| 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 |
| 12.0.674400179654656.1 |
$x^{12} + x^{10} + 5 x^{8} + 27 x^{6} + 35 x^{4} + 49 x^{2} + 49$ |
$12$ |
[0,6] |
$2^{12}\cdot 7^{8}\cdot 13^{4}$ |
$3$ |
$17.2085048979$ |
$37.31774244321726$ |
|
|
? |
$C_2^4:C_3$ (as 12T32) |
$[2]$ |
$2$ |
$5$ |
$204.153577186$ |
| 12.4.674400179654656.1 |
$x^{12} - 11 x^{10} + 48 x^{8} - 105 x^{6} + 118 x^{4} - 60 x^{2} + 1$ |
$12$ |
[4,4] |
$2^{12}\cdot 7^{8}\cdot 13^{4}$ |
$3$ |
$17.2085048979$ |
$37.31774244321726$ |
|
|
? |
$C_2^4:C_3$ (as 12T32) |
trivial |
$2$ |
$7$ |
$778.845984996$ |
| 12.0.674400179654656.2 |
$x^{12} + 4 x^{10} + 17 x^{8} + 48 x^{6} + 84 x^{4} + 98 x^{2} + 49$ |
$12$ |
[0,6] |
$2^{12}\cdot 7^{8}\cdot 13^{4}$ |
$3$ |
$17.2085048979$ |
$37.31774244321726$ |
|
|
? |
$C_2^4:C_3$ (as 12T32) |
$[2]$ |
$2$ |
$5$ |
$205.547207833$ |
| 12.4.2088270645760000.1 |
$x^{12} - 9 x^{10} + 28 x^{8} - 33 x^{6} + 18 x^{4} - 14 x^{2} + 1$ |
$12$ |
[4,4] |
$2^{12}\cdot 5^{4}\cdot 13^{8}$ |
$3$ |
$18.908143892$ |
$34.96704216279658$ |
|
|
? |
$C_2^4:C_3$ (as 12T32) |
trivial |
$2$ |
$7$ |
$1208.70820526$ |
| 12.4.55895067029733376.4 |
$x^{12} + 13 x^{10} - 13 x^{8} - 66 x^{6} - 13 x^{4} + 13 x^{2} + 1$ |
$12$ |
[4,4] |
$2^{16}\cdot 31^{8}$ |
$2$ |
$24.8664882538$ |
$39.473089612875896$ |
|
|
|
$C_2^4:C_3$ (as 12T32) |
$[2]$ |
$2$ |
$7$ |
$12238.13012$ |
| 12.4.223580268118933504.7 |
$x^{12} - 5 x^{10} - 61 x^{8} - 126 x^{6} - 61 x^{4} - 5 x^{2} + 1$ |
$12$ |
[4,4] |
$2^{18}\cdot 31^{8}$ |
$2$ |
$27.9116893396$ |
$39.473089612875896$ |
|
|
|
$C_2^4:C_3$ (as 12T32) |
$[2]$ |
$2$ |
$7$ |
$36967.075634$ |
| 12.0.223...504.46 |
$x^{12} - 4 x^{10} - 10 x^{8} + 50 x^{6} - 35 x^{4} + 230 x^{2} + 256$ |
$12$ |
[0,6] |
$2^{18}\cdot 31^{8}$ |
$2$ |
$27.9116893396$ |
$39.473089612875896$ |
|
|
|
$C_2^4:C_3$ (as 12T32) |
$[2, 2]$ |
$2$ |
$5$ |
$8563.11488514$ |
| 12.4.223...504.46 |
$x^{12} - 2 x^{10} + 21 x^{8} + 210 x^{6} + 148 x^{4} - 696 x^{2} + 256$ |
$12$ |
[4,4] |
$2^{18}\cdot 31^{8}$ |
$2$ |
$27.9116893396$ |
$39.473089612875896$ |
|
|
|
$C_2^4:C_3$ (as 12T32) |
$[2]$ |
$2$ |
$7$ |
$42921.0704224$ |
| 12.0.223...504.47 |
$x^{12} + 2 x^{10} - 14 x^{8} + 74 x^{6} + 137 x^{4} + 536 x^{2} + 256$ |
$12$ |
[0,6] |
$2^{18}\cdot 31^{8}$ |
$2$ |
$27.9116893396$ |
$39.473089612875896$ |
|
|
|
$C_2^4:C_3$ (as 12T32) |
$[2, 2]$ |
$2$ |
$5$ |
$9942.30814088$ |
| 12.4.894321072475734016.3 |
