| 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 |
| 12.8.44804009850925.1 |
$x^{12} - 4 x^{11} + 3 x^{10} + x^{9} - 4 x^{8} + 3 x^{7} + x^{6} + 9 x^{5} + 3 x^{4} - 12 x^{3} - 4 x^{2} + 3 x + 1$ |
$12$ |
[8,2] |
$5^{2}\cdot 13^{11}$ |
$2$ |
$13.7280780714$ |
$23.474683296117743$ |
|
|
? |
$C_4\times A_4$ (as 12T29) |
trivial |
$2$ |
$9$ |
$219.591054766$ |
| 12.8.1120100246273125.1 |
$x^{12} - 3 x^{11} - 4 x^{10} + 12 x^{9} + 3 x^{8} + 4 x^{7} + 27 x^{6} - 81 x^{5} - 82 x^{4} + 77 x^{3} + 81 x^{2} + 17 x + 1$ |
$12$ |
[8,2] |
$5^{4}\cdot 13^{11}$ |
$2$ |
$17.9516652428$ |
$23.474683296117743$ |
|
|
? |
$C_4\times A_4$ (as 12T29) |
trivial |
$2$ |
$9$ |
$1287.01375469$ |
| 12.8.1593224064453125.1 |
$x^{12} - 2 x^{11} - 8 x^{10} + 15 x^{9} + 26 x^{8} - 25 x^{7} - 72 x^{6} - 21 x^{5} + 151 x^{4} + 45 x^{3} - 90 x^{2} - 30 x + 5$ |
$12$ |
[8,2] |
$5^{9}\cdot 13^{8}$ |
$2$ |
$18.4865727752$ |
$18.48657277522785$ |
|
|
? |
$C_4\times A_4$ (as 12T29) |
trivial |
$2$ |
$9$ |
$2342.56496701$ |
| 12.4.1722266138669557.1 |
$x^{12} - 2 x^{11} + 4 x^{10} - 21 x^{9} + 55 x^{8} - 58 x^{7} - 27 x^{6} + 145 x^{5} - 212 x^{4} + 190 x^{3} - 107 x^{2} + 32 x + 1$ |
$12$ |
[4,4] |
$13^{11}\cdot 31^{2}$ |
$2$ |
$18.6069427727$ |
$58.45149002624982$ |
|
|
? |
$C_4\times A_4$ (as 12T29) |
trivial |
$2$ |
$7$ |
$513.312151562$ |
| 12.12.3958882310427733.1 |
$x^{12} - 4 x^{11} - 10 x^{10} + 53 x^{9} + 9 x^{8} - 205 x^{7} + 105 x^{6} + 204 x^{5} - 101 x^{4} - 90 x^{3} + 22 x^{2} + 16 x + 1$ |
$12$ |
[12,0] |
$13^{11}\cdot 47^{2}$ |
$2$ |
$19.9433318554$ |
$71.97201612445268$ |
|
|
? |
$C_4\times A_4$ (as 12T29) |
trivial |
$2$ |
$11$ |
$5234.40251791$ |
| 12.4.7340688973975552.3 |
$x^{12} - 26 x^{8} + 78 x^{4} + 65 x^{2} + 13$ |
$12$ |
[4,4] |
$2^{12}\cdot 13^{11}$ |
$2$ |
$20.9963950402$ |
$35.31158664504155$ |
|
|
? |
$C_4\times A_4$ (as 12T29) |
trivial |
$2$ |
$7$ |
$983.699811524$ |
| 12.8.7340688973975552.3 |
$x^{12} - 26 x^{8} + 78 x^{4} - 65 x^{2} + 13$ |
$12$ |
[8,2] |
$2^{12}\cdot 13^{11}$ |
$2$ |
$20.9963950402$ |
$29.69338662673638$ |
|
|
? |
$C_4\times A_4$ (as 12T29) |
trivial |
$2$ |
$9$ |
$3316.50732182$ |
| 12.12.11184873019184917.1 |
$x^{12} - 4 x^{11} - 10 x^{10} + 40 x^{9} + 48 x^{8} - 140 x^{7} - 129 x^{6} + 191 x^{5} + 146 x^{4} - 103 x^{3} - 56 x^{2} + 16 x + 1$ |
