| 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 |
| 14.12.404...875.1 |
$x^{14} - 2 x^{13} - 11 x^{12} + 19 x^{11} + 49 x^{10} - 67 x^{9} - 111 x^{8} + 108 x^{7} + 131 x^{6} - 78 x^{5} - 74 x^{4} + 20 x^{3} + 16 x^{2} - x - 1$ |
$14$ |
[12,1] |
$-\,5^{7}\cdot 549979\cdot 9402901$ |
$3$ |
$18.096719598$ |
$5084976.936564708$ |
|
|
✓ |
$S_7\wr C_2$ (as 14T61) |
trivial |
$2$ |
$12$ |
$7355.69293249$ |
| 14.12.541...875.1 |
$x^{14} - 2 x^{13} - 5 x^{12} + 8 x^{11} + 4 x^{10} + 15 x^{9} + 4 x^{8} - 110 x^{7} + 29 x^{6} + 163 x^{5} - 83 x^{4} - 68 x^{3} + 52 x^{2} - 6 x - 1$ |
$14$ |
[12,1] |
$-\,5^{7}\cdot 93739\cdot 73979509$ |
$3$ |
$18.4799825378$ |
$5888448.519835679$ |
|
|
? |
$S_7\wr C_2$ (as 14T61) |
trivial |
$2$ |
$12$ |
$8681.66988897$ |
| 14.12.664...416.1 |
$x^{14} - 9 x^{12} + 27 x^{10} - 24 x^{8} - 21 x^{6} + 41 x^{4} - 15 x^{2} + 1$ |
$14$ |
[12,1] |
$-\,2^{14}\cdot 71^{2}\cdot 283583^{2}$ |
$3$ |
$22.1029268954$ |
|
|
|
✓ |
$C_2^7.S_7$ (as 14T57) |
trivial |
$2$ |
$12$ |
$35356.8667379$ |
| 14.12.664...416.2 |
$x^{14} - 6 x^{12} + 4 x^{10} + 34 x^{8} - 74 x^{6} + 52 x^{4} - 13 x^{2} + 1$ |
$14$ |
[12,1] |
$-\,2^{14}\cdot 71^{2}\cdot 283583^{2}$ |
$3$ |
$22.1029268954$ |
|
|
|
? |
$C_2^7.S_7$ (as 14T57) |
trivial |
$2$ |
$12$ |
$41389.0345601$ |
| 14.12.811...328.1 |
$x^{14} - 8 x^{12} + 5 x^{10} + 88 x^{8} - 238 x^{6} + 200 x^{4} - 39 x^{2} + 2$ |
$14$ |
[12,1] |
$-\,2^{15}\cdot 3967^{4}$ |
$2$ |
$22.4214758346$ |
$299.60467825276874$ |
|
|
? |
$C_2^7.\GL(3,2)$ (as 14T51) |
trivial |
$2$ |
$12$ |
$72386.2571671$ |
| 14.12.312...912.1 |
$x^{14} - 10 x^{12} + 28 x^{10} - x^{8} - 84 x^{6} + 107 x^{4} - 50 x^{2} + 8$ |
$14$ |
[12,1] |
$-\,2^{5}\cdot 149^{4}\cdot 211^{4}$ |
$3$ |
$24.6889020486$ |
$3984.4875467161523$ |
|
|
? |
$C_2^7.A_7$ (as 14T56) |
trivial |
$2$ |
$12$ |
$251060.515176$ |
| 14.12.322...875.1 |
$x^{14} - 5 x^{13} - 5 x^{12} + 62 x^{11} - 57 x^{10} - 201 x^{9} + 352 x^{8} + 89 x^{7} - 402 x^{6} + 36 x^{5} + 165 x^{4} - 15 x^{3} - 23 x^{2} + x + 1$ |
$14$ |
[12,1] |
$-\,5^{3}\cdot 7\cdot 577^{6}$ |
$3$ |
$24.7459707437$ |
$142.10911300827965$ |
|
|
? |
$C_2\wr D_7$ (as 14T38) |
trivial |
$2$ |
$12$ |
$111053.892686$ |
| 14.12.341...136.1 |
$x^{14} - 7 x^{13} + 6 x^{12} + 53 x^{11} - 98 x^{10} - 127 x^{9} + 309 x^{8} + 174 x^{7} - 406 x^{6} - 232 x^{5} + 238 x^{4} + 226 x^{3} - 48 x^{2} - 86 x - 2$ |
$14$ |
[12,1] |
$-\,2^{22}\cdot 19\cdot 809^{4}$ |
$3$ |
$24.8444343727$ |
$624.8192259500752$ |
|
|
? |
$C_2^7.\GL(3,2)$ (as 14T51) |
trivial |
$2$ |
$12$ |
$183002.663841$ |
| 14.12.632...635.1 |
$x^{14} - 3 x^{13} - 13 x^{12} + 29 x^{11} + 71 x^{10} - 77 x^{9} - 196 x^{8} + 23 x^{7} + 220 x^{6} + 74 x^{5} - 96 x^{4} - 55 x^{3} + 11 x^{2} + 9 x + 1$ |
$14$ |
[12,1] |
$-\,5\cdot 7^{3}\cdot 577^{6}$ |
$3$ |
$25.9644979095$ |
