| 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 |
| 12.6.1174204773937152.1 |
$x^{12} - 4 x^{9} + 5 x^{8} - 20 x^{6} - 10 x^{5} + 4 x^{4} + 72 x^{3} - 12 x^{2} - 24 x - 3$ |
$12$ |
[6,3] |
$-\,2^{12}\cdot 3^{7}\cdot 107^{4}$ |
$3$ |
$18.0223735391$ |
$57.72490687318343$ |
|
|
? |
$C_2^2:A_4^2:D_6$ (as 12T268) |
trivial |
$2$ |
$8$ |
$1974.3240383$ |
| 12.4.1785233613312000.1 |
$x^{12} - 10 x^{9} + 3 x^{8} - 18 x^{7} + 18 x^{6} + 18 x^{5} + 30 x^{3} + 18 x^{2} - 3$ |
$12$ |
[4,4] |
$2^{12}\cdot 3^{20}\cdot 5^{3}$ |
$3$ |
$18.6627048578$ |
$38.59499394931745$ |
|
|
? |
$A_4\wr C_2$ (as 12T129) |
trivial |
$2$ |
$7$ |
$1711.63277559$ |
| 12.4.759575758737920000.1 |
$x^{12} - 4 x^{11} - 4 x^{10} + 44 x^{9} - 57 x^{8} - 120 x^{7} + 472 x^{6} - 520 x^{5} - 265 x^{4} + 1452 x^{3} - 1724 x^{2} + 852 x - 119$ |
$12$ |
[4,4] |
$2^{12}\cdot 5^{4}\cdot 197^{5}$ |
$3$ |
$30.906340952771572$ |
$76.83313011256358$ |
|
|
? |
$C_2^6:S_3^2$ (as 12T239) |
trivial |
$2$ |
$7$ |
$36432.62975329957$ |
| 12.8.474...000.1 |
$x^{12} - 36 x^{10} - 70 x^{9} + 171 x^{8} + 500 x^{7} + 338 x^{6} + 200 x^{5} - 1126 x^{4} - 4040 x^{3} - 4066 x^{2} - 2030 x - 841$ |
$12$ |
[8,2] |
$2^{12}\cdot 5^{8}\cdot 197^{5}$ |
$3$ |
$52.84909962902834$ |
$114.89232747123341$ |
|
|
? |
$C_2^6:S_3^2$ (as 12T239) |
$[2]$ |
$2$ |
$9$ |
$890942.4471116633$ |
| 12.0.115...000.1 |
$x^{12} - 6 x^{10} - 26 x^{9} + 152 x^{8} - 100 x^{7} + 332 x^{6} - 1640 x^{5} + 2444 x^{4} - 2328 x^{3} + 4864 x^{2} - 9968 x + 7576$ |
$12$ |
[0,6] |
$2^{12}\cdot 5^{7}\cdot 7^{4}\cdot 197^{4}$ |
$4$ |
$56.92249403418581$ |
$420.42614995331354$ |
|
|
? |
$C_2^2:A_4^2:D_6$ (as 12T268) |
$[2, 2]$ |
$2$ |
$5$ |
$148774.98794401492$ |
| 12.12.316...000.1 |
$x^{12} - 6 x^{11} - 36 x^{10} + 138 x^{9} + 675 x^{8} - 432 x^{7} - 4536 x^{6} - 3816 x^{5} + 7551 x^{4} + 16014 x^{3} + 11196 x^{2} + 3294 x + 333$ |
$12$ |
[12,0] |
$2^{12}\cdot 3^{20}\cdot 5^{3}\cdot 11^{6}$ |
$4$ |
$61.8971895866$ |
$128.0051137159229$ |
|
|
? |
$A_4\wr C_2$ (as 12T129) |
trivial |
$2$ |
$11$ |
$14375090.647$ |
| 12.8.179...000.2 |
$x^{12} - 56 x^{10} - 84 x^{9} + 976 x^{8} + 3424 x^{7} - 2754 x^{6} - 32958 x^{5} - 63181 x^{4} - 498 x^{3} + 115140 x^{2} + 23730 x + 1225$ |
$12$ |
[8,2] |
$2^{12}\cdot 5^{5}\cdot 7^{4}\cdot 197^{6}$ |
$4$ |
$105.00257686854629$ |
$281.1559117398418$ |
|
|
? |
$C_2^2:A_4^2:D_6$ (as 12T268) |
$[2]$ |
$2$ |
$9$ |
$151614658.72121155$ |
