| 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 |
| 12.0.21523360500000000.1 |
$x^{12} + 6 x^{10} - 10 x^{9} + 36 x^{8} - 60 x^{7} + 276 x^{6} - 720 x^{5} + 1776 x^{4} - 2360 x^{3} + 2160 x^{2} - 1200 x + 400$ |
$12$ |
[0,6] |
$2^{8}\cdot 3^{16}\cdot 5^{9}$ |
$3$ |
$22.9654965503$ |
$22.965496550279074$ |
✓ |
✓ |
? |
$C_3 : C_4$ (as 12T5) |
$[2, 2]$ |
$10$ |
$5$ |
$1592.03444914$ |
| 12.0.33270205387539712.1 |
$x^{12} - 2 x^{11} + 14 x^{10} - 13 x^{9} + 39 x^{8} + 54 x^{7} + 179 x^{6} + 486 x^{5} + 1161 x^{4} + 1475 x^{3} + 1463 x^{2} + 931 x + 343$ |
$12$ |
[0,6] |
$2^{8}\cdot 37^{9}$ |
$2$ |
$23.8143074842$ |
$23.81430748424474$ |
✓ |
✓ |
? |
$C_3 : C_4$ (as 12T5) |
$[2, 2]$ |
$2$ |
$5$ |
$220.342128705$ |
| 12.12.193...000.1 |
$x^{12} - 24 x^{10} - 10 x^{9} + 216 x^{8} + 180 x^{7} - 844 x^{6} - 1080 x^{5} + 1056 x^{4} + 2200 x^{3} + 720 x^{2} - 240 x - 80$ |
$12$ |
[12,0] |
$2^{8}\cdot 3^{18}\cdot 5^{9}$ |
$3$ |
$27.5801135012$ |
$27.580113501197143$ |
|
✓ |
? |
$C_3 : C_4$ (as 12T5) |
trivial |
$2$ |
$11$ |
$69710.1521385$ |
| 12.0.106...000.1 |
$x^{12} - 3 x^{11} + 2 x^{9} + 43 x^{8} - 74 x^{7} - 71 x^{6} - 26 x^{5} + 271 x^{4} + 720 x^{3} - 406 x^{2} - 1633 x + 1699$ |
$12$ |
[0,6] |
$2^{8}\cdot 5^{8}\cdot 13^{9}$ |
$3$ |
$31.7778258663$ |
$31.777825866337707$ |
✓ |
✓ |
? |
$C_3 : C_4$ (as 12T5) |
$[2, 2]$ |
$2$ |
$5$ |
$1640.26926328$ |
| 12.0.227...613.1 |
$x^{12} - 4 x^{11} + 22 x^{10} - 87 x^{9} + 172 x^{8} - 668 x^{7} + 1077 x^{6} - 2082 x^{5} + 6332 x^{4} - 607 x^{3} + 21724 x^{2} + 4618 x + 26261$ |
$12$ |
[0,6] |
$11^{8}\cdot 13^{9}$ |
$2$ |
$33.8625223227$ |
$33.86252232274932$ |
✓ |
✓ |
? |
$C_3 : C_4$ (as 12T5) |
$[2, 2]$ |
$2$ |
$5$ |
$2726.62299235$ |
| 12.0.348...000.1 |
$x^{12} - x^{11} + 12 x^{10} - 18 x^{9} + 145 x^{8} + 78 x^{7} + 1427 x^{6} + 156 x^{5} + 15931 x^{4} - 7080 x^{3} + 3150 x^{2} - 1375 x + 625$ |
$12$ |
[0,6] |
$2^{8}\cdot 5^{9}\cdot 17^{8}$ |
$3$ |
$35.0924304576$ |
$35.09243045761278$ |
✓ |
✓ |
? |
$C_3 : C_4$ (as 12T5) |
$[2, 2, 2, 2]$ |
$10$ |
$5$ |
$7502.80335755$ |
| 12.12.550...000.1 |
