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 |
12.0.1381408203125.1 |
$x^{12} - 6 x^{11} + 10 x^{10} + 5 x^{9} - 24 x^{8} + 29 x^{6} - 24 x^{4} + 5 x^{3} + 10 x^{2} - 6 x + 1$ |
$12$ |
[0,6] |
$5^{9}\cdot 29^{4}$ |
$2$ |
$10.272910455$ |
$31.561635639558343$ |
|
|
✓ |
$(C_3\times C_3):C_4$ (as 12T17) |
trivial |
$10$ |
$5$ |
$64.4867620531$ |
12.0.1803751953125.2 |
$x^{12} - 5 x^{11} + 16 x^{10} - 35 x^{9} + 61 x^{8} - 85 x^{7} + 106 x^{6} - 120 x^{5} + 126 x^{4} - 110 x^{3} + 75 x^{2} - 30 x + 5$ |
$12$ |
[0,6] |
$5^{9}\cdot 31^{4}$ |
$2$ |
$10.5038392776$ |
$32.99655748259533$ |
|
|
? |
$(C_3\times C_3):C_4$ (as 12T17) |
trivial |
$10$ |
$5$ |
$75.4332875798$ |
12.0.20624432955392.2 |
$x^{12} + 4 x^{8} + 4 x^{6} + 5 x^{4} + 12 x^{2} + 2$ |
$12$ |
[0,6] |
$2^{33}\cdot 7^{4}$ |
$2$ |
$12.8686157938$ |
$24.616776431006123$ |
|
|
|
$(C_3\times C_3):C_4$ (as 12T17) |
trivial |
$2$ |
$5$ |
$232.384832441$ |
12.0.41085390865563648.12 |
$x^{12} - 24 x^{8} - 12 x^{6} + 189 x^{4} + 324 x^{2} + 18$ |
$12$ |
[0,6] |
$2^{33}\cdot 3^{14}$ |
$2$ |
$24.2367259333$ |
$30.93861708477606$ |
|
|
|
$(C_3\times C_3):C_4$ (as 12T17) |
$[2]$ |
$2$ |
$5$ |
$5956.74164502$ |
12.0.41085390865563648.20 |
$x^{12} + 12 x^{10} - 8 x^{9} + 78 x^{8} - 72 x^{7} + 308 x^{6} - 288 x^{5} + 711 x^{4} - 592 x^{3} + 924 x^{2} - 816 x + 526$ |
$12$ |
[0,6] |
$2^{33}\cdot 3^{14}$ |
$2$ |
$24.2367259333$ |
$30.93861708477606$ |
|
|
|
$(C_3\times C_3):C_4$ (as 12T17) |
$[2]$ |
$2$ |
$5$ |
$6058.14180821$ |
12.0.49519263525896192.12 |
$x^{12} - 4 x^{11} - 2 x^{10} + 20 x^{9} + 15 x^{8} - 40 x^{7} - 60 x^{6} + 80 x^{5} + 270 x^{4} + 288 x^{3} + 192 x^{2} + 128 x + 64$ |
$12$ |
[0,6] |
$2^{33}\cdot 7^{8}$ |
$2$ |
$24.616776431$ |
$24.616776431006123$ |
|
|
|
$(C_3\times C_3):C_4$ (as 12T17) |
$[3, 3]$ |
$2$ |
$5$ |
$2643.94789139$ |
12.12.136...125.1 |
$x^{12} - 6 x^{11} + 55 x^{9} - 84 x^{8} - 60 x^{7} + 189 x^{6} - 60 x^{5} - 84 x^{4} + 55 x^{3} - 6 x + 1$ |
$12$ |
[12,0] |
$3^{14}\cdot 5^{9}\cdot 11^{4}$ |
$3$ |
$26.7916747439$ |
$76.06024196897057$ |
|
|
? |
$(C_3\times C_3):C_4$ (as 12T17) |
trivial |
$2$ |
$11$ |
$59761.38389$ |
12.0.369...832.57 |
$x^{12} - 12 x^{10} + 18 x^{8} + 124 x^{6} + 81 x^{4} + 144 x^{2} + 32$ |
$12$ |
[0,6] |
$2^{33}\cdot 3^{16}$ |
$2$ |
$29.1067798457$ |
$47.429446013156884$ |
|
|
|
$(C_3\times C_3):C_4$ (as 12T17) |
trivial |
$2$ |
$5$ |
$50344.2311125$ |
12.0.369...832.60 |
$x^{12} - 12 x^{10} + 54 x^{8} - 24 x^{7} + 124 x^{6} - 360 x^{5} + 783 x^{4} - 704 x^{3} + 468 x^{2} - 192 x + 46$ |
$12$ |
[0,6] |
$2^{33}\cdot 3^{16}$ |
$2$ |
$29.1067798457$ |
$47.429446013156884$ |
|
|
|
$(C_3\times C_3):C_4$ (as 12T17) |
trivial |
$2$ |
$5$ |
$79964.5012412$ |
12.12.867...152.1 |
$x^{12} - 6 x^{11} - x^{10} + 60 x^{9} - 92 x^{8} - 58 x^{7} + 193 x^{6} - 58 x^{5} - 92 x^{4} + 60 x^{3} - x^{2} - 6 x + 1$ |
$12$ |
[12,0] |
$2^{8}\cdot 13^{4}\cdot 17^{9}$ |
$3$ |
$31.2491209932$ |
$73.47714215210142$ |
|
|
|
$(C_3\times C_3):C_4$ (as 12T17) |
trivial |
$2$ |
$11$ |
$159031.293256$ |