$142.10911300827965$ |
|
|
? |
$C_2\wr D_7$ (as 14T38) |
trivial |
$2$ |
$12$ |
$161538.001828$ |
| 14.12.806...703.1 |
$x^{14} - 5 x^{13} - 2 x^{12} + 42 x^{11} - 27 x^{10} - 134 x^{9} + 128 x^{8} + 204 x^{7} - 213 x^{6} - 153 x^{5} + 151 x^{4} + 52 x^{3} - 41 x^{2} - 7 x + 1$ |
$14$ |
[12,1] |
$-\,3\cdot 17^{2}\cdot 93075271168633709$ |
$3$ |
$26.4191049765$ |
$3493631247.9099717$ |
|
|
✓ |
$S_{14}$ (as 14T63) |
trivial |
$2$ |
$12$ |
$208508.048504$ |
| 14.12.581...576.1 |
$x^{14} - 2 x^{13} - 18 x^{12} + 38 x^{11} + 102 x^{10} - 198 x^{9} - 316 x^{8} + 396 x^{7} + 842 x^{6} - 544 x^{5} - 1298 x^{4} + 602 x^{3} + 808 x^{2} - 256 x - 146$ |
$14$ |
[12,1] |
$-\,2^{16}\cdot 11\cdot 73^{8}$ |
$3$ |
$30.421133547$ |
|
|
|
? |
$C_2\wr C_7:C_3$ (as 14T44) |
trivial |
$2$ |
$12$ |
$704633.197578$ |
| 14.12.107...988.1 |
$x^{14} - 4 x^{13} - 7 x^{12} + 41 x^{11} + 10 x^{10} - 160 x^{9} + 24 x^{8} + 298 x^{7} - 70 x^{6} - 266 x^{5} + 47 x^{4} + 95 x^{3} - 6 x^{2} - 8 x - 1$ |
$14$ |
[12,1] |
$-\,2^{2}\cdot 3\cdot 89409527120714407499$ |
$3$ |
$31.7821459307$ |
$32755370940.482002$ |
|
|
✓ |
$S_{14}$ (as 14T63) |
trivial |
$2$ |
$12$ |
$1499120.51116$ |
| 14.12.338...624.1 |
$x^{14} - 13 x^{12} + 53 x^{10} - 45 x^{8} - 141 x^{6} + 217 x^{4} - 57 x^{2} + 1$ |
$14$ |
[12,1] |
$-\,2^{22}\cdot 73^{8}$ |
$2$ |
$34.4987259015$ |
|
|
|
? |
$C_2\wr C_7:C_3$ (as 14T44) |
trivial |
$2$ |
$12$ |
$2066965.35264$ |
| 14.12.400...736.1 |
$x^{14} - 19 x^{12} + 113 x^{10} - 213 x^{8} + 92 x^{6} + 91 x^{4} - 80 x^{2} + 16$ |
$14$ |
[12,1] |
$-\,2^{12}\cdot 149^{4}\cdot 211^{4}$ |
$3$ |
$34.9153801173$ |
|
|
|
? |
$C_2^7.A_7$ (as 14T56) |
trivial |
$2$ |
$12$ |
$2818983.90237$ |
| 14.12.985...648.1 |
$x^{14} - 3 x^{12} - 50 x^{10} + 276 x^{8} - 516 x^{6} + 426 x^{4} - 152 x^{2} + 17$ |
$14$ |
[12,1] |
$-\,2^{14}\cdot 17\cdot 29^{12}$ |
$3$ |
$43.8938022298$ |
$292.4589096608059$ |
|
|
? |
$C_2 \wr C_7$ (as 14T29) |
trivial |
$2$ |
$12$ |
$6667756.09619$ |
| 14.12.985...648.2 |
$x^{14} - 14 x^{12} + 55 x^{10} - 48 x^{8} - 107 x^{6} + 198 x^{4} - 103 x^{2} + 17$ |
$14$ |
[12,1] |
$-\,2^{14}\cdot 17\cdot 29^{12}$ |
$3$ |
$43.8938022298$ |
$292.4589096608059$ |
|
|
? |
$C_2 \wr C_7$ (as 14T29) |
trivial |
$2$ |
$12$ |
$4761814.27223$ |
| 14.12.633...744.1 |
$x^{14} - 24 x^{12} + 194 x^{10} - 607 x^{8} + 531 x^{6} + 127 x^{4} - 55 x^{2} + 1$ |
$14$ |
[12,1] |
$-\,2^{12}\cdot 7^{8}\cdot 173^{6}$ |
$3$ |
$50.1304371652$ |
$188.39724552501244$ |
|
|
? |
$C_2\wr F_7$ (as 14T48) |
trivial |
$2$ |
$12$ |
$126296523.288$ |
| 14.12.633...744.2 |
$x^{14} - 13 x^{12} + 52 x^{10} - 49 x^{8} - 89 x^{6} + 164 x^{4} - 65 x^{2} + 4$ |
$14$ |
[12,1] |
$-\,2^{12}\cdot 7^{8}\cdot 173^{6}$ |
$3$ |
$50.1304371652$ |
$188.39724552501244$ |
|
|
? |
$C_2\wr F_7$ (as 14T48) |
trivial |
$2$ |
$12$ |
$74552137.0255$ |