$x^{12} - 39 x^{10} + 486 x^{8} - 120 x^{7} - 2259 x^{6} + 1380 x^{5} + 3126 x^{4} - 2980 x^{3} - 15 x^{2} + 420 x + 5$ |
$12$ |
[12,0] |
$2^{16}\cdot 3^{16}\cdot 5^{9}$ |
$3$ |
$36.4554533829$ |
$36.455453382885054$ |
|
✓ |
? |
$C_3 : C_4$ (as 12T5) |
trivial |
$2$ |
$11$ |
$468513.10341$ |
| 12.0.849...000.1 |
$x^{12} - x^{11} + 15 x^{10} - 15 x^{9} + 211 x^{8} - 780 x^{7} + 3839 x^{6} - 13190 x^{5} + 45121 x^{4} - 106605 x^{3} + 202860 x^{2} - 230256 x + 136161$ |
$12$ |
[0,6] |
$2^{8}\cdot 5^{9}\cdot 19^{8}$ |
$3$ |
$37.7934525305$ |
$37.793452530486654$ |
✓ |
✓ |
? |
$C_3 : C_4$ (as 12T5) |
$[4, 12]$ |
$10$ |
$5$ |
$3242.18396587$ |
| 12.12.851...272.1 |
$x^{12} - 4 x^{11} - 35 x^{10} + 158 x^{9} + 322 x^{8} - 1932 x^{7} - 227 x^{6} + 8104 x^{5} - 4280 x^{4} - 10266 x^{3} + 7031 x^{2} + 1128 x - 67$ |
$12$ |
[12,0] |
$2^{16}\cdot 37^{9}$ |
$2$ |
$37.8028567524$ |
$37.802856752384265$ |
|
✓ |
? |
$C_3 : C_4$ (as 12T5) |
trivial |
$2$ |
$11$ |
$365171.313867$ |
| 12.12.242...048.1 |
$x^{12} - 2 x^{11} - 60 x^{10} + 61 x^{9} + 1223 x^{8} + 54 x^{7} - 9515 x^{6} - 8838 x^{5} + 17219 x^{4} + 21899 x^{3} - 609 x^{2} - 2695 x + 343$ |
$12$ |
[12,0] |
$2^{8}\cdot 3^{6}\cdot 37^{9}$ |
$3$ |
$41.2475905098$ |
$41.24759050977966$ |
|
✓ |
? |
$C_3 : C_4$ (as 12T5) |
trivial |
$2$ |
$11$ |
$316765.282891$ |
| 12.12.254...857.1 |
$x^{12} - 3 x^{11} - 24 x^{10} + 69 x^{9} + 176 x^{8} - 499 x^{7} - 326 x^{6} + 1172 x^{5} - 411 x^{4} - 211 x^{3} + 40 x^{2} + 16 x + 1$ |
$12$ |
[12,0] |
$11^{8}\cdot 17^{9}$ |
$2$ |
$41.4093564529$ |
$41.40935645289189$ |
|
✓ |
? |
$C_3 : C_4$ (as 12T5) |
trivial |
$2$ |
$11$ |
$328936.323755$ |
| 12.0.265...000.1 |
$x^{12} - 4 x^{11} + 26 x^{10} - 15 x^{9} + 25 x^{8} + 666 x^{7} - 1189 x^{6} + 4836 x^{5} + 2075 x^{4} - 7025 x^{3} + 54071 x^{2} - 35249 x + 68051$ |
$12$ |
[0,6] |
$2^{8}\cdot 5^{10}\cdot 13^{9}$ |
$3$ |
$41.5546072168$ |
$41.55460721677449$ |
✓ |
✓ |
? |
$C_3 : C_4$ (as 12T5) |
$[2, 4, 4]$ |
$2$ |
$5$ |
$1640.26926328$ |
| 12.0.391...000.1 |
$x^{12} - x^{11} + 16 x^{10} - 14 x^{9} + 237 x^{8} - 334 x^{7} + 3651 x^{6} - 4632 x^{5} + 53719 x^{4} - 61132 x^{3} + 69938 x^{2} - 73695 x + 83521$ |
