| 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 |
| 12.2.175122415616.1 |
$x^{12} - 4 x^{11} + 10 x^{10} - 16 x^{9} + 17 x^{8} - 6 x^{7} - 12 x^{6} + 30 x^{5} - 37 x^{4} + 30 x^{3} - 17 x^{2} + 6 x - 1$ |
$12$ |
[2,5] |
$-\,2^{18}\cdot 71\cdot 97^{2}$ |
$3$ |
$8.64858672911$ |
$234.72537144501445$ |
|
|
? |
$S_4^2:D_4$ (as 12T260) |
trivial |
$2$ |
$6$ |
$3.6007962841$ |
| 12.0.321244102656.1 |
$x^{12} - 4 x^{10} - 2 x^{9} + 6 x^{8} + 4 x^{7} - x^{6} + 4 x^{5} + 6 x^{4} - 2 x^{3} - 4 x^{2} + 1$ |
$12$ |
[0,6] |
$2^{18}\cdot 3^{6}\cdot 41^{2}$ |
$3$ |
$9.097099195303167$ |
$31.368774282716245$ |
|
|
? |
$S_3^2:C_2^2$ (as 12T77) |
trivial |
$6$ |
$5$ |
$13.569644605427053$ |
| 12.2.353996898304.1 |
$x^{12} - 2 x^{11} + x^{10} + 4 x^{7} - 4 x^{6} + 2 x^{5} - 2 x^{4} + 4 x^{2} - 4 x + 1$ |
$12$ |
[2,5] |
$-\,2^{18}\cdot 7^{3}\cdot 31\cdot 127$ |
$4$ |
$9.170998478582437$ |
$469.54446008871196$ |
|
|
? |
$S_3\wr D_4$ (as 12T274) |
trivial |
$2$ |
$6$ |
$5.5369431385384855$ |
| 12.0.458838245376.1 |
$x^{12} - 6 x^{11} + 17 x^{10} - 28 x^{9} + 24 x^{8} - 20 x^{6} + 18 x^{5} - 6 x^{4} - 4 x^{3} + 8 x^{2} - 4 x + 1$ |
$12$ |
[0,6] |
$2^{18}\cdot 3^{6}\cdot 7^{4}$ |
$3$ |
$9.3714106217$ |
$17.926863604818365$ |
|
|
? |
$C_6\times S_3$ (as 12T18) |
trivial |
$6$ |
$5$ |
$16.1633727166$ |
| 12.4.882697830400.1 |
$x^{12} - 4 x^{11} + 4 x^{10} + 4 x^{9} - 9 x^{8} + 2 x^{7} + 4 x^{6} - 2 x^{5} - x^{4} + 2 x^{3} + x^{2} - 2 x - 1$ |
$12$ |
[4,4] |
$2^{18}\cdot 5^{2}\cdot 367^{2}$ |
$3$ |
$9.89656173762$ |
$121.16104984688768$ |
|
|
✓ |
$S_4^2:C_2^2$ (as 12T236) |
trivial |
$2$ |
$7$ |
$12.36210531$ |
| 12.4.1115674640384.1 |
$x^{12} - 2 x^{11} - x^{10} + 8 x^{9} - 8 x^{8} - 4 x^{7} + 16 x^{6} - 10 x^{5} - 5 x^{4} + 10 x^{3} - 3 x^{2} - 2 x + 1$ |
$12$ |
[4,4] |
$2^{18}\cdot 593\cdot 7177$ |
$3$ |
$10.091633353502836$ |
$5835.039674243869$ |
|
|
✓ |
$S_6\wr C_2$ (as 12T299) |
trivial |
$2$ |
$7$ |
$14.246262892000614$ |
| 12.4.1463445356544.1 |
$x^{12} - 2 x^{9} - 3 x^{6} + 2 x^{3} + 1$ |
$12$ |
[4,4] |
$2^{18}\cdot 3^{4}\cdot 41^{3}$ |
$3$ |
$10.3224164393$ |
$31.368774282716245$ |
|
|
? |
$S_3^2:C_2^2$ (as 12T78) |
trivial |
$2$ |
$7$ |
$16.8275117865$ |
