$S_3\wr C_4$ (as 12T264) |
trivial |
$[2]$ |
$2$ |
$11$ |
$5929.96351848$ |
| 12.12.8208085798828125.1 |
$x^{12} - x^{11} - 22 x^{10} + 14 x^{9} + 153 x^{8} - 62 x^{7} - 396 x^{6} + 84 x^{5} + 361 x^{4} - 87 x^{3} - 112 x^{2} + 37 x + 1$ |
$12$ |
[12,0] |
$3^{6}\cdot 5^{9}\cdot 7^{8}$ |
$3$ |
$21.1927260375$ |
$21.192726037501743$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
trivial |
$[2]$ |
$2$ |
$11$ |
$7868.47835349$ |
| 12.8.9138614080078125.1 |
$x^{12} - x^{11} - 3 x^{10} + 9 x^{9} - 9 x^{8} - 32 x^{7} + 21 x^{6} + 59 x^{5} + 8 x^{4} - 42 x^{3} - 23 x^{2} + 2 x + 1$ |
$12$ |
[8,2] |
$3^{2}\cdot 5^{9}\cdot 151^{4}$ |
$3$ |
$21.3832326676$ |
$164.22505984760411$ |
|
|
? |
$A_4^2:C_4$ (as 12T159) |
trivial |
$[2]$ |
$2$ |
$9$ |
$5403.8323885$ |
| 12.12.21445928455078125.1 |
$x^{12} - 3 x^{11} - 18 x^{10} + 52 x^{9} + 94 x^{8} - 279 x^{7} - 122 x^{6} + 452 x^{5} + 25 x^{4} - 228 x^{3} + 30 x^{2} + 36 x - 9$ |
$12$ |
[12,0] |
$3^{6}\cdot 5^{9}\cdot 3881^{2}$ |
$3$ |
$22.9586001509$ |
$360.7945361423178$ |
|
|
? |
$S_3^2:C_4$ (as 12T79) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$13482.0819399$ |
| 12.12.26436901658203125.1 |
$x^{12} - 2 x^{11} - 17 x^{10} + 28 x^{9} + 102 x^{8} - 114 x^{7} - 268 x^{6} + 144 x^{5} + 252 x^{4} - 54 x^{3} - 55 x^{2} - 2 x + 1$ |
$12$ |
[12,0] |
$3^{6}\cdot 5^{9}\cdot 31^{2}\cdot 139^{2}$ |
$4$ |
$23.3624048871$ |
$380.1687174475287$ |
|
|
? |
$S_3^2:C_4$ (as 12T79) |
trivial |
$[2]$ |
$2$ |
$11$ |
$16295.3925214$ |
| 12.4.42684757595703125.1 |
$x^{12} - x^{11} - 2 x^{10} + 9 x^{9} - 7 x^{8} - 12 x^{7} + 24 x^{6} - x^{5} - 14 x^{4} - 7 x^{3} + 3 x^{2} + 7 x + 1$ |
$12$ |
[4,4] |
$5^{9}\cdot 7^{6}\cdot 431^{2}$ |
$3$ |
$24.3139807369$ |
$183.6602445838084$ |
|
|
? |
$A_5^2:C_4$ (as 12T278) |
$[2]$ |
$[2, 4]$ |
$2$ |
$7$ |
$1929.27333365$ |
| 12.12.47502004500000000.1 |
$x^{12} - x^{11} - 23 x^{10} + 19 x^{9} + 161 x^{8} - 122 x^{7} - 369 x^{6} + 334 x^{5} + 163 x^{4} - 167 x^{3} - 8 x^{2} + 12 x + 1$ |
$12$ |
[12,0] |
$2^{8}\cdot 3^{6}\cdot 5^{9}\cdot 19^{4}$ |
$4$ |
$24.5316067795$ |
$65.46017997624544$ |
|
|
? |
$C_3\times (C_3 : C_4)$ (as 12T19) |
trivial |
$[2]$ |
$2$ |
$11$ |
$20063.9174821$ |
| 12.8.62306284500000000.1 |
$x^{12} - 3 x^{11} + 7 x^{10} + 13 x^{9} - 77 x^{8} + 4 x^{7} + 161 x^{6} - 72 x^{5} - 89 x^{4} + 109 x^{3} + 22 x^{2} - 16 x + 1$ |
$12$ |
[8,2] |
$2^{8}\cdot 3^{2}\cdot 5^{9}\cdot 61^{4}$ |