$12$ |
[0,6] |
$2^{8}\cdot 5^{9}\cdot 23^{8}$ |
$3$ |
$42.927216069$ |
$42.92721606897351$ |
✓ |
✓ |
? |
$C_3 : C_4$ (as 12T5) |
$[4, 4]$ |
$10$ |
$5$ |
$14744.5413899$ |
| 12.0.465...125.1 |
$x^{12} - 4 x^{11} + 23 x^{10} - 25 x^{9} + 311 x^{8} + 635 x^{7} + 5347 x^{6} + 19242 x^{5} + 57661 x^{4} + 63330 x^{3} + 67590 x^{2} + 18225 x + 2025$ |
$12$ |
[0,6] |
$5^{9}\cdot 47^{8}$ |
$2$ |
$43.5471170346$ |
$43.547117034639534$ |
✓ |
✓ |
? |
$C_3 : C_4$ (as 12T5) |
$[2, 2, 2, 2]$ |
$10$ |
$5$ |
$22045.6143754$ |
| 12.0.495...000.1 |
$x^{12} + 18 x^{10} - 28 x^{9} + 234 x^{8} - 108 x^{7} + 936 x^{6} - 36 x^{5} + 5112 x^{4} - 4456 x^{3} + 24156 x^{2} - 9504 x + 19036$ |
$12$ |
[0,6] |
$2^{16}\cdot 3^{18}\cdot 5^{9}$ |
$3$ |
$43.7807011852$ |
$43.78070118520269$ |
✓ |
✓ |
? |
$C_3 : C_4$ (as 12T5) |
$[2, 2, 4, 4]$ |
$2$ |
$5$ |
$1592.03444914$ |
| 12.0.116...848.1 |
$x^{12} + 24 x^{10} - 2 x^{9} + 216 x^{8} - 36 x^{7} + 2484 x^{6} - 216 x^{5} + 20736 x^{4} + 29864 x^{3} + 58320 x^{2} + 181776 x + 145232$ |
$12$ |
[0,6] |
$2^{8}\cdot 3^{16}\cdot 13^{9}$ |
$3$ |
$47.0225147085$ |
$47.022514708519914$ |
✓ |
✓ |
|
$C_3 : C_4$ (as 12T5) |
$[3, 6, 6]$ |
$2$ |
$5$ |
$3416.07942432$ |
| 12.12.271...000.1 |
$x^{12} - 6 x^{11} - 38 x^{10} + 206 x^{9} + 515 x^{8} - 2348 x^{7} - 2964 x^{6} + 10132 x^{5} + 7015 x^{4} - 12222 x^{3} - 7526 x^{2} + 2126 x + 1093$ |
$12$ |
[12,0] |
$2^{16}\cdot 5^{8}\cdot 13^{9}$ |
$3$ |
$50.4441542095$ |
$50.44415420948674$ |
|
✓ |
? |
$C_3 : C_4$ (as 12T5) |
trivial |
$2$ |
$11$ |
$1507027.09552$ |
| 12.12.275...173.1 |
$x^{12} - 5 x^{11} - 34 x^{10} + 204 x^{9} + 211 x^{8} - 2360 x^{7} + 1659 x^{6} + 5901 x^{5} - 5641 x^{4} - 3679 x^{3} + 2925 x^{2} + 468 x - 351$ |
$12$ |
[12,0] |
$11^{10}\cdot 13^{9}$ |
$2$ |
$50.4992295011$ |
$50.4992295011254$ |
|
✓ |
? |
$C_3 : C_4$ (as 12T5) |
trivial |
$2$ |
$11$ |
$2003231.11492$ |
| 12.0.279...656.1 |
$x^{12} - 2 x^{11} + 42 x^{10} - 41 x^{9} + 107 x^{8} + 250 x^{7} + 1649 x^{6} + 4230 x^{5} + 14153 x^{4} + 18097 x^{3} + 24757 x^{2} + 18411 x + 6859$ |
$12$ |
[0,6] |
$2^{8}\cdot 101^{9}$ |
$2$ |