$12$ |
[12,0] |
$13^{11}\cdot 79^{2}$ |
$2$ |
$21.7463273633$ |
$93.31002058984804$ |
|
|
? |
$C_4\times A_4$ (as 12T29) |
trivial |
$2$ |
$11$ |
$8697.951762$ |
| 12.8.49519263525896192.3 |
$x^{12} - 4 x^{10} - 22 x^{8} + 56 x^{6} - 8 x^{4} - 32 x^{2} + 8$ |
$12$ |
[8,2] |
$2^{33}\cdot 7^{8}$ |
$2$ |
$24.616776431$ |
$31.92400938372945$ |
|
|
? |
$C_4\times A_4$ (as 12T29) |
trivial |
$2$ |
$9$ |
$14790.8704332$ |
| 12.4.49519263525896192.10 |
$x^{12} + 4 x^{10} - 22 x^{8} - 56 x^{6} - 8 x^{4} + 32 x^{2} + 8$ |
$12$ |
[4,4] |
$2^{33}\cdot 7^{8}$ |
$2$ |
$24.616776431$ |
$31.92400938372945$ |
|
|
? |
$C_4\times A_4$ (as 12T29) |
trivial |
$2$ |
$7$ |
$3434.1112172$ |
| 12.8.61132828589969773.1 |
$x^{12} - 3 x^{11} - 9 x^{10} + 29 x^{9} + 41 x^{8} - 82 x^{7} - 263 x^{6} + 36 x^{5} + 705 x^{4} + 468 x^{3} - 182 x^{2} - 169 x - 13$ |
$12$ |
[8,2] |
$7^{8}\cdot 13^{9}$ |
$2$ |
$25.052796318948193$ |
$25.052796318948193$ |
|
|
? |
$C_4\times A_4$ (as 12T29) |
trivial |
$2$ |
$9$ |
$12117.551502516422$ |
| 12.0.125854463671248325.1 |
$x^{12} - 2 x^{11} + 17 x^{10} - 34 x^{9} + 159 x^{8} - 305 x^{7} + 909 x^{6} - 1493 x^{5} + 2869 x^{4} - 3385 x^{3} + 3910 x^{2} - 2646 x + 1171$ |
$12$ |
[0,6] |
$5^{2}\cdot 13^{11}\cdot 53^{2}$ |
$3$ |
$26.6065798684$ |
$170.89827401179497$ |
✓ |
|
? |
$C_4\times A_4$ (as 12T29) |
$[2, 2, 4]$ |
$2$ |
$5$ |
$120.784031363$ |
| 12.0.180092405836384093.1 |
$x^{12} - 4 x^{11} + 29 x^{10} - 51 x^{9} + 256 x^{8} - 166 x^{7} + 963 x^{6} + 126 x^{5} + 1810 x^{4} + 1054 x^{3} + 2336 x^{2} + 1472 x + 1223$ |
$12$ |
[0,6] |
$13^{11}\cdot 317^{2}$ |
$2$ |
$27.4130873531$ |
$186.91509281243734$ |
✓ |
|
? |
$C_4\times A_4$ (as 12T29) |
$[3, 6]$ |
$2$ |
$5$ |
$120.784031363$ |
| 12.8.369768517790072832.1 |
$x^{12} - 36 x^{8} + 40 x^{6} + 36 x^{4} - 48 x^{2} + 8$ |
$12$ |
[8,2] |
$2^{33}\cdot 3^{16}$ |
$2$ |
$29.1067798457$ |
$37.74682341248098$ |
|
|
? |
$C_4\times A_4$ (as 12T29) |
trivial |
$2$ |
$9$ |
$29068.1942306$ |
| 12.4.369...832.27 |
$x^{12} - 36 x^{8} - 40 x^{6} + 36 x^{4} + 48 x^{2} + 8$ |
$12$ |
[4,4] |
$2^{33}\cdot 3^{16}$ |
$2$ |
$29.1067798457$ |
$37.74682341248098$ |
|
|
? |
$C_4\times A_4$ (as 12T29) |
trivial |
$2$ |
$7$ |
$8822.71166878$ |
| 12.8.469804094334435328.2 |
$x^{12} - 104 x^{8} + 1248 x^{4} - 2080 x^{2} + 832$ |