$4$ |
$25.09252243677443$ |
$142.4605722057373$ |
|
|
? |
$A_4^2:C_4$ (as 12T159) |
trivial |
$[2]$ |
$2$ |
$9$ |
$13534.481903374366$ |
| 12.8.193710244500000000.2 |
$x^{12} - 3 x^{10} - 2 x^{9} - 36 x^{8} - 48 x^{7} + 92 x^{6} + 216 x^{5} + 225 x^{4} + 248 x^{3} + 216 x^{2} + 96 x + 16$ |
$12$ |
[8,2] |
$2^{8}\cdot 3^{18}\cdot 5^{9}$ |
$3$ |
$27.5801135012$ |
$93.94537035861741$ |
|
|
? |
$C_3:S_3^3:C_4$ (as 12T245) |
trivial |
$[2, 2]$ |
$2$ |
$9$ |
$19433.1189468$ |
| 12.8.289369624500000000.1 |
$x^{12} - 3 x^{11} + 9 x^{10} + 19 x^{9} - 75 x^{8} + 192 x^{7} - 187 x^{6} - 204 x^{5} + 279 x^{4} + 11 x^{3} - 42 x^{2} + 1$ |
$12$ |
[8,2] |
$2^{8}\cdot 3^{14}\cdot 5^{9}\cdot 11^{2}$ |
$4$ |
$28.51813223118492$ |
$171.55158998906003$ |
|
|
? |
$C_3:S_3^3:C_4$ (as 12T245) |
trivial |
$[2]$ |
$2$ |
$9$ |
$23766.397630604413$ |
| 12.0.300342961072265625.2 |
$x^{12} - 5 x^{11} + 19 x^{10} - 54 x^{9} + 116 x^{8} - 217 x^{7} + 305 x^{6} - 297 x^{5} + 258 x^{4} - 238 x^{3} + 221 x^{2} - 109 x + 41$ |
$12$ |
[0,6] |
$3^{8}\cdot 5^{9}\cdot 29^{3}\cdot 31^{2}$ |
$4$ |
$28.6067237118$ |
$817.2144566356151$ |
|
|
|
$(C_3^2\times S_3^2):C_4$ (as 12T209) |
$[2]$ |
$[2]$ |
$2$ |
$5$ |
$5193.55523784$ |
| 12.0.435848050125000000.1 |
$x^{12} + 3 x^{10} - x^{9} - 21 x^{8} + 84 x^{7} - 12 x^{6} + 318 x^{5} + 285 x^{4} - 1184 x^{3} + 1149 x^{2} - 1137 x + 971$ |
$12$ |
[0,6] |
$2^{6}\cdot 3^{20}\cdot 5^{9}$ |
$3$ |
$29.508327325118774$ |
$37.4222358010528$ |
|
|
? |
$C_3\times S_4$ (as 12T45) |
$[8]$ |
$[8]$ |
$2$ |
$5$ |
$1362.5474857609888$ |
| 12.8.123...625.1 |
$x^{12} - x^{11} - 14 x^{10} + 37 x^{9} - 20 x^{8} - 276 x^{7} + 87 x^{6} + 408 x^{5} + 69 x^{4} + 72 x^{3} - 143 x^{2} - 120 x + 16$ |
$12$ |
[8,2] |
$5^{9}\cdot 229^{5}$ |
$2$ |
$32.1730539751$ |
$50.59938571007813$ |
|
|
|
$C_4:S_4$ (as 12T54) |
$[2]$ |
$[2, 2]$ |
$2$ |
$9$ |
$37171.8222915$ |
| 12.0.225...000.1 |
$x^{12} + 35 x^{10} + 455 x^{8} + 2800 x^{6} + 8575 x^{4} + 12250 x^{2} + 6125$ |
$12$ |
[0,6] |
$2^{12}\cdot 5^{9}\cdot 7^{10}$ |
$3$ |
$33.8458843071$ |
$33.8458843070916$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[2, 26]$ |
$[2, 26]$ |
$2$ |
$5$ |
$104.882003477$ |
| 12.12.241...125.1 |
$x^{12} - 3 x^{11} - 28 x^{10} + 98 x^{9} + 233 x^{8} - 1071 x^{7} - 374 x^{6} + 4658 x^{5} - 2354 x^{4} - 7196 x^{3} + 6782 x^{2} + 1684 x - 2399$ |
$12$ |
[12,0] |
$3^{6}\cdot 5^{9}\cdot 7^{4}\cdot 29^{4}$ |