| 12.4.1506176925696.1 |
$x^{12} - 2 x^{10} - 2 x^{9} - 4 x^{8} + 5 x^{6} - 4 x^{4} - 2 x^{3} - 2 x^{2} + 1$ |
$12$ |
[4,4] |
$2^{18}\cdot 3^{2}\cdot 17^{2}\cdot 47^{2}$ |
$4$ |
$10.3472037064$ |
$138.47743498491008$ |
|
|
? |
$S_4^2:C_2^2$ (as 12T236) |
trivial |
$2$ |
$7$ |
$17.494747575$ |
| 12.2.1687248699392.3 |
$x^{12} - 2 x^{11} - x^{10} + 10 x^{9} - 11 x^{8} - 14 x^{7} + 42 x^{6} - 20 x^{5} - 34 x^{4} + 56 x^{3} - 35 x^{2} + 10 x - 1$ |
$12$ |
[2,5] |
$-\,2^{18}\cdot 23^{5}$ |
$2$ |
$10.4455567243$ |
$13.564659966250536$ |
|
|
? |
$(C_6\times C_2):C_2$ (as 12T13) |
trivial |
$2$ |
$6$ |
$15.4837872745$ |
| 12.6.8192886833152.1 |
$x^{12} - 2 x^{10} - 2 x^{9} - 2 x^{8} + 4 x^{7} + 3 x^{6} + 4 x^{5} - 2 x^{4} - 2 x^{3} - 2 x^{2} + 1$ |
$12$ |
[6,3] |
$-\,2^{18}\cdot 7\cdot 2113^{2}$ |
$3$ |
$11.915705098690154$ |
$343.98837189649305$ |
|
|
✓ |
$S_4^2:D_4$ (as 12T260) |
trivial |
$2$ |
$8$ |
$64.12166932416741$ |
| 12.6.10578455953408.1 |
$x^{12} - 2 x^{11} - x^{10} - 2 x^{9} + 3 x^{8} + 14 x^{7} - 20 x^{6} + 34 x^{4} + 12 x^{3} - x^{2} + 2 x + 1$ |
$12$ |
[6,3] |
$-\,2^{18}\cdot 7^{9}$ |
$2$ |
$12.1721844145$ |
$14.315066180821045$ |
|
|
? |
$D_4 \times C_3$ (as 12T14) |
trivial |
$2$ |
$8$ |
$74.2304379605$ |
| 12.6.12110614233088.1 |
$x^{12} - 4 x^{11} + 4 x^{10} + 4 x^{9} - 15 x^{8} + 14 x^{7} + 12 x^{6} - 22 x^{5} - 7 x^{4} + 10 x^{3} + 5 x^{2} - 2 x - 1$ |
$12$ |
[6,3] |
$-\,2^{18}\cdot 7^{3}\cdot 367^{2}$ |
$3$ |
$12.3101642483$ |
$143.3596874996594$ |
|
|
? |
$D_6\wr C_2$ (as 12T125) |
trivial |
$2$ |
$8$ |
$76.0465779983$ |
| 12.8.16135716339712.1 |
$x^{12} - 2 x^{11} - 3 x^{10} + 10 x^{9} - 11 x^{8} + 2 x^{7} + 24 x^{6} - 38 x^{5} + 31 x^{4} - 20 x^{3} - 2 x^{2} + 8 x - 1$ |
$12$ |
[8,2] |
$2^{18}\cdot 367^{2}\cdot 457$ |
$3$ |
$12.6080818889$ |
$1158.3401918262182$ |
|
|
? |
$S_4^2:D_4$ (as 12T260) |
trivial |
$2$ |
$9$ |
$119.057952469$ |
| 12.0.24904730935296.4 |
$x^{12} - 10 x^{10} + 32 x^{8} - 24 x^{6} - 48 x^{4} + 64 x^{2} + 64$ |
$12$ |
[0,6] |
$2^{18}\cdot 3^{6}\cdot 19^{4}$ |
$3$ |
$13.07244493634025$ |
$34.88253362095716$ |
|
|
? |
$C_6\times S_3$ (as 12T18) |
trivial |
$6$ |
$5$ |
$74.34391887043572$ |
| 12.4.26873856000000.1 |