$12$ |
[8,2] |
$2^{18}\cdot 13^{11}$ |
$2$ |
$29.6933866267$ |
$49.93812474233042$ |
|
|
? |
$C_4\times A_4$ (as 12T29) |
trivial |
$2$ |
$9$ |
$26529.2851581$ |
| 12.4.469804094334435328.8 |
$x^{12} - 104 x^{8} + 1248 x^{4} + 2080 x^{2} + 832$ |
$12$ |
[4,4] |
$2^{18}\cdot 13^{11}$ |
$2$ |
$29.6933866267$ |
$49.93812474233042$ |
|
|
? |
$C_4\times A_4$ (as 12T29) |
trivial |
$2$ |
$7$ |
$9433.19929969$ |
| 12.8.242...408.11 |
$x^{12} - 84 x^{8} + 280 x^{6} + 196 x^{4} - 784 x^{2} + 392$ |
$12$ |
[8,2] |
$2^{33}\cdot 7^{10}$ |
$2$ |
$34.0471571079$ |
$44.153700060986644$ |
|
|
? |
$C_4\times A_4$ (as 12T29) |
trivial |
$2$ |
$9$ |
$78775.3601298$ |
| 12.4.242...408.31 |
$x^{12} - 84 x^{8} - 280 x^{6} + 196 x^{4} + 784 x^{2} + 392$ |
$12$ |
[4,4] |
$2^{33}\cdot 7^{10}$ |
$2$ |
$34.0471571079$ |
$44.153700060986644$ |
|
|
? |
$C_4\times A_4$ (as 12T29) |
trivial |
$2$ |
$7$ |
$26593.1943077$ |
| 12.8.332...488.3 |
$x^{12} - 12 x^{10} + 18 x^{8} + 120 x^{6} - 216 x^{4} + 72$ |
$12$ |
[8,2] |
$2^{33}\cdot 3^{18}$ |
$2$ |
$34.9554075629$ |
$45.331555176551156$ |
|
|
? |
$C_4\times A_4$ (as 12T29) |
trivial |
$2$ |
$9$ |
$114055.098646$ |
| 12.4.332...488.35 |
$x^{12} + 12 x^{10} + 18 x^{8} - 120 x^{6} - 216 x^{4} + 72$ |
$12$ |
[4,4] |
$2^{33}\cdot 3^{18}$ |
$2$ |
$34.9554075629$ |
$45.331555176551156$ |
|
|
? |
$C_4\times A_4$ (as 12T29) |
trivial |
$2$ |
$7$ |
$43388.9537517$ |
| 12.0.652...000.1 |
$x^{12} + 35 x^{10} + 425 x^{8} + 2350 x^{6} + 6225 x^{4} + 7500 x^{2} + 3125$ |
$12$ |
[0,6] |
$2^{12}\cdot 5^{9}\cdot 13^{8}$ |
$3$ |
$36.9731455504557$ |
$52.287923881048904$ |
✓ |
|
? |
$C_4\times A_4$ (as 12T29) |
$[2, 2, 10]$ |
$2$ |
$5$ |
$615.5445050404002$ |
| 12.4.652...000.1 |
$x^{12} + 10 x^{10} - 25 x^{8} - 400 x^{6} - 525 x^{4} + 1875 x^{2} + 3125$ |
$12$ |
[4,4] |
$2^{12}\cdot 5^{9}\cdot 13^{8}$ |
$3$ |
$36.9731455504557$ |
$36.9731455504557$ |
|
|
? |
$C_4\times A_4$ (as 12T29) |
$[2, 2]$ |
$2$ |
$7$ |
$19129.88218219619$ |
| 12.12.652...000.2 |
$x^{12} - 35 x^{10} + 425 x^{8} - 2350 x^{6} + 6225 x^{4} - 7500 x^{2} + 3125$ |
$12$ |
[12,0] |
$2^{12}\cdot 5^{9}\cdot 13^{8}$ |
$3$ |
$36.9731455504557$ |
$62.18117110806405$ |
|
|
? |
$C_4\times A_4$ (as 12T29) |
trivial |
$2$ |
$11$ |
$423380.53161278967$ |
| 12.8.700...832.3 |