$4$ |
$34.0371725724$ |
$144.63358437489208$ |
|
|
? |
$C_6.D_6$ (as 12T39) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$163746.298789$ |
| 12.12.295...000.1 |
$x^{12} - 4 x^{11} - 32 x^{10} + 124 x^{9} + 339 x^{8} - 1252 x^{7} - 1458 x^{6} + 4864 x^{5} + 2480 x^{4} - 6484 x^{3} - 1580 x^{2} + 2052 x - 239$ |
$12$ |
[12,0] |
$2^{18}\cdot 5^{9}\cdot 7^{8}$ |
$3$ |
$34.6075767003$ |
$34.607576700316336$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
trivial |
$[2]$ |
$2$ |
$11$ |
$193697.65851$ |
| 12.0.295...000.1 |
$x^{12} - 4 x^{11} + 28 x^{10} - 76 x^{9} + 359 x^{8} - 772 x^{7} + 2662 x^{6} - 4216 x^{5} + 11540 x^{4} - 13284 x^{3} + 37260 x^{2} - 26468 x + 52681$ |
$12$ |
[0,6] |
$2^{18}\cdot 5^{9}\cdot 7^{8}$ |
$3$ |
$34.6075767003$ |
$34.607576700316336$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[146]$ |
$[146]$ |
$2$ |
$5$ |
$104.882003477$ |
| 12.0.309...000.1 |
$x^{12} + 30 x^{10} + 315 x^{8} + 1500 x^{6} + 3375 x^{4} + 3375 x^{2} + 1125$ |
$12$ |
[0,6] |
$2^{12}\cdot 3^{18}\cdot 5^{9}$ |
$3$ |
$34.7487655586$ |
$34.748765558648074$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[10, 10]$ |
$[10, 10]$ |
$2$ |
$5$ |
$201.000834787$ |
| 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 |
$[2]$ |
$2$ |
$11$ |
$413348.51768$ |
| 12.12.110...125.1 |
$x^{12} - 42 x^{10} - 19 x^{9} + 639 x^{8} + 531 x^{7} - 4122 x^{6} - 4653 x^{5} + 9900 x^{4} + 13904 x^{3} - 4356 x^{2} - 11253 x - 3509$ |
$12$ |
[12,0] |
$3^{18}\cdot 5^{9}\cdot 11^{4}$ |
$3$ |
$38.6402813871$ |
$118.99821203205568$ |
|
|
? |
$C_3^2:C_{12}$ (as 12T73) |
trivial |
$[2]$ |
$2$ |
$11$ |
$387641.416817$ |
| 12.12.131...125.1 |
$x^{12} - x^{11} - 33 x^{10} + 31 x^{9} + 407 x^{8} - 342 x^{7} - 2337 x^{6} + 1623 x^{5} + 6392 x^{4} - 3122 x^{3} - 7965 x^{2} + 1986 x + 3691$ |
$12$ |
[12,0] |
$3^{4}\cdot 5^{9}\cdot 7^{6}\cdot 29^{4}$ |
$4$ |
$39.1997178241$ |
$144.63358437489208$ |
|
|
? |
$C_6.D_6$ (as 12T39) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$472938.685831$ |
| 12.0.220...000.1 |
$x^{12} + 18 x^{10} - 4 x^{9} + 234 x^{8} + 36 x^{7} + 1738 x^{6} + 72 x^{5} + 8355 x^{4} + 3624 x^{3} + 40764 x^{2} + 21732 x + 70471$ |
$12$ |
[0,6] |
$2^{18}\cdot 3^{16}\cdot 5^{9}$ |
$3$ |
$40.9198628762$ |
$40.91986287620002$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[218]$ |
$[218]$ |
$2$ |
$5$ |
$201.000834787$ |
| 12.12.220...000.1 |