$x^{12} - 2 x^{9} - 7 x^{6} - 2 x^{3} + 1$ |
$12$ |
[4,4] |
$2^{18}\cdot 3^{8}\cdot 5^{6}$ |
$3$ |
$13.1556052098$ |
$22.786176627742247$ |
|
|
? |
$S_3\times D_6$ (as 12T37) |
trivial |
$2$ |
$7$ |
$99.3611078272$ |
| 12.4.29260310118400.1 |
$x^{12} - 4 x^{10} - 2 x^{9} - 4 x^{7} - 7 x^{6} - 4 x^{5} - 2 x^{3} - 4 x^{2} + 1$ |
$12$ |
[4,4] |
$2^{18}\cdot 5^{2}\cdot 2113^{2}$ |
$3$ |
$13.2492077631$ |
$290.7232360854564$ |
|
|
? |
$S_4^2:C_2^2$ (as 12T236) |
trivial |
$2$ |
$7$ |
$87.3221647013$ |
| 12.0.29293554171904.1 |
$x^{12} - 6 x^{11} + 11 x^{10} - 6 x^{9} + 4 x^{8} - 6 x^{7} - 3 x^{6} - 4 x^{5} + 21 x^{4} - 18 x^{3} + 6 x^{2} + 1$ |
$12$ |
[0,6] |
$2^{18}\cdot 11^{2}\cdot 31^{4}$ |
$3$ |
$13.250461532512325$ |
$52.230259428802384$ |
|
|
? |
$C_2^4:S_4$ (as 12T136) |
trivial |
$2$ |
$5$ |
$47.97553051948835$ |
| 12.8.30967526064128.1 |
$x^{12} - 6 x^{10} - 2 x^{9} + 9 x^{8} + 8 x^{7} - x^{6} - 14 x^{5} - 6 x^{4} + 10 x^{3} + 5 x^{2} - 2 x - 1$ |
$12$ |
[8,2] |
$2^{18}\cdot 118131737$ |
$2$ |
$13.3119662942$ |
$30741.728903885676$ |
|
|
✓ |
$S_6\wr C_2$ (as 12T299) |
trivial |
$2$ |
$9$ |
$175.399901193$ |
| 12.8.36767438995456.1 |
$x^{12} - 4 x^{11} - 2 x^{10} + 20 x^{9} + x^{8} - 46 x^{7} - 2 x^{6} + 58 x^{5} + 3 x^{4} - 34 x^{3} + x^{2} + 6 x - 1$ |
$12$ |
[8,2] |
$2^{18}\cdot 13^{2}\cdot 911^{2}$ |
$3$ |
$13.5037777544$ |
$307.80513316057613$ |
|
|
? |
$S_4^2:C_2^2$ (as 12T236) |
trivial |
$2$ |
$9$ |
$196.084738415$ |
| 12.2.47784725839872.1 |
$x^{12} - 2 x^{9} + x^{6} + 2 x^{3} - 1$ |
$12$ |
[2,5] |
$-\,2^{18}\cdot 3^{12}\cdot 7^{3}$ |
$3$ |
$13.8019598027$ |
$37.334018470425725$ |
|
|
✓ |
$S_3^3:C_2$ (as 12T156) |
trivial |
$2$ |
$6$ |
$78.760232386$ |
| 12.6.47784725839872.1 |
$x^{12} - 6 x^{10} + 9 x^{8} + 2 x^{6} - 6 x^{4} - 7$ |
$12$ |
[6,3] |
$-\,2^{18}\cdot 3^{12}\cdot 7^{3}$ |
$3$ |
$13.8019598027$ |
$55.98052058686458$ |
|
|
? |
$S_4^2:C_2^2$ (as 12T235) |
trivial |
$2$ |
$8$ |
$200.722095458$ |
| 12.8.58003456000000.1 |
$x^{12} - 4 x^{11} + 2 x^{10} + 4 x^{9} + 12 x^{8} - 26 x^{7} - 22 x^{6} + 72 x^{5} - 32 x^{4} - 32 x^{3} + 27 x^{2} - 2 x - 1$ |
$12$ |
[8,2] |
$2^{18}\cdot 5^{6}\cdot 7^{2}\cdot 17^{2}$ |
$4$ |
$14.0266670802$ |