| 16.0.108...656.1 |
$x^{16} - 8 x^{15} + 48 x^{14} - 193 x^{13} + 695 x^{12} - 2004 x^{11} + 5226 x^{10} - 10962 x^{9} + 20754 x^{8} - 31044 x^{7} + 40308 x^{6} - 37044 x^{5} + 32268 x^{4} - 38256 x^{3} - 2880 x^{2} + 21752 x + 6296$ |
$16$ |
[0,8] |
$2^{12}\cdot 3^{12}\cdot 163^{8}$ |
$3$ |
$48.9448768355$ |
|
|
|
? |
$C_2^8:\PGU(3,2)$ (as 16T1859) |
$[2]$ |
$2$ |
$7$ |
$8712444.53743$ |
| 16.0.108...656.3 |
$x^{16} - 8 x^{15} + 24 x^{14} - 16 x^{13} + 5 x^{12} - 318 x^{11} + 848 x^{10} + 266 x^{9} - 894 x^{8} - 6808 x^{7} + 8432 x^{6} + 13092 x^{5} + 2664 x^{4} - 46248 x^{3} + 5736 x^{2} + 24896 x + 9512$ |
$16$ |
[0,8] |
$2^{12}\cdot 3^{12}\cdot 163^{8}$ |
$3$ |
$48.9448768355$ |
|
|
|
? |
$C_2^8:\PGU(3,2)$ (as 16T1859) |
$[2]$ |
$2$ |
$7$ |
$51496894.4339$ |
| 16.0.108...656.4 |
$x^{16} - 3 x^{15} + 10 x^{14} - 28 x^{13} + 98 x^{12} - 173 x^{11} + 244 x^{10} - 322 x^{9} + 1371 x^{8} - 3858 x^{7} + 7986 x^{6} - 11046 x^{5} + 11887 x^{4} - 9003 x^{3} + 4474 x^{2} - 998 x + 77$ |
$16$ |
[0,8] |
$2^{12}\cdot 3^{12}\cdot 163^{8}$ |
$3$ |
$48.94487683549677$ |
|
|
|
? |
$C_2^8:\PGU(3,2)$ (as 16T1859) |
$[2]$ |
$2$ |
$7$ |
$11805168.152779523$ |
| 16.4.173...496.1 |
$x^{16} - 4 x^{15} - 7 x^{14} + 42 x^{13} - 28 x^{12} + 20 x^{11} - 537 x^{10} + 1994 x^{9} - 1405 x^{8} - 2688 x^{7} + 3530 x^{6} - 2080 x^{5} - 23759 x^{4} - 11516 x^{3} + 35605 x^{2} + 56452 x + 48903$ |
$16$ |
[4,6] |
$2^{16}\cdot 3^{12}\cdot 163^{8}$ |
$3$ |
$58.2055957757$ |
|
|
|
? |
$C_2^8:\PGU(3,2)$ (as 16T1859) |
trivial |
$2$ |
$9$ |
$229030781.298$ |
| 16.4.173...496.3 |
$x^{16} - 15 x^{14} - 6 x^{13} + 27 x^{12} - 168 x^{11} - 270 x^{10} - 42 x^{9} - 4209 x^{8} - 9818 x^{7} - 18801 x^{6} - 33768 x^{5} - 20306 x^{4} - 27924 x^{3} + 22833 x^{2} + 5346 x + 44631$ |
$16$ |
[4,6] |
$2^{16}\cdot 3^{12}\cdot 163^{8}$ |
$3$ |
$58.2055957757$ |
|
|
|
? |
$C_2^8:\PGU(3,2)$ (as 16T1859) |
trivial |
$2$ |
$9$ |
$186234458.317$ |
| 16.4.173...496.5 |
$x^{16} + 3 x^{14} - 30 x^{13} - 150 x^{12} + 18 x^{11} + 1276 x^{10} + 84 x^{9} - 3003 x^{8} + 6140 x^{7} - 3531 x^{6} - 16806 x^{5} + 9791 x^{4} - 8382 x^{3} - 16713 x^{2} - 216 x + 7776$ |
$16$ |
[4,6] |
$2^{16}\cdot 3^{12}\cdot 163^{8}$ |
$3$ |
$58.20559577570462$ |
|
|
|
? |
$C_2^8:\PGU(3,2)$ (as 16T1859) |
trivial |
$2$ |
$9$ |
$511111178.07112306$ |
| 18.4.458...000.1 |
