| 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 |
| 12.0.73645476129.1 |
$x^{12} - x^{11} - x^{10} + 2 x^{9} - 2 x^{7} + 3 x^{5} - 2 x^{4} + 2 x^{2} - 2 x + 1$ |
$12$ |
[0,6] |
$3^{6}\cdot 19^{2}\cdot 23^{4}$ |
$3$ |
$8.046286759$ |
$36.207733980463345$ |
|
|
? |
$C_2^2\times S_4$ (as 12T48) |
trivial |
$6$ |
$5$ |
$4.99030501888$ |
| 12.0.81462863889.1 |
$x^{12} - x^{11} + 2 x^{10} - 3 x^{9} + 3 x^{8} - 3 x^{7} + 5 x^{6} - 3 x^{5} + 3 x^{4} - 4 x^{3} + x^{2} - x + 1$ |
$12$ |
[0,6] |
$3^{6}\cdot 11^{2}\cdot 31^{4}$ |
$3$ |
$8.11421740276$ |
$31.984371183438952$ |
|
|
✓ |
$C_2^2\times S_4$ (as 12T48) |
trivial |
$6$ |
$5$ |
$5.40994597563$ |
| 12.0.214253265625.1 |
$x^{12} - x^{11} + 5 x^{9} - 7 x^{8} + 5 x^{7} + 7 x^{6} - 19 x^{5} + 27 x^{4} - 22 x^{3} + 13 x^{2} - 5 x + 1$ |
$12$ |
[0,6] |
$5^{6}\cdot 7^{2}\cdot 23^{4}$ |
$3$ |
$8.79516424681$ |
$28.372521918222215$ |
|
|
? |
$C_2^2\times S_4$ (as 12T48) |
trivial |
$2$ |
$5$ |
$3.77871153902$ |
| 12.0.307465814016.1 |
$x^{12} - 2 x^{10} + 3 x^{8} + 3 x^{4} - 2 x^{2} + 1$ |
$12$ |
[0,6] |
$2^{18}\cdot 3^{2}\cdot 19^{4}$ |
$3$ |
$9.063927079939377$ |
$22.623940727226856$ |
|
|
? |
$C_2^2\times S_4$ (as 12T48) |
trivial |
$4$ |
$5$ |
$13.076275628704112$ |
| 12.0.529074390625.1 |
$x^{12} - 4 x^{11} + 10 x^{10} - 18 x^{9} + 26 x^{8} - 35 x^{7} + 40 x^{6} - 40 x^{5} + 42 x^{4} - 36 x^{3} + 21 x^{2} - 7 x + 1$ |
$12$ |
[0,6] |
$5^{6}\cdot 11^{2}\cdot 23^{4}$ |
$3$ |
$9.48330521614$ |
$35.566838487557476$ |
|
|
? |
$C_2^2\times S_4$ (as 12T48) |
trivial |
$2$ |
$5$ |
$5.43134866729$ |
| 12.0.553553856144.1 |
$x^{12} - x^{11} + x^{10} - 4 x^{9} + 2 x^{8} - x^{7} + 5 x^{6} - x^{5} + 2 x^{4} - 4 x^{3} + x^{2} - x + 1$ |
$12$ |
[0,6] |
$2^{4}\cdot 3^{6}\cdot 83^{4}$ |
$3$ |
$9.51911682280682$ |
$31.559467676119$ |
|
|
? |
$C_2^2\times S_4$ (as 12T48) |
trivial |
$6$ |
$5$ |
$19.5967222887936$ |
| 12.0.741637881856.1 |
$x^{12} - 2 x^{10} + 4 x^{6} - 2 x^{2} + 1$ |
$12$ |
[0,6] |
$2^{20}\cdot 29^{4}$ |
$2$ |
$9.75399792215$ |
$25.616305216426433$ |
|
|
? |
$C_2^2\times S_4$ (as 12T48) |
trivial |
$4$ |
$5$ |
$24.870288878$ |
| 12.0.982540877824.1 |
$x^{12} - x^{8} + 3 x^{4} + 1$ |
$12$ |
[0,6] |
$2^{26}\cdot 11^{4}$ |
$2$ |
$9.98533299144$ |
$21.059254724775883$ |
|
|
? |
$C_2^2\times S_4$ (as 12T48) |
trivial |
$4$ |
$5$ |
$26.4973662518$ |
| 12.4.1263657015625.1 |
$x^{12} - x^{11} - x^{10} - 3 x^{9} + x^{8} + 2 x^{7} - x^{6} + 11 x^{5} - 11 x^{4} + 20 x^{3} - 7 x^{2} + 13 x + 1$ |
$12$ |
[4,4] |
$5^{6}\cdot 17^{2}\cdot 23^{4}$ |
$3$ |
$10.19692209$ |
$44.21538193886829$ |
|
|
? |
$C_2^2\times S_4$ (as 12T48) |
trivial |
$2$ |
$7$ |
$15.3002273809$ |
| 12.0.1916696264704.1 |