$68.99275324264136$ |
|
|
? |
$S_3^2:C_2^2$ (as 12T77) |
trivial |
$2$ |
$9$ |
$251.0296206$ |
| 12.4.61959527727104.1 |
$x^{12} - 4 x^{11} + 2 x^{10} + 2 x^{9} - 8 x^{8} + 12 x^{7} - 11 x^{6} + 12 x^{5} - 8 x^{4} + 2 x^{3} + 2 x^{2} - 4 x + 1$ |
$12$ |
[4,4] |
$2^{18}\cdot 7^{8}\cdot 41$ |
$3$ |
$14.104001372882252$ |
$66.27284508488681$ |
|
|
? |
$C_2\wr C_6$ (as 12T134) |
trivial |
$2$ |
$7$ |
$146.6837187544787$ |
| 12.8.65995668717568.1 |
$x^{12} - 8 x^{10} - 4 x^{9} + 25 x^{8} + 18 x^{7} - 34 x^{6} - 26 x^{5} + 15 x^{4} + 14 x^{3} + x^{2} - 2 x - 1$ |
$12$ |
[8,2] |
$2^{18}\cdot 127\cdot 863\cdot 2297$ |
$4$ |
$14.178369366660123$ |
$44877.92303571991$ |
|
|
✓ |
$S_6\wr C_2$ (as 12T299) |
trivial |
$2$ |
$9$ |
$279.83494560634995$ |
| 12.0.101559956668416.2 |
$x^{12} + 8 x^{6} + 64$ |
$12$ |
[0,6] |
$2^{18}\cdot 3^{18}$ |
$2$ |
$14.6969384567$ |
$14.696938456699069$ |
✓ |
✓ |
? |
$C_6\times C_2$ (as 12T2) |
trivial |
$18$ |
$5$ |
$481.700375615$ |
| 12.0.101559956668416.7 |
$x^{12} - 2 x^{9} + 5 x^{6} + 2 x^{3} + 1$ |
$12$ |
[0,6] |
$2^{18}\cdot 3^{18}$ |
$2$ |
$14.6969384567$ |
$18.760906587882975$ |
|
|
? |
$C_6\times S_3$ (as 12T18) |
trivial |
$6$ |
$5$ |
$470.414846988$ |
| 12.6.122023936000000.1 |
$x^{12} - 2 x^{10} - 4 x^{9} - 9 x^{8} + 2 x^{7} + 20 x^{6} + 22 x^{5} + 13 x^{4} - 2 x^{3} - 9 x^{2} - 6 x - 1$ |
$12$ |
[6,3] |
$-\,2^{18}\cdot 5^{6}\cdot 31^{3}$ |
$3$ |
$14.9234906946$ |
$110.61942767882832$ |
|
|
? |
$S_3\wr C_2^2$ (as 12T261) |
trivial |
$2$ |
$8$ |
$280.158137734$ |
| 12.2.234842190774272.1 |
$x^{12} - 4 x^{11} + 4 x^{10} - 2 x^{9} + 2 x^{8} - 3 x^{6} + 2 x^{4} - 2 x^{3} + 4 x^{2} - 4 x + 1$ |
$12$ |
[2,5] |
$-\,2^{18}\cdot 23\cdot 79^{4}$ |
$3$ |
$15.760307142697759$ |
$249.74318098249037$ |
|
|
✓ |
$A_4^2:D_4$ (as 12T208) |
trivial |
$2$ |
$6$ |
$261.45473434246924$ |
| 12.2.323950103756800.1 |
$x^{12} - 4 x^{11} + 8 x^{10} - 12 x^{9} + 23 x^{8} - 42 x^{7} + 54 x^{6} - 66 x^{5} + 73 x^{4} - 58 x^{3} + 37 x^{2} - 14 x - 1$ |
$12$ |
[2,5] |
$-\,2^{18}\cdot 5^{2}\cdot 367^{3}$ |
$3$ |
$16.188496297891863$ |
$121.16104984688768$ |
|
|
? |
$S_4^2:C_2^2$ (as 12T235) |
$[2]$ |
$2$ |
$6$ |
$123.76853682360934$ |
| 12.0.358157744603136.2 |