$x^{12} + 4 x^{10} - 46 x^{8} + 8 x^{6} + 88 x^{4} - 64 x^{2} + 8$ |
$12$ |
[8,2] |
$2^{33}\cdot 13^{8}$ |
$2$ |
$37.1930153725$ |
$48.23337349185383$ |
|
|
? |
$C_4\times A_4$ (as 12T29) |
trivial |
$2$ |
$9$ |
$101614.604445$ |
| 12.4.700...832.14 |
$x^{12} - 4 x^{10} - 46 x^{8} - 8 x^{6} + 88 x^{4} + 64 x^{2} + 8$ |
$12$ |
[4,4] |
$2^{33}\cdot 13^{8}$ |
$2$ |
$37.1930153725$ |
$48.23337349185383$ |
|
|
? |
$C_4\times A_4$ (as 12T29) |
trivial |
$2$ |
$7$ |
$56296.4349842$ |
| 12.8.145...272.3 |
$x^{12} + 8 x^{10} - 52 x^{8} - 40 x^{6} + 148 x^{4} - 80 x^{2} + 8$ |
$12$ |
[8,2] |
$2^{33}\cdot 19^{8}$ |
$2$ |
$47.8999310991$ |
$62.11852531439938$ |
|
|
? |
$C_4\times A_4$ (as 12T29) |
trivial |
$2$ |
$9$ |
$607963.728028$ |
| 12.4.145...272.14 |
$x^{12} - 8 x^{10} - 52 x^{8} + 40 x^{6} + 148 x^{4} + 80 x^{2} + 8$ |
$12$ |
[4,4] |
$2^{33}\cdot 19^{8}$ |
$2$ |
$47.8999310991$ |
$62.11852531439938$ |
|
|
|
$C_4\times A_4$ (as 12T29) |
trivial |
$2$ |
$7$ |
$722702.488938$ |
| 12.8.484...125.1 |
$x^{12} - 3 x^{11} - 39 x^{10} + 125 x^{9} + 240 x^{8} - 753 x^{7} + 114 x^{6} + 462 x^{5} - 750 x^{4} + 2115 x^{3} - 3129 x^{2} + 1617 x + 251$ |
$12$ |
[8,2] |
$3^{16}\cdot 5^{9}\cdot 7^{8}$ |
$3$ |
$52.940479380274844$ |
$52.940479380274844$ |
|
|
? |
$C_4\times A_4$ (as 12T29) |
$[3]$ |
$2$ |
$9$ |
$697232.9820818221$ |
| 12.8.793...125.1 |
$x^{12} - x^{11} - 32 x^{10} + 5 x^{9} + 171 x^{8} - 55 x^{7} + 1092 x^{6} + 368 x^{5} - 5094 x^{4} + 4535 x^{3} - 11320 x^{2} + 11160 x - 2305$ |
$12$ |
[8,2] |
$5^{9}\cdot 67^{8}$ |
$2$ |
$55.158278721977574$ |
$55.158278721977574$ |
|
|
? |
$C_4\times A_4$ (as 12T29) |
trivial |
$2$ |
$9$ |
$1810052.2115730867$ |
| 12.8.118...608.4 |
$x^{12} - 156 x^{8} + 520 x^{6} + 676 x^{4} - 2704 x^{2} + 1352$ |
$12$ |
[8,2] |
$2^{33}\cdot 13^{10}$ |
$2$ |
$57.0320017457$ |
$73.96135574474955$ |
|
|
? |
$C_4\times A_4$ (as 12T29) |
$[2]$ |
$2$ |
$9$ |
$710952.416565$ |
| 12.4.118...608.18 |
$x^{12} - 156 x^{8} - 520 x^{6} + 676 x^{4} + 2704 x^{2} + 1352$ |
$12$ |
[4,4] |
$2^{33}\cdot 13^{10}$ |
$2$ |
$57.0320017457$ |
$73.96135574474955$ |
|
|
? |
$C_4\times A_4$ (as 12T29) |
$[2]$ |
$2$ |
$7$ |
$290311.162469$ |
| 12.8.732...072.1 |
$x^{12} - 8 x^{10} - 100 x^{8} + 224 x^{6} + 228 x^{4} - 288 x^{2} + 32$ |
$12$ |
[8,2] |
$2^{33}\cdot 31^{8}$ |