$50.5740454034$ |
$50.57404540337717$ |
✓ |
✓ |
? |
$C_3 : C_4$ (as 12T5) |
$[4, 20]$ |
$2$ |
$5$ |
$1356.3184458$ |
| 12.0.352...000.1 |
$x^{12} + 6 x^{10} + 216 x^{8} - 240 x^{7} + 1296 x^{6} + 960 x^{5} + 12216 x^{4} + 640 x^{3} + 89040 x^{2} + 107040 x + 299120$ |
$12$ |
[0,6] |
$2^{22}\cdot 3^{16}\cdot 5^{9}$ |
$3$ |
$51.5557965965$ |
$51.555796596536176$ |
✓ |
✓ |
? |
$C_3 : C_4$ (as 12T5) |
$[2, 8, 8]$ |
$2$ |
$5$ |
$1592.03444914$ |
| 12.12.352...000.1 |
$x^{12} - 54 x^{10} + 936 x^{8} - 240 x^{7} - 5984 x^{6} + 3360 x^{5} + 10056 x^{4} - 4160 x^{3} - 4080 x^{2} + 1440 x - 80$ |
$12$ |
[12,0] |
$2^{22}\cdot 3^{16}\cdot 5^{9}$ |
$3$ |
$51.5557965965$ |
$51.555796596536176$ |
|
✓ |
? |
$C_3 : C_4$ (as 12T5) |
trivial |
$2$ |
$11$ |
$3679891.36342$ |
| 12.0.426...000.1 |
$x^{12} - 4 x^{11} + 28 x^{10} - 65 x^{9} + 581 x^{8} + 310 x^{7} + 8967 x^{6} + 19812 x^{5} + 145651 x^{4} - 119595 x^{3} + 47535 x^{2} - 7125 x + 9025$ |
$12$ |
[0,6] |
$2^{8}\cdot 5^{9}\cdot 31^{8}$ |
$3$ |
$52.3787700592$ |
$52.37877005920099$ |
✓ |
✓ |
? |
$C_3 : C_4$ (as 12T5) |
$[3, 6, 6]$ |
$10$ |
$5$ |
$10042.6435644$ |
| 12.0.519...000.1 |
$x^{12} - 2 x^{11} + 88 x^{10} - 87 x^{9} + 2333 x^{8} + 646 x^{7} + 27041 x^{6} + 44886 x^{5} + 212283 x^{4} + 330183 x^{3} + 712233 x^{2} + 610173 x + 531441$ |
$12$ |
[0,6] |
$2^{8}\cdot 5^{6}\cdot 37^{9}$ |
$3$ |
$53.2504103719$ |
$53.25041037185324$ |
✓ |
✓ |
? |
$C_3 : C_4$ (as 12T5) |
$[2, 2, 2, 4, 20]$ |
$2$ |
$5$ |
$220.342128705$ |
| 12.0.545...408.1 |
$x^{12} + 74 x^{10} + 2072 x^{8} + 27380 x^{6} + 169756 x^{4} + 405224 x^{2} + 202612$ |
$12$ |
[0,6] |
$2^{22}\cdot 37^{9}$ |
$2$ |
$53.4613127157$ |
$53.461312715669166$ |
✓ |
✓ |
? |
$C_3 : C_4$ (as 12T5) |
$[2, 4, 100]$ |
$2$ |
$5$ |
$220.342128705$ |
| 12.12.545...408.1 |
$x^{12} - 74 x^{10} + 2072 x^{8} - 27380 x^{6} + 169756 x^{4} - 405224 x^{2} + 202612$ |
$12$ |
[12,0] |
$2^{22}\cdot 37^{9}$ |
$2$ |
$53.4613127157$ |
$53.461312715669166$ |
|
✓ |
? |
$C_3 : C_4$ (as 12T5) |
trivial |
$2$ |
$11$ |
$2014428.146$ |
| 12.0.624...549.2 |