$x^{12} - 42 x^{10} - 4 x^{9} + 594 x^{8} + 36 x^{7} - 3382 x^{6} + 432 x^{5} + 7215 x^{4} - 2696 x^{3} - 3576 x^{2} + 1332 x - 109$ |
$12$ |
[12,0] |
$2^{18}\cdot 3^{16}\cdot 5^{9}$ |
$3$ |
$40.9198628762$ |
$40.91986287620002$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
trivial |
$[2]$ |
$2$ |
$11$ |
$285279.649624$ |
| 12.12.241...125.1 |
$x^{12} - x^{11} - 38 x^{10} + 46 x^{9} + 447 x^{8} - 632 x^{7} - 1642 x^{6} + 2478 x^{5} + 1037 x^{4} - 1617 x^{3} - 330 x^{2} + 251 x + 31$ |
$12$ |
[12,0] |
$3^{6}\cdot 5^{9}\cdot 19^{8}$ |
$3$ |
$41.237329341$ |
$41.237329340989255$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
trivial |
$[2]$ |
$2$ |
$11$ |
$457836.50034$ |
| 12.0.336...000.1 |
$x^{12} - 4 x^{11} + 43 x^{10} - 126 x^{9} + 814 x^{8} - 1852 x^{7} + 8517 x^{6} - 14386 x^{5} + 51505 x^{4} - 61084 x^{3} + 200870 x^{2} - 138098 x + 354061$ |
$12$ |
[0,6] |
$2^{12}\cdot 3^{6}\cdot 5^{9}\cdot 7^{8}$ |
$4$ |
$42.385452075$ |
$42.385452075003485$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[2, 194]$ |
$[2, 194]$ |
$2$ |
$5$ |
$104.882003477$ |
| 12.0.543...125.1 |
$x^{12} - x^{11} + 38 x^{10} - 6 x^{9} + 713 x^{8} + 278 x^{7} + 8204 x^{6} + 4344 x^{5} + 62061 x^{4} + 12933 x^{3} + 275688 x^{2} + 17977 x + 557801$ |
$12$ |
[0,6] |
$5^{9}\cdot 7^{8}\cdot 13^{6}$ |
$3$ |
$44.1161772283$ |
$44.116177228268$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[2, 2, 74]$ |
$[2, 2, 74]$ |
$2$ |
$5$ |
$104.882003477$ |
| 12.0.986...125.1 |
$x^{12} - 3 x^{11} + 24 x^{10} - 24 x^{9} + 273 x^{8} - 114 x^{7} + 1520 x^{6} - 336 x^{5} + 5496 x^{4} - 363 x^{3} + 10686 x^{2} - 2670 x + 7921$ |
$12$ |
[0,6] |
$3^{18}\cdot 5^{9}\cdot 19^{4}$ |
$3$ |
$46.361831653874425$ |
$75.73317874146682$ |
|
|
? |
$C_2^4:C_{12}$ (as 12T99) |
$[2, 4, 4]$ |
$[2, 4, 4]$ |
$2$ |
$5$ |
$3153.9783425305222$ |
| 12.0.228...000.1 |
$x^{12} + 12 x^{10} - 12 x^{9} + 54 x^{8} - 108 x^{7} + 192 x^{6} - 324 x^{5} + 585 x^{4} - 532 x^{3} + 756 x^{2} - 624 x + 656$ |
$12$ |
[0,6] |
$2^{18}\cdot 3^{12}\cdot 5^{9}\cdot 29^{2}$ |
$4$ |
$49.73094949258433$ |
$234.22859052096263$ |
|
|
? |
$C_3:S_3^3:C_4$ (as 12T245) |
$[2]$ |
$[2]$ |
$2$ |
$5$ |
$70306.32457498257$ |
| 12.0.271...125.1 |
$x^{12} - x^{11} + 53 x^{10} - 11 x^{9} + 1303 x^{8} + 438 x^{7} + 18804 x^{6} + 9784 x^{5} + 170686 x^{4} + 49088 x^{3} + 900838 x^{2} + 99987 x + 2139101$ |
$12$ |
[0,6] |
$5^{9}\cdot 7^{8}\cdot 17^{6}$ |