$2$ |
$66.3855591089$ |
$78.94617922575179$ |
|
|
|
$C_4\times A_4$ (as 12T29) |
trivial |
$2$ |
$9$ |
$22725675.7334$ |
| 12.12.732...072.2 |
$x^{12} - 44 x^{10} + 602 x^{8} - 3280 x^{6} + 7824 x^{4} - 7680 x^{2} + 2048$ |
$12$ |
[12,0] |
$2^{33}\cdot 31^{8}$ |
$2$ |
$66.3855591089$ |
$78.94617922575179$ |
|
|
|
$C_4\times A_4$ (as 12T29) |
trivial |
$2$ |
$11$ |
$74920957.6143$ |
| 12.8.732...072.2 |
$x^{12} - 4 x^{10} - 118 x^{8} + 400 x^{6} + 208 x^{4} - 1280 x^{2} + 512$ |
$12$ |
[8,2] |
$2^{33}\cdot 31^{8}$ |
$2$ |
$66.3855591089$ |
$66.38555910891195$ |
|
|
|
$C_4\times A_4$ (as 12T29) |
trivial |
$2$ |
$9$ |
$21622775.5814$ |
| 12.8.732...072.3 |
$x^{12} - 16 x^{10} - 28 x^{8} + 800 x^{6} - 1436 x^{4} - 1280 x^{2} + 2048$ |
$12$ |
[8,2] |
$2^{33}\cdot 31^{8}$ |
$2$ |
$66.3855591089$ |
$78.94617922575179$ |
|
|
|
$C_4\times A_4$ (as 12T29) |
trivial |
$2$ |
$9$ |
$26313580.9695$ |
| 12.8.732...072.4 |
$x^{12} - 28 x^{10} + 170 x^{8} + 304 x^{6} - 2544 x^{4} + 1536 x^{2} + 2048$ |
$12$ |
[8,2] |
$2^{33}\cdot 31^{8}$ |
$2$ |
$66.3855591089$ |
$78.94617922575179$ |
|
|
|
$C_4\times A_4$ (as 12T29) |
trivial |
$2$ |
$9$ |
$33888946.2695$ |
| 12.4.732...072.12 |
$x^{12} + 8 x^{10} - 100 x^{8} - 224 x^{6} + 228 x^{4} + 288 x^{2} + 32$ |
$12$ |
[4,4] |
$2^{33}\cdot 31^{8}$ |
$2$ |
$66.3855591089$ |
$78.94617922575179$ |
|
|
|
$C_4\times A_4$ (as 12T29) |
$[2]$ |
$2$ |
$7$ |
$7912136.09849$ |
| 12.4.732...072.39 |
$x^{12} + 4 x^{10} - 118 x^{8} - 400 x^{6} + 208 x^{4} + 1280 x^{2} + 512$ |
$12$ |
[4,4] |
$2^{33}\cdot 31^{8}$ |
$2$ |
$66.3855591089$ |
$66.38555910891195$ |
|
|
|
$C_4\times A_4$ (as 12T29) |
$[2]$ |
$2$ |
$7$ |
$5213252.16877$ |
| 12.4.732...072.45 |
$x^{12} + 28 x^{10} + 170 x^{8} - 304 x^{6} - 2544 x^{4} - 1536 x^{2} + 2048$ |
$12$ |
[4,4] |
$2^{33}\cdot 31^{8}$ |
$2$ |
$66.3855591089$ |
$78.94617922575179$ |
|
|
|
$C_4\times A_4$ (as 12T29) |
$[2]$ |
$2$ |
$7$ |
$4491192.5498$ |
| 12.4.732...072.50 |
$x^{12} + 16 x^{10} - 28 x^{8} - 800 x^{6} - 1436 x^{4} + 1280 x^{2} + 2048$ |
$12$ |
[4,4] |
$2^{33}\cdot 31^{8}$ |
$2$ |
$66.3855591089$ |
$78.94617922575179$ |
|
|
|
$C_4\times A_4$ (as 12T29) |
$[2]$ |
$2$ |
$7$ |
$5906134.58032$ |
| 12.0.732...072.91 |
$x^{12} + 44 x^{10} + 602 x^{8} + 3280 x^{6} + 7824 x^{4} + 7680 x^{2} + 2048$ |