$x^{18} + 45 x^{16} - 20 x^{15} + 540 x^{14} - 588 x^{13} + 940 x^{12} - 2340 x^{11} - 1770 x^{10} - 11580 x^{9} - 7074 x^{8} + 12420 x^{7} - 8260 x^{6} - 8100 x^{5} - 4020 x^{4} + 2740 x^{3} - 495 x^{2} + 300 x + 125$ |
$18$ |
[4,7] |
$-\,2^{18}\cdot 3^{18}\cdot 5^{15}\cdot 23^{6}$ |
$4$ |
$65.2432418875$ |
|
|
|
? |
$A_6^3.D_6$ (as 18T972) |
trivial |
$2$ |
$10$ |
$2714685526.95$ |
| 18.4.810...000.1 |
$x^{18} - 45 x^{16} - 30 x^{15} + 855 x^{14} + 1260 x^{13} - 5535 x^{12} - 2250 x^{11} + 35775 x^{10} - 137200 x^{9} - 904635 x^{8} - 1332900 x^{7} + 430800 x^{6} + 2971800 x^{5} + 2888100 x^{4} + 1575000 x^{3} + 1526625 x^{2} + 1080000 x + 146875$ |
$18$ |
[4,7] |
$-\,2^{18}\cdot 3^{39}\cdot 5^{17}$ |
$3$ |
$98.839616498$ |
|
|
|
? |
$A_6^3.S_4$ (as 18T975) |
trivial |
$2$ |
$10$ |
$533901666157$ |
| 18.10.184...000.1 |
$x^{18} - 3 x^{17} - 33 x^{16} + 97 x^{15} - 120 x^{14} - 3282 x^{13} - 8414 x^{12} - 28119 x^{11} + 10641 x^{10} - 103975 x^{9} - 1642035 x^{8} + 254820 x^{7} + 17547325 x^{6} + 60394035 x^{5} + 53593305 x^{4} - 326205513 x^{3} - 642256371 x^{2} + 332014959 x + 920890279$ |
$18$ |
[10,4] |
$2^{12}\cdot 3^{18}\cdot 5^{18}\cdot 7^{12}\cdot 13^{3}$ |
$5$ |
$133.6084241$ |
|
|
|
|
$S_6\wr C_3$ (as 18T974) |
trivial |
$2$ |
$13$ |
$5291905923500$ |
| 18.4.132...000.1 |
$x^{18} - 180 x^{16} - 190 x^{15} + 12150 x^{14} + 23802 x^{13} - 346360 x^{12} - 764490 x^{11} + 4521945 x^{10} + 10041430 x^{9} - 20267376 x^{8} - 7061370 x^{7} + 144139885 x^{6} - 121774470 x^{5} - 1150369200 x^{4} - 2443872464 x^{3} - 4116032160 x^{2} - 4515537600 x - 1994392000$ |
$18$ |
[4,7] |
$-\,2^{12}\cdot 3^{18}\cdot 5^{18}\cdot 23^{9}\cdot 59^{4}$ |
$5$ |
$282.595023788$ |
|
|
|
? |
$A_6^3.S_3$ (as 18T970) |
trivial |
$2$ |
$10$ |
$1505555800020000$ |
| 18.12.158...000.1 |
$x^{18} - 90 x^{16} - 460 x^{15} + 13725 x^{14} - 31470 x^{13} - 915575 x^{12} - 886050 x^{11} + 56220300 x^{10} + 230860250 x^{9} - 3459598200 x^{8} + 7811340000 x^{7} + 6867748500 x^{6} - 31122216000 x^{5} + 1013332500 x^{4} + 37058516000 x^{3} - 11178180000 x^{2} - 14232300000 x + 6452375000$ |
$18$ |
[12,3] |
$-\,2^{12}\cdot 3^{18}\cdot 5^{18}\cdot 7^{12}\cdot 167^{3}\cdot 449^{4}$ |
$6$ |
$794.360128047$ |
|
|
|
? |
$S_6\wr C_3$ (as 18T974) |
trivial |
$2$ |
$14$ |
$72946411820200000000$ |
| 18.10.705...832.1 |
$x^{18} - 6 x^{17} - 108 x^{16} + 772 x^{15} + 4433 x^{14} - 42980 x^{13} - 59090 x^{12} + 1276064 x^{11} - 1383341 x^{10} - 19685190 x^{9} + 62494500 x^{8} + 97962900 x^{7} - 831660421 x^{6} + 1128484528 x^{5} + 2650963946 x^{4} - 11922524032 x^{3} + 18891897112 x^{2} - 14638620448 x + 4638050792$ |