$x^{12} + 2 x^{8} - 2 x^{6} + 2 x^{4} + 1$ |
$12$ |
[0,6] |
$2^{26}\cdot 13^{4}$ |
$2$ |
$10.5571357994$ |
$24.255161140409015$ |
|
|
|
$C_2^2\times S_4$ (as 12T48) |
trivial |
$2$ |
$5$ |
$16.5597740445$ |
| 12.0.2552632508416.1 |
$x^{12} - 2 x^{11} + 2 x^{10} + 2 x^{7} - 4 x^{6} + 2 x^{5} + 2 x^{2} - 2 x + 1$ |
$12$ |
[0,6] |
$2^{16}\cdot 79^{4}$ |
$2$ |
$10.8122403515$ |
$35.552777669262355$ |
|
|
|
$C_2^2\times S_4$ (as 12T48) |
trivial |
$4$ |
$5$ |
$59.9335658639$ |
| 12.0.2966551527424.3 |
$x^{12} + 3 x^{8} - 2 x^{6} + 10 x^{4} - 12 x^{2} + 4$ |
$12$ |
[0,6] |
$2^{22}\cdot 29^{4}$ |
$2$ |
$10.9484924869$ |
$36.226926254958926$ |
|
|
? |
$C_2^2\times S_4$ (as 12T48) |
trivial |
$4$ |
$5$ |
$93.1104211556$ |
| 12.0.2966551527424.4 |
$x^{12} - 4 x^{8} + 4 x^{4} + 16$ |
$12$ |
[0,6] |
$2^{22}\cdot 29^{4}$ |
$2$ |
$10.9484924869$ |
$36.226926254958926$ |
|
|
|
$C_2^2\times S_4$ (as 12T48) |
trivial |
$4$ |
$5$ |
$40.0506066938$ |
| 12.0.3070625382400.1 |
$x^{12} + x^{10} - 2 x^{8} + x^{6} - 2 x^{4} + x^{2} + 1$ |
$12$ |
[0,6] |
$2^{16}\cdot 5^{2}\cdot 37^{4}$ |
$3$ |
$10.9799973753$ |
$34.27355800696023$ |
|
|
? |
$C_2^2\times S_4$ (as 12T48) |
trivial |
$4$ |
$5$ |
$43.373149047$ |
| 12.0.3930163511296.1 |
$x^{12} + 2 x^{10} + 7 x^{8} + 27 x^{4} - 10 x^{2} + 1$ |
$12$ |
[0,6] |
$2^{28}\cdot 11^{4}$ |
$2$ |
$11.2081573226$ |
$21.059254724775883$ |
|
|
? |
$C_2^2\times S_4$ (as 12T48) |
trivial |
$2$ |
$5$ |
$35.4095840581$ |
| 12.0.3930163511296.4 |
$x^{12} - 2 x^{10} + 7 x^{8} + 27 x^{4} + 10 x^{2} + 1$ |
$12$ |
[0,6] |
$2^{28}\cdot 11^{4}$ |
$2$ |
$11.2081573226$ |
$21.059254724775883$ |
|
|
? |
$C_2^2\times S_4$ (as 12T48) |
trivial |
$2$ |
$5$ |
$31.2467158614$ |
| 12.0.4694952902656.3 |
$x^{12} - 6 x^{10} + 14 x^{8} - 16 x^{6} + 9 x^{4} - 2 x^{2} + 1$ |
$12$ |
[0,6] |
$2^{24}\cdot 23^{4}$ |
$2$ |
$11.3754679194$ |
$24.87769606749656$ |
|
|
✓ |
$C_2^2\times S_4$ (as 12T48) |
trivial |
$2$ |
$5$ |
$19.7121209198$ |
| 12.0.4694952902656.6 |
$x^{12} + x^{8} + 2 x^{4} + 1$ |
$12$ |
[0,6] |
$2^{24}\cdot 23^{4}$ |
$2$ |
$11.3754679194$ |
$24.87769606749656$ |
|
|
✓ |
$C_2^2\times S_4$ (as 12T48) |
trivial |
$4$ |
$5$ |
$59.5204478423$ |
| 12.0.4694952902656.9 |
$x^{12} + 6 x^{10} + 14 x^{8} + 16 x^{6} + 9 x^{4} + 2 x^{2} + 1$ |
$12$ |
[0,6] |
$2^{24}\cdot 23^{4}$ |
$2$ |
$11.3754679194$ |
$24.87769606749656$ |
|
|
✓ |
$C_2^2\times S_4$ (as 12T48) |
trivial |
$2$ |
$5$ |
$24.7622219167$ |
| 12.0.5015306502144.2 |
$x^{12} + 3 x^{10} - 7 x^{6} + 3 x^{2} + 1$ |
$12$ |
[0,6] |
$2^{20}\cdot 3^{14}$ |
$2$ |
$11.438211516$ |
$24.23672593327708$ |
|
|
|
$C_2^2\times S_4$ (as 12T48) |
trivial |
$6$ |
$5$ |
$98.2732697513$ |