$x^{12} - 3 x^{11} - 9 x^{10} - 25 x^{9} + 180 x^{8} - 1113 x^{7} + 6164 x^{6} - 10653 x^{5} + 30396 x^{4} - 21701 x^{3} + 15279 x^{2} - 4650 x + 2693$ |
$12$ |
[0,6] |
$3^{16}\cdot 29^{9}$ |
$2$ |
$54.0704733301$ |
$54.0704733301356$ |
✓ |
✓ |
? |
$C_3 : C_4$ (as 12T5) |
$[2, 2, 2, 2]$ |
$2$ |
$5$ |
$7489.36668694$ |
| 12.12.773...000.1 |
$x^{12} - 3 x^{11} - 39 x^{10} + 119 x^{9} + 433 x^{8} - 1478 x^{7} - 1267 x^{6} + 6292 x^{5} - 1003 x^{4} - 7353 x^{3} + 2298 x^{2} + 2384 x - 173$ |
$12$ |
[12,0] |
$2^{8}\cdot 3^{6}\cdot 5^{8}\cdot 13^{9}$ |
$4$ |
$55.0408089546$ |
$55.040808954573386$ |
|
✓ |
? |
$C_3 : C_4$ (as 12T5) |
trivial |
$2$ |
$11$ |
$4959098.65638$ |
| 12.12.892...000.1 |
$x^{12} - 4 x^{11} - 53 x^{10} + 198 x^{9} + 890 x^{8} - 3088 x^{7} - 5373 x^{6} + 17254 x^{5} + 16066 x^{4} - 39580 x^{3} - 27645 x^{2} + 32370 x + 22405$ |
$12$ |
[12,0] |
$2^{16}\cdot 5^{9}\cdot 17^{8}$ |
$3$ |
$55.7057610245$ |
$55.705761024535406$ |
|
✓ |
? |
$C_3 : C_4$ (as 12T5) |
trivial |
$2$ |
$11$ |
$4137428.77768$ |
| 12.0.100...000.1 |
$x^{12} - 4 x^{11} + 32 x^{10} - 23 x^{9} + 303 x^{8} - 38 x^{7} + 3223 x^{6} - 10028 x^{5} + 28963 x^{4} - 82513 x^{3} + 121977 x^{2} - 15829 x + 6311$ |
$12$ |
[0,6] |
$2^{8}\cdot 5^{9}\cdot 17^{10}$ |
$3$ |
$56.2714709902$ |
$56.27147099020761$ |
✓ |
✓ |
? |
$C_3 : C_4$ (as 12T5) |
$[2, 2, 2, 2, 2]$ |
$2$ |
$5$ |
$7502.80335755$ |
| 12.12.105...632.1 |
$x^{12} - 54 x^{10} - 2 x^{9} + 684 x^{8} - 348 x^{7} - 2300 x^{6} + 720 x^{5} + 3264 x^{4} + 120 x^{3} - 1584 x^{2} - 432 x + 48$ |
$12$ |
[12,0] |
$2^{8}\cdot 3^{18}\cdot 13^{9}$ |
$3$ |
$56.4710756388$ |
$56.47107563876871$ |
|
✓ |
? |
$C_3 : C_4$ (as 12T5) |
$[3]$ |
$2$ |
$11$ |
$1670237.73069$ |
| 12.12.165...877.1 |
$x^{12} - 3 x^{11} - 55 x^{10} + 159 x^{9} + 904 x^{8} - 3065 x^{7} - 3952 x^{6} + 21883 x^{5} - 12742 x^{4} - 32763 x^{3} + 48637 x^{2} - 20240 x + 1249$ |
$12$ |
[12,0] |
$3^{6}\cdot 11^{8}\cdot 13^{9}$ |
$3$ |
$58.6516091354$ |
$58.6516091354371$ |
|
✓ |
? |
$C_3 : C_4$ (as 12T5) |
trivial |
$2$ |
$11$ |
$3563867.34537$ |
| 12.0.173...669.1 |
$x^{12} - 5 x^{11} + 54 x^{10} - 122 x^{9} + 433 x^{8} - 1078 x^{7} + 4875 x^{6} - 10397 x^{5} + 23869 x^{4} + 14489 x^{3} + 73305 x^{2} - 134592 x + 105011$ |