$3$ |
$50.4487787342$ |
$50.448778734178404$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[962]$ |
$[962]$ |
$2$ |
$5$ |
$104.882003477$ |
| 12.0.405...125.1 |
$x^{12} - 3 x^{11} + 39 x^{10} - 111 x^{9} + 825 x^{8} - 2268 x^{7} + 11158 x^{6} - 24144 x^{5} + 86724 x^{4} - 123364 x^{3} + 373878 x^{2} - 349125 x + 845101$ |
$12$ |
[0,6] |
$3^{16}\cdot 5^{9}\cdot 13^{6}$ |
$3$ |
$52.1627948248$ |
$52.16279482482122$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[914]$ |
$[914]$ |
$2$ |
$5$ |
$201.000834787$ |
| 12.0.487...000.1 |
$x^{12} + 12 x^{10} - 8 x^{9} + 54 x^{8} - 72 x^{7} + 192 x^{6} - 216 x^{5} + 585 x^{4} - 488 x^{3} + 756 x^{2} - 816 x + 576$ |
$12$ |
[0,6] |
$2^{6}\cdot 3^{8}\cdot 5^{9}\cdot 29^{6}$ |
$4$ |
$52.9690686095$ |
$234.22859052096263$ |
|
|
|
$C_3:S_3^3:C_4$ (as 12T247) |
$[8]$ |
$[8]$ |
$2$ |
$5$ |
$2040263.73226$ |
| 12.0.977...125.1 |
$x^{12} - x^{11} + 93 x^{10} - 94 x^{9} + 3204 x^{8} - 3298 x^{7} + 52912 x^{6} - 59464 x^{5} + 463265 x^{4} - 537436 x^{3} + 2225015 x^{2} - 1732597 x + 5417371$ |
$12$ |
[0,6] |
$5^{9}\cdot 7^{10}\cdot 11^{6}$ |
$3$ |
$56.1270494722$ |
$56.127049472200405$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[2, 2, 628]$ |
$[2, 2, 628]$ |
$2$ |
$5$ |
$104.882003477$ |
| 12.12.121...125.1 |
$x^{12} - x^{11} - 54 x^{10} + 58 x^{9} + 948 x^{8} - 1163 x^{7} - 6275 x^{6} + 7932 x^{5} + 14751 x^{4} - 15011 x^{3} - 15281 x^{2} + 8215 x + 5851$ |
$12$ |
[12,0] |
$3^{6}\cdot 5^{9}\cdot 31^{8}$ |
$3$ |
$57.1517140347$ |
$57.15171403472212$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
trivial |
$[2]$ |
$2$ |
$11$ |
$5165196.85962$ |
| 12.0.134...125.1 |
$x^{12} + 78 x^{10} - x^{9} + 2079 x^{8} - 441 x^{7} + 25088 x^{6} - 15957 x^{5} + 152430 x^{4} - 166064 x^{3} + 599634 x^{2} - 332247 x + 1522711$ |
$12$ |
[0,6] |
$3^{18}\cdot 5^{9}\cdot 11^{6}$ |
$3$ |
$57.624308643$ |
$57.62430864303005$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[2, 2, 458]$ |
$[2, 2, 458]$ |
$2$ |
$5$ |
$201.000834787$ |
| 12.12.166...125.1 |
$x^{12} - x^{11} - 97 x^{10} + 39 x^{9} + 3503 x^{8} + 188 x^{7} - 58846 x^{6} - 22116 x^{5} + 469536 x^{4} + 268488 x^{3} - 1560312 x^{2} - 899663 x + 1333151$ |
$12$ |
[12,0] |
$5^{9}\cdot 7^{8}\cdot 23^{6}$ |
$3$ |
$58.6800012745$ |
$58.68000127446573$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
trivial |
$[2]$ |
$2$ |
$11$ |
$3414742.12191$ |