$x^{12} + 4 x^{10} + 36 x^{8} + 72 x^{6} + 320 x^{4} + 224 x^{2} + 64$ |
$12$ |
[0,6] |
$2^{18}\cdot 3^{6}\cdot 37^{4}$ |
$3$ |
$16.324486492569463$ |
$54.39681060743917$ |
|
|
? |
$C_6\times S_3$ (as 12T18) |
trivial |
$6$ |
$5$ |
$710.5798149352412$ |
| 12.6.833089536000000.1 |
$x^{12} - 2 x^{11} - 3 x^{10} - 2 x^{9} + 5 x^{8} + 18 x^{7} + 16 x^{5} + 18 x^{4} + 4 x^{3} + 9 x^{2} + 6 x + 1$ |
$12$ |
[6,3] |
$-\,2^{18}\cdot 3^{8}\cdot 5^{6}\cdot 31$ |
$4$ |
$17.5142269615$ |
$248.27123610451955$ |
|
|
? |
$S_3\wr C_2^2$ (as 12T261) |
trivial |
$2$ |
$8$ |
$790.819189364$ |
| 12.0.1101670627147776.2 |
$x^{12} + 10 x^{10} + 76 x^{8} + 224 x^{6} + 496 x^{4} + 192 x^{2} + 64$ |
$12$ |
[0,6] |
$2^{18}\cdot 3^{6}\cdot 7^{8}$ |
$3$ |
$17.9268636048$ |
$17.926863604818365$ |
✓ |
✓ |
? |
$C_6\times C_2$ (as 12T2) |
$[3]$ |
$6$ |
$5$ |
$279.150027194$ |
| 12.0.1101670627147776.6 |
$x^{12} - 2 x^{11} - x^{10} + 4 x^{9} - 14 x^{8} + 16 x^{7} - 10 x^{6} + 22 x^{5} + 82 x^{4} - 104 x^{3} + 156 x^{2} - 16 x + 1$ |
$12$ |
[0,6] |
$2^{18}\cdot 3^{6}\cdot 7^{8}$ |
$3$ |
$17.926863604818365$ |
$24.794421938893013$ |
|
|
|
$C_6\times S_3$ (as 12T18) |
$[4]$ |
$2$ |
$5$ |
$192.03014058956524$ |
| 12.6.1203435363631104.1 |
$x^{12} - 4 x^{11} - 2 x^{10} + 20 x^{9} - 26 x^{8} - 2 x^{7} + 54 x^{6} - 64 x^{5} + 54 x^{4} - 28 x^{3} + 5 x^{2} - 2 x + 1$ |
$12$ |
[6,3] |
$-\,2^{18}\cdot 3^{2}\cdot 17^{3}\cdot 47^{3}$ |
$4$ |
$18.059340955741412$ |
$138.47743498491008$ |
|
|
? |
$S_4^2:C_2^2$ (as 12T235) |
trivial |
$2$ |
$8$ |
$1147.5870937214715$ |
| 12.0.1416001889763328.1 |
$x^{12} - 4 x^{11} + 8 x^{10} - 10 x^{9} + 13 x^{8} - 4 x^{7} + 19 x^{6} + 58 x^{5} + 122 x^{4} + 174 x^{3} + 185 x^{2} + 126 x + 41$ |
$12$ |
[0,6] |
$2^{18}\cdot 7^{8}\cdot 937$ |
$3$ |
$18.3057974532$ |
$316.8206511931203$ |
✓ |
|
? |
$C_2\wr C_6$ (as 12T134) |
trivial |
$2$ |
$5$ |
$279.150027194$ |
| 12.4.1600000000000000.1 |
$x^{12} - 6 x^{11} + 21 x^{10} - 50 x^{9} + 90 x^{8} - 126 x^{7} + 131 x^{6} - 96 x^{5} + 25 x^{4} + 30 x^{3} - 56 x^{2} + 36 x - 1$ |
$12$ |
[4,4] |
$2^{18}\cdot 5^{14}$ |
$2$ |
$18.493111943$ |
$34.27271426496622$ |
|
|
? |
$C_2\times S_5$ (as 12T123) |
trivial |
$2$ |