$12$ |
[0,6] |
$229^{9}$ |
$1$ |
$58.8676381609$ |
$58.86763816093301$ |
✓ |
✓ |
? |
$C_3 : C_4$ (as 12T5) |
$[2, 2, 2, 34]$ |
$2$ |
$5$ |
$1444.72403292$ |
| 12.12.217...000.1 |
$x^{12} - 6 x^{11} - 50 x^{10} + 300 x^{9} + 836 x^{8} - 4720 x^{7} - 6416 x^{6} + 27160 x^{5} + 25256 x^{4} - 47040 x^{3} - 36000 x^{2} + 15424 x + 4496$ |
$12$ |
[12,0] |
$2^{16}\cdot 5^{9}\cdot 19^{8}$ |
$3$ |
$59.9933663044$ |
$59.99336630440473$ |
|
✓ |
? |
$C_3 : C_4$ (as 12T5) |
$[3]$ |
$2$ |
$11$ |
$4041408.2696$ |
| 12.12.253...000.1 |
$x^{12} - 3 x^{11} - 48 x^{10} + 140 x^{9} + 711 x^{8} - 2100 x^{7} - 2867 x^{6} + 10476 x^{5} - 5589 x^{4} - 1770 x^{3} + 870 x^{2} - 15 x - 5$ |
$12$ |
[12,0] |
$2^{8}\cdot 3^{16}\cdot 5^{9}\cdot 7^{6}$ |
$4$ |
$60.7609926072$ |
$60.760992607150186$ |
|
✓ |
? |
$C_3 : C_4$ (as 12T5) |
trivial |
$2$ |
$11$ |
$5974740.7808$ |
| 12.12.254...000.1 |
$x^{12} - x^{11} - 58 x^{10} + 48 x^{9} + 1113 x^{8} - 872 x^{7} - 8557 x^{6} + 5848 x^{5} + 27233 x^{4} - 10622 x^{3} - 36288 x^{2} + 1659 x + 12391$ |
$12$ |
[12,0] |
$2^{8}\cdot 3^{6}\cdot 5^{9}\cdot 17^{8}$ |
$4$ |
$60.7818725137$ |
$60.781872513662876$ |
|
✓ |
? |
$C_3 : C_4$ (as 12T5) |
trivial |
$2$ |
$11$ |
$13091443.5078$ |
| 12.12.306...000.1 |
$x^{12} - 4 x^{11} - 60 x^{10} + 255 x^{9} + 871 x^{8} - 4400 x^{7} - 841 x^{6} + 22500 x^{5} - 26729 x^{4} - 645 x^{3} + 11135 x^{2} - 829 x - 1129$ |
$12$ |
[12,0] |
$2^{8}\cdot 5^{9}\cdot 19^{10}$ |
$3$ |
$61.7365232055$ |
$61.73652320549103$ |
|
✓ |
? |
$C_3 : C_4$ (as 12T5) |
$[3]$ |
$2$ |
$11$ |
$2307007.55678$ |
| 12.0.307...697.1 |
$x^{12} - 5 x^{11} + 41 x^{10} - 81 x^{9} + 278 x^{8} - 316 x^{7} + 2315 x^{6} - 7280 x^{5} + 17286 x^{4} + 34538 x^{3} + 86932 x^{2} + 51353 x + 332929$ |
$12$ |
[0,6] |
$11^{10}\cdot 17^{9}$ |
$2$ |
$61.7538343741$ |
$61.753834374105026$ |
✓ |
✓ |
|
$C_3 : C_4$ (as 12T5) |
$[2, 2, 34]$ |
$2$ |
$5$ |
$3083.51591562$ |
| 12.0.317...000.1 |
$x^{12} + 60 x^{10} + 1260 x^{8} + 12300 x^{6} + 59400 x^{4} + 135000 x^{2} + 112500$ |
$12$ |
[0,6] |
$2^{22}\cdot 3^{18}\cdot 5^{9}$ |