$18$ |
[10,4] |
$2^{21}\cdot 3^{6}\cdot 61^{12}\cdot 2887^{2}\cdot 4568667737539^{2}$ |
$5$ |
$3101.69680734$ |
|
|
|
|
$A_6^3.C_6$ (as 18T969) |
trivial |
$2$ |
$13$ |
$202089295576000000000000000$ |
| 28.2.119...904.1 |
$x^{28} - 2 x - 1$ |
$28$ |
[2,13] |
$-\,2^{28}\cdot 5167\cdot 353915647\cdot 3141620149\cdot 77184457201040359$ |
$5$ |
$48.0035802664$ |
|
|
|
✓ |
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$14$ |
$4100907986522.6587$ |
| 28.0.252...264.1 |
$x^{28} - 2 x + 3$ |
$28$ |
[0,14] |
$2^{28}\cdot 3^{27}\cdot 13\cdot 6553\cdot 20327\cdot 42022097279\cdot 1696876609651$ |
$7$ |
$80.7679823424$ |
|
|
|
✓ |
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$13$ |
$10505974365221896$ |
| 28.0.617...208.1 |
$x^{28} - 2 x + 5$ |
$28$ |
[0,14] |
$2^{26}\cdot 53\cdot 137\cdot 5167\cdot 182453\cdot 1981277\cdot 67\!\cdots\!51$ |
$7$ |
$125.79479702$ |
$7.425367777949566e+25$ |
|
|
? |
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$13$ |
$7257941571662790000$ |
| 28.2.246...168.1 |
$x^{28} - 2 x - 5$ |
$28$ |
[2,13] |
$-\,2^{28}\cdot 347\cdot 10313\cdot 7313389\cdot 4719485717\cdot 5637211457\cdot 1321243754190655553$ |
$7$ |
$132.179718077$ |
|
|
|
✓ |
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$14$ |
$18376264601489019000$ |
| 29.1.689...128.1 |
$x^{29} - x - 2$ |
$29$ |
[1,14] |
$2^{28}\cdot 23\cdot 2505541501481\cdot 44556647066894154934970530051$ |
$4$ |
$56.6301417736$ |
|
|
|
✓ |
$S_{29}$ (as 29T8) |
trivial |
$2$ |
$14$ |
$261495167861816.16$ |
| 29.1.227...752.1 |
$x^{29} + 3 x - 2$ |
$29$ |
[1,14] |
$2^{28}\cdot 8447\cdot 10\!\cdots\!11$ |
$3$ |
$74.8827563475$ |
|
|
|
✓ |
$S_{29}$ (as 29T8) |
trivial |
$2$ |
$14$ |
$23857799922719012$ |
| 29.1.154...216.1 |
$x^{29} + 5 x - 2$ |
$29$ |
[1,14] |
$2^{26}\cdot 337\cdot 709\cdot 224066062071001\cdot 7834502381769247\cdot 54834197285853919$ |
$6$ |
$118.977638654$ |
$3.712683889182923e+26$ |
|
|
|
$S_{29}$ (as 29T8) |
trivial |
$2$ |
$14$ |
$22143705810942657000$ |
| 29.3.617...136.1 |
$x^{29} - 5 x - 2$ |
$29$ |
[3,13] |
$-\,2^{28}\cdot 3\cdot 47\cdot 19231\cdot 1239599\cdot 17156593\cdot 53138329\cdot 7505402452445630661805687$ |
$8$ |
$124.80329013$ |
|
|
|
✓ |
$S_{29}$ (as 29T8) |
trivial |
$2$ |
$15$ |
$48016386518967206000$ |