$7$ |
$900.412330298$ |
| 12.2.1721036800000000.1 |
$x^{12} - 2 x^{11} - 7 x^{10} + 20 x^{9} + 14 x^{8} - 84 x^{7} + 58 x^{6} + 118 x^{5} - 192 x^{4} - 76 x^{3} + 314 x^{2} - 164 x - 137$ |
$12$ |
[2,5] |
$-\,2^{18}\cdot 5^{8}\cdot 7^{5}$ |
$3$ |
$18.6058356209$ |
$21.881345138484406$ |
|
|
? |
$(C_6\times C_2):C_2$ (as 12T13) |
trivial |
$2$ |
$6$ |
$484.094640855$ |
| 12.8.1726519263363072.1 |
$x^{12} - 22 x^{9} + 15 x^{8} - 12 x^{7} + 65 x^{6} - 30 x^{5} - 48 x^{4} + 34 x^{3} + 3 x^{2} - 6 x + 1$ |
$12$ |
[8,2] |
$2^{18}\cdot 3^{18}\cdot 17$ |
$3$ |
$18.610767588863997$ |
$60.597029630172464$ |
|
|
? |
$C_2\wr C_6$ (as 12T134) |
trivial |
$2$ |
$9$ |
$1801.3672180169626$ |
| 12.12.1952518144000000.1 |
$x^{12} - 4 x^{11} - 6 x^{10} + 32 x^{9} + 12 x^{8} - 86 x^{7} - 14 x^{6} + 92 x^{5} + 10 x^{4} - 40 x^{3} - 5 x^{2} + 6 x + 1$ |
$12$ |
[12,0] |
$2^{18}\cdot 5^{6}\cdot 271\cdot 1759$ |
$4$ |
$18.8025285386$ |
$4366.641730208697$ |
|
|
? |
$S_3\wr C_2^2$ (as 12T261) |
trivial |
$2$ |
$11$ |
$3404.04609138$ |
| 12.4.2176782336000000.1 |
$x^{12} - 2 x^{9} - 5 x^{6} + 6 x^{3} - 1$ |
$12$ |
[4,4] |
$2^{18}\cdot 3^{12}\cdot 5^{6}$ |
$3$ |
$18.973665961$ |
$29.086964776206095$ |
|
|
? |
$S_3^3$ (as 12T117) |
trivial |
$2$ |
$7$ |
$837.255550788$ |
| 12.10.2400465930944512.1 |
$x^{12} - 2 x^{11} - 9 x^{10} + 16 x^{9} + 30 x^{8} - 44 x^{7} - 44 x^{6} + 50 x^{5} + 24 x^{4} - 24 x^{3} - 2 x^{2} + 4 x - 1$ |
$12$ |
[10,1] |
$-\,2^{18}\cdot 41^{3}\cdot 132863$ |
$3$ |
$19.128957204122404$ |
$6601.444084440919$ |
|
|
✓ |
$S_3\wr D_4$ (as 12T274) |
trivial |
$2$ |
$10$ |
$2971.0853091765143$ |
| 12.0.3010437727911936.2 |
$x^{12} + 104 x^{6} + 3136$ |
$12$ |
[0,6] |
$2^{18}\cdot 3^{14}\cdot 7^{4}$ |
$3$ |
$19.493319633379368$ |
$37.289378982440624$ |
|
|
|
$C_6\times S_3$ (as 12T18) |
trivial |
$6$ |
$5$ |
$3351.2225601651035$ |
| 12.0.3046955213389824.2 |
$x^{12} - 4 x^{10} + 28 x^{8} - 64 x^{6} + 176 x^{4} + 160 x^{2} + 64$ |
$12$ |
[0,6] |
$2^{18}\cdot 3^{8}\cdot 11^{6}$ |
$3$ |
$19.512915890792843$ |
$40.58850068501063$ |
|
|
? |
$C_6\times S_3$ (as 12T18) |
trivial |
$2$ |
$5$ |
$475.6052021158521$ |
| 12.12.6146560000000000.1 |