$3$ |
$61.9152613863$ |
$61.915261386317475$ |
✓ |
✓ |
? |
$C_3 : C_4$ (as 12T5) |
$[2, 2, 10, 10]$ |
$2$ |
$5$ |
$1592.03444914$ |
| 12.12.317...000.1 |
$x^{12} - 60 x^{10} + 1260 x^{8} - 12300 x^{6} + 59400 x^{4} - 135000 x^{2} + 112500$ |
$12$ |
[12,0] |
$2^{22}\cdot 3^{18}\cdot 5^{9}$ |
$3$ |
$61.9152613863$ |
$61.915261386317475$ |
|
✓ |
? |
$C_3 : C_4$ (as 12T5) |
$[2]$ |
$2$ |
$11$ |
$4365747.902$ |
| 12.12.391...088.1 |
$x^{12} - 2 x^{11} - 134 x^{10} + 135 x^{9} + 5885 x^{8} + 646 x^{7} - 100609 x^{6} - 114510 x^{5} + 523305 x^{4} + 785727 x^{3} - 690363 x^{2} - 846369 x + 531441$ |
$12$ |
[12,0] |
$2^{8}\cdot 7^{6}\cdot 37^{9}$ |
$3$ |
$63.0067352485$ |
$63.00673524853582$ |
|
✓ |
? |
$C_3 : C_4$ (as 12T5) |
trivial |
$2$ |
$11$ |
$4909459.41704$ |
| 12.12.429...912.2 |
$x^{12} - 52 x^{10} - 8 x^{9} + 864 x^{8} - 32 x^{7} - 5804 x^{6} + 1456 x^{5} + 15613 x^{4} - 4192 x^{3} - 15456 x^{2} + 1336 x + 3902$ |
$12$ |
[12,0] |
$2^{33}\cdot 29^{8}$ |
$2$ |
$63.4986491978$ |
$63.49864919784482$ |
|
✓ |
|
$C_3 : C_4$ (as 12T5) |
trivial |
$2$ |
$11$ |
$29190718.8092$ |
| 12.0.429...912.146 |
$x^{12} - 28 x^{10} - 8 x^{9} + 384 x^{8} - 160 x^{7} - 1900 x^{6} + 1072 x^{5} + 1869 x^{4} + 11552 x^{3} + 52808 x^{2} - 9288 x + 33262$ |
$12$ |
[0,6] |
$2^{33}\cdot 29^{8}$ |
$2$ |
$63.4986491978$ |
$63.49864919784482$ |
✓ |
✓ |
|
$C_3 : C_4$ (as 12T5) |
$[2, 2, 4, 4]$ |
$2$ |
$5$ |
$34583.0412036$ |
| 12.12.489...857.1 |
$x^{12} - x^{11} - 81 x^{10} - 55 x^{9} + 2187 x^{8} + 4623 x^{7} - 19442 x^{6} - 69890 x^{5} + 4263 x^{4} + 257547 x^{3} + 289908 x^{2} - 19988 x - 119128$ |
$12$ |
[12,0] |
$257^{9}$ |
$1$ |
$64.187408596$ |
$64.18740859595064$ |
|
✓ |
|
$C_3 : C_4$ (as 12T5) |
trivial |
$2$ |
$11$ |
$9021039.03079$ |
| 12.12.562...941.2 |
$x^{12} - 57 x^{10} - 92 x^{9} + 990 x^{8} + 2802 x^{7} - 4810 x^{6} - 25443 x^{5} - 15819 x^{4} + 57737 x^{3} + 116550 x^{2} + 83475 x + 21625$ |
$12$ |
[12,0] |
$3^{18}\cdot 29^{9}$ |
$2$ |
$64.935229606$ |
$64.93522960601831$ |
|
✓ |
? |
$C_3 : C_4$ (as 12T5) |
trivial |
$2$ |
$11$ |
$6418973.82526$ |
| 12.12.619...000.1 |