$12$ |
[0,6] |
$2^{33}\cdot 31^{8}$ |
$2$ |
$66.3855591089$ |
$78.94617922575179$ |
✓ |
|
|
$C_4\times A_4$ (as 12T29) |
$[2, 58]$ |
$2$ |
$5$ |
$34680.608017$ |
| 12.8.153...904.3 |
$x^{12} - 364 x^{8} + 1768 x^{6} + 18148 x^{4} - 114608 x^{2} + 65000$ |
$12$ |
[8,2] |
$2^{33}\cdot 13^{11}$ |
$2$ |
$70.6231732901$ |
$91.58692459755245$ |
|
|
|
$C_4\times A_4$ (as 12T29) |
$[2]$ |
$2$ |
$9$ |
$13921447.5172$ |
| 12.8.153...904.8 |
$x^{12} - 572 x^{8} + 3432 x^{6} - 988 x^{4} - 6448 x^{2} + 2600$ |
$12$ |
[8,2] |
$2^{33}\cdot 13^{11}$ |
$2$ |
$70.6231732901$ |
$91.58692459755245$ |
|
|
? |
$C_4\times A_4$ (as 12T29) |
$[2]$ |
$2$ |
$9$ |
$6585674.90846$ |
| 12.4.153...904.14 |
$x^{12} - 364 x^{8} - 1768 x^{6} + 18148 x^{4} + 114608 x^{2} + 65000$ |
$12$ |
[4,4] |
$2^{33}\cdot 13^{11}$ |
$2$ |
$70.6231732901$ |
$91.58692459755245$ |
|
|
|
$C_4\times A_4$ (as 12T29) |
$[2]$ |
$2$ |
$7$ |
$5554903.1389$ |
| 12.4.153...904.31 |
$x^{12} - 572 x^{8} - 3432 x^{6} - 988 x^{4} + 6448 x^{2} + 2600$ |
$12$ |
[4,4] |
$2^{33}\cdot 13^{11}$ |
$2$ |
$70.6231732901$ |
$91.58692459755245$ |
|
|
? |
$C_4\times A_4$ (as 12T29) |
$[2]$ |
$2$ |
$7$ |
$2311647.36647$ |
| 12.8.526...192.4 |
$x^{12} - 228 x^{8} + 760 x^{6} + 1444 x^{4} - 5776 x^{2} + 2888$ |
$12$ |
[8,2] |
$2^{33}\cdot 19^{10}$ |
$2$ |
$78.2457015658$ |
$101.47212077197112$ |
|
|
|
$C_4\times A_4$ (as 12T29) |
trivial |
$2$ |
$9$ |
$22011031.2113$ |
| 12.4.526...192.19 |
$x^{12} - 228 x^{8} - 760 x^{6} + 1444 x^{4} + 5776 x^{2} + 2888$ |
$12$ |
[4,4] |
$2^{33}\cdot 19^{10}$ |
$2$ |
$78.2457015658$ |
$101.47212077197112$ |
|
|
? |
$C_4\times A_4$ (as 12T29) |
trivial |
$2$ |
$7$ |
$8066218.49632$ |
| 12.8.132...125.1 |
$x^{12} - 3 x^{11} + 41 x^{10} - 115 x^{9} + 80 x^{8} + 607 x^{7} - 6096 x^{6} + 10007 x^{5} + 8760 x^{4} - 16795 x^{3} - 2519 x^{2} + 6032 x - 1159$ |
$12$ |
[8,2] |
$5^{9}\cdot 127^{8}$ |
$2$ |
$84.48183087096399$ |
$84.48183087096399$ |
|
|
? |
$C_4\times A_4$ (as 12T29) |
trivial |
$2$ |
$9$ |
$38485281.66907484$ |
| 12.8.191...125.1 |
$x^{12} + 10 x^{10} - 625 x^{8} - 1150 x^{6} + 49225 x^{4} - 107500 x^{2} + 50000$ |
$12$ |
[8,2] |
$5^{9}\cdot 7^{8}\cdot 19^{8}$ |
$3$ |
$87.12215257437191$ |
$87.12215257437191$ |
|
|
? |
$C_4\times A_4$ (as 12T29) |
$[3]$ |
$2$ |
$9$ |
$11022550.920680089$ |