$x^{12} - 4 x^{11} - 8 x^{10} + 50 x^{9} - 15 x^{8} - 164 x^{7} + 151 x^{6} + 162 x^{5} - 220 x^{4} - 10 x^{3} + 77 x^{2} - 18 x - 1$ |
$12$ |
[12,0] |
$2^{18}\cdot 5^{10}\cdot 7^{4}$ |
$3$ |
$20.6880398353$ |
$39.574796511339834$ |
|
|
? |
$C_6\times S_3$ (as 12T18) |
trivial |
$2$ |
$11$ |
$6453.74913935$ |
| 12.0.7169347584000000.3 |
$x^{12} - 2 x^{11} + 5 x^{10} - 18 x^{9} + 29 x^{8} + 2 x^{7} - 2 x^{6} + 22 x^{5} + 13 x^{4} - 8 x^{3} + 8 x^{2} + 4 x + 1$ |
$12$ |
[0,6] |
$2^{18}\cdot 3^{6}\cdot 5^{6}\cdot 7^{4}$ |
$4$ |
$20.955111195189506$ |
$40.085685643740796$ |
|
|
? |
$C_6\times S_3$ (as 12T18) |
$[4]$ |
$2$ |
$5$ |
$413.5133199041304$ |
| 12.0.7443476394541056.1 |
$x^{12} - 2 x^{11} + 9 x^{10} - 10 x^{9} + 45 x^{8} - 54 x^{7} + 94 x^{6} - 42 x^{5} + 45 x^{4} - 20 x^{3} + 16 x^{2} - 4 x + 1$ |
$12$ |
[0,6] |
$2^{18}\cdot 3^{6}\cdot 79^{4}$ |
$3$ |
$21.02073922784017$ |
$90.19663768479226$ |
✓ |
|
? |
$C_6\times S_3$ (as 12T18) |
$[7]$ |
$6$ |
$5$ |
$522.899840495368$ |
| 12.0.8226356490141696.34 |
$x^{12} - 24 x^{6} + 576$ |
$12$ |
[0,6] |
$2^{18}\cdot 3^{22}$ |
$2$ |
$21.196653174$ |
$30.57086393216915$ |
|
|
? |
$C_6\times S_3$ (as 12T18) |
trivial |
$6$ |
$5$ |
$4586.97528369$ |
| 12.8.10292358967197696.1 |
$x^{12} - 12 x^{10} - 4 x^{9} + 23 x^{8} + 24 x^{7} - 2 x^{6} - 84 x^{5} + 60 x^{4} + 80 x^{3} - 100 x^{2} + 12 x + 9$ |
$12$ |
[8,2] |
$2^{18}\cdot 3^{2}\cdot 257^{4}$ |
$3$ |
$21.59614544725274$ |
$78.53661566428744$ |
|
|
? |
$C_2^4:S_4$ (as 12T136) |
trivial |
$2$ |
$9$ |
$6036.542938474503$ |
| 12.0.13263845122637824.1 |
$x^{12} - 4 x^{11} + 2 x^{10} - 2 x^{9} + 55 x^{8} - 184 x^{7} + 225 x^{6} + 42 x^{5} - 156 x^{4} - 54 x^{3} + 189 x^{2} - 106 x + 23$ |
$12$ |
[0,6] |
$2^{18}\cdot 11^{6}\cdot 13^{4}$ |
$3$ |
$22.057474551809886$ |
$51.86450503718846$ |
|
|
? |
$C_6\times S_3$ (as 12T18) |
trivial |
$2$ |
$5$ |
$1256.547316830405$ |
| 12.12.14003989580611584.1 |
$x^{12} - 18 x^{10} - 8 x^{9} + 81 x^{8} + 54 x^{7} - 120 x^{6} - 102 x^{5} + 45 x^{4} + 54 x^{3} + 3 x^{2} - 6 x - 1$ |
$12$ |
[12,0] |
$2^{18}\cdot 3^{16}\cdot 17\cdot 73$ |
$4$ |
$22.15751140817659$ |
$431.11442768403583$ |
|
|
? |
$C_2\wr C_6$ (as 12T134) |
trivial |
$2$ |
$11$ |
$10781.91758130257$ |