$x^{12} - 3 x^{11} - 58 x^{10} + 150 x^{9} + 1101 x^{8} - 2730 x^{7} - 8177 x^{6} + 21366 x^{5} + 17601 x^{4} - 62100 x^{3} + 23900 x^{2} + 12135 x - 6005$ |
$12$ |
[12,0] |
$2^{8}\cdot 3^{6}\cdot 5^{9}\cdot 19^{8}$ |
$4$ |
$65.4601799762$ |
$65.46017997624544$ |
|
✓ |
? |
$C_3 : C_4$ (as 12T5) |
$[3]$ |
$2$ |
$11$ |
$3979499.96028$ |
| 12.0.620...288.1 |
$x^{12} - 4 x^{11} + 113 x^{10} - 434 x^{9} + 5206 x^{8} - 17324 x^{7} + 118617 x^{6} - 319124 x^{5} + 1328608 x^{4} - 2507766 x^{3} + 5953375 x^{2} - 4561268 x + 4200913$ |
$12$ |
[0,6] |
$2^{16}\cdot 3^{6}\cdot 37^{9}$ |
$3$ |
$65.4764685664$ |
$65.47646856637776$ |
✓ |
✓ |
? |
$C_3 : C_4$ (as 12T5) |
$[2, 2, 2, 14, 28]$ |
$2$ |
$5$ |
$220.342128705$ |
| 12.12.678...000.1 |
$x^{12} - 4 x^{11} - 71 x^{10} + 290 x^{9} + 1260 x^{8} - 5024 x^{7} - 5579 x^{6} + 18984 x^{5} + 8220 x^{4} - 16870 x^{3} - 831 x^{2} + 3024 x - 459$ |
$12$ |
[12,0] |
$2^{16}\cdot 5^{10}\cdot 13^{9}$ |
$3$ |
$65.96382721$ |
$65.96382721003316$ |
|
✓ |
? |
$C_3 : C_4$ (as 12T5) |
$[2]$ |
$2$ |
$11$ |
$9865250.24047$ |
| 12.12.931...848.1 |
$x^{12} - 4 x^{11} - 61 x^{10} + 218 x^{9} + 1110 x^{8} - 3512 x^{7} - 7551 x^{6} + 20532 x^{5} + 15967 x^{4} - 36774 x^{3} - 14482 x^{2} + 18652 x + 7036$ |
$12$ |
[12,0] |
$2^{12}\cdot 11^{8}\cdot 13^{9}$ |
$3$ |
$67.7250446455$ |
$67.72504464549864$ |
|
✓ |
|
$C_3 : C_4$ (as 12T5) |
$[2, 2]$ |
$2$ |
$11$ |
$3927746.26013$ |
| 12.12.100...000.1 |
$x^{12} - 4 x^{11} - 69 x^{10} + 294 x^{9} + 1442 x^{8} - 6896 x^{7} - 8589 x^{6} + 56982 x^{5} + 1674 x^{4} - 166988 x^{3} + 55283 x^{2} + 123410 x + 3581$ |
$12$ |
[12,0] |
$2^{16}\cdot 5^{9}\cdot 23^{8}$ |
$3$ |
$68.142707946$ |
$68.14270794595475$ |
|
✓ |
? |
$C_3 : C_4$ (as 12T5) |
trivial |
$2$ |
$11$ |
$15635866.4176$ |
| 12.0.173...000.1 |
$x^{12} - 6 x^{11} + 79 x^{10} - 262 x^{9} + 2036 x^{8} - 2582 x^{7} + 18759 x^{6} + 7090 x^{5} + 60484 x^{4} - 119238 x^{3} + 740767 x^{2} - 672574 x + 1284583$ |
$12$ |
[0,6] |
$2^{22}\cdot 5^{8}\cdot 13^{9}$ |
$3$ |
$71.3388070255$ |
$71.338807025496$ |
✓ |
✓ |
? |
$C_3 : C_4$ (as 12T5) |
$[2, 16, 16]$ |
$2$ |
$5$ |
$1640.26926328$ |