$x^{12} - 2 x^{11} - 13 x^{10} + 26 x^{9} + 30 x^{8} - 102 x^{7} + 119 x^{6} - 186 x^{5} + 537 x^{4} - 216 x^{3} + 84 x^{2} - 160 x - 2$ |
$12$ |
[4,4] |
$2^{20}\cdot 31^{8}$ |
$2$ |
$31.329811988$ |
$39.473089612875896$ |
|
|
|
$C_2^4:C_3$ (as 12T32) |
$[2]$ |
$2$ |
$7$ |
$32636.0978676$ |
| 12.0.894...016.43 |
$x^{12} + 12 x^{10} + 74 x^{8} + 272 x^{6} + 569 x^{4} + 612 x^{2} + 256$ |
$12$ |
[0,6] |
$2^{20}\cdot 31^{8}$ |
$2$ |
$31.329811988$ |
$39.473089612875896$ |
|
|
|
$C_2^4:C_3$ (as 12T32) |
$[2, 2, 4]$ |
$2$ |
$5$ |
$7508.05174925$ |
| 12.4.894...016.53 |
$x^{12} - 8 x^{10} + 7 x^{8} - 16 x^{6} + 63 x^{4} - 648 x^{2} + 729$ |
$12$ |
[4,4] |
$2^{20}\cdot 31^{8}$ |
$2$ |
$31.329811988$ |
$39.473089612875896$ |
|
|
|
$C_2^4:C_3$ (as 12T32) |
$[2]$ |
$2$ |
$7$ |
$28108.8306139$ |
| 12.0.357...064.8 |
$x^{12} - 2 x^{10} - 18 x^{8} + 138 x^{6} - 287 x^{4} + 540 x^{2} + 4$ |
$12$ |
[0,6] |
$2^{22}\cdot 31^{8}$ |
$2$ |
$35.1665249371$ |
$39.473089612875896$ |
|
|
? |
$C_2^4:C_3$ (as 12T32) |
$[2, 2, 2]$ |
$2$ |
$5$ |
$11417.8658301$ |
| 12.4.357...064.44 |
$x^{12} + 6 x^{10} - 100 x^{8} - 688 x^{6} - 400 x^{4} + 96 x^{2} + 64$ |
$12$ |
[4,4] |
$2^{22}\cdot 31^{8}$ |
$2$ |
$35.1665249371$ |
$39.473089612875896$ |
|
|
? |
$C_2^4:C_3$ (as 12T32) |
$[2, 2]$ |
$2$ |
$7$ |
$49291.071693$ |
| 12.12.476...336.1 |
$x^{12} - 30 x^{10} + 320 x^{8} - 1435 x^{6} + 2390 x^{4} - 519 x^{2} + 1$ |
$12$ |
[12,0] |
$2^{12}\cdot 7^{8}\cdot 13^{4}\cdot 29^{4}$ |
$4$ |
$52.8699791427$ |
$200.9621932869232$ |
|
|
? |
$C_2^4:C_3$ (as 12T32) |
$[2]$ |
$2$ |
$11$ |
$2607428.78738$ |
| 12.12.190...216.1 |
$x^{12} - 36 x^{10} + 388 x^{8} - 1190 x^{6} + 943 x^{4} - 100 x^{2} + 1$ |
$12$ |
[12,0] |
$2^{12}\cdot 7^{8}\cdot 13^{4}\cdot 41^{4}$ |
$4$ |
$59.3386632702$ |
$238.950141124441$ |
|
|
? |
$C_2^4:C_3$ (as 12T32) |
$[2]$ |
$2$ |
$11$ |
$5075200.5857$ |
| 12.12.112...176.1 |
$x^{12} - 49 x^{10} + 769 x^{8} - 4928 x^{6} + 12484 x^{4} - 10656 x^{2} + 256$ |
$12$ |
[12,0] |
$2^{16}\cdot 11^{4}\cdot 43^{8}$ |
$3$ |
$68.78332929423473$ |
$162.8303304701146$ |
|
|
|
$C_2^4:C_3$ (as 12T32) |
trivial |
$2$ |
$11$ |
$76405833.5716623$ |
| 12.12.156...216.1 |
$x^{12} - 39 x^{10} + 599 x^{8} - 4558 x^{6} + 17615 x^{4} - 31335 x^{2} + 19321$ |
$12$ |
[12,0] |
$2^{16}\cdot 23^{4}\cdot 31^{8}$ |
$3$ |
$70.71698484991832$ |
$189.3062874879781$ |
|
|
|
$C_2^4:C_3$ (as 12T32) |
$[2]$ |
$2$ |
$11$ |
$44518760.54725902$ |