| 12.0.5061276073984.2 |
$x^{12} - x^{10} - 4 x^{8} + 9 x^{6} - 4 x^{4} - x^{2} + 1$ |
$12$ |
[0,6] |
$2^{20}\cdot 13^{6}$ |
$2$ |
$11.4469117752$ |
$24.255161140409015$ |
|
|
|
$C_2^2\times S_4$ (as 12T48) |
trivial |
$2$ |
$5$ |
$32.3579085032$ |
| 12.0.5061276073984.3 |
$x^{12} + 2 x^{10} + 6 x^{8} - 2 x^{6} + x^{4} - 4 x^{2} + 4$ |
$12$ |
[0,6] |
$2^{20}\cdot 13^{6}$ |
$2$ |
$11.4469117752$ |
$27.385300168092183$ |
|
|
|
$C_2^2\times S_4$ (as 12T48) |
trivial |
$2$ |
$5$ |
$45.2990394392$ |
| 12.0.5061276073984.4 |
$x^{12} - 2 x^{11} + 2 x^{10} - 2 x^{9} - 2 x^{8} + 2 x^{7} + 2 x^{6} + 6 x^{5} + x^{4} - 4 x^{3} + 4$ |
$12$ |
[0,6] |
$2^{20}\cdot 13^{6}$ |
$2$ |
$11.4469117752$ |
$27.385300168092183$ |
|
|
? |
$C_2^2\times S_4$ (as 12T48) |
trivial |
$4$ |
$5$ |
$131.621790577$ |
| 12.4.5985973890625.1 |
$x^{12} - x^{11} - 3 x^{10} + 2 x^{9} - 4 x^{8} + 22 x^{7} - 18 x^{6} + x^{5} - 20 x^{4} + 24 x^{3} + 4 x^{2} - 8 x + 1$ |
$12$ |
[4,4] |
$5^{6}\cdot 23^{4}\cdot 37^{2}$ |
$3$ |
$11.6081025152$ |
$65.23036102920173$ |
|
|
? |
$C_2^2\times S_4$ (as 12T48) |
trivial |
$2$ |
$7$ |
$46.7840863584$ |
| 12.0.7666785058816.1 |
$x^{12} - 2 x^{10} + 9 x^{8} - 8 x^{6} + 9 x^{4} - 2 x^{2} + 1$ |
$12$ |
[0,6] |
$2^{28}\cdot 13^{4}$ |
$2$ |
$11.8499842736$ |
$28.844410203711913$ |
|
|
? |
$C_2^2\times S_4$ (as 12T48) |
trivial |
$4$ |
$5$ |
$100.344238552$ |
| 12.0.7666785058816.3 |
$x^{12} - 6 x^{11} + 21 x^{10} - 50 x^{9} + 89 x^{8} - 120 x^{7} + 126 x^{6} - 108 x^{5} + 84 x^{4} - 60 x^{3} + 34 x^{2} - 12 x + 2$ |
$12$ |
[0,6] |
$2^{28}\cdot 13^{4}$ |
$2$ |
$11.8499842736$ |
$24.255161140409015$ |
|
|
? |
$C_2^2\times S_4$ (as 12T48) |
trivial |
$2$ |
$5$ |
$47.3303901109$ |
| 12.0.7666785058816.5 |
$x^{12} + x^{10} + 2 x^{8} - 2 x^{6} + 13 x^{4} - 11 x^{2} + 4$ |
$12$ |
[0,6] |
$2^{28}\cdot 13^{4}$ |
$2$ |
$11.8499842736$ |
$28.844410203711913$ |
|
|
|
$C_2^2\times S_4$ (as 12T48) |
trivial |
$4$ |
$5$ |
$232.830467004$ |
| 12.0.7666785058816.6 |
$x^{12} + 2 x^{10} - x^{8} - 12 x^{6} + 2 x^{4} + 8 x^{2} + 4$ |
$12$ |
[0,6] |
$2^{28}\cdot 13^{4}$ |
$2$ |
$11.8499842736$ |
$28.844410203711913$ |
|
|
|
$C_2^2\times S_4$ (as 12T48) |
trivial |
$2$ |
$5$ |
$31.5945278497$ |
| 12.0.8745694265344.2 |
$x^{12} - 5 x^{8} + 7 x^{4} + 1$ |
$12$ |
[0,6] |
$2^{26}\cdot 19^{4}$ |
$2$ |
$11.9807183213$ |
$27.677283073598154$ |
|
|
? |
$C_2^2\times S_4$ (as 12T48) |
trivial |
$4$ |
$5$ |
$88.4622108004$ |
| 12.0.8745694265344.3 |
$x^{12} + 4 x^{10} + 6 x^{8} + 10 x^{6} + 6 x^{4} + 4 x^{2} + 1$ |
$12$ |
[0,6] |
$2^{26}\cdot 19^{4}$ |
$2$ |
$11.9807183213$ |
$29.323059968612448$ |
|
|
? |
$C_2^2\times S_4$ (as 12T48) |
trivial |
$2$ |
$5$ |
$86.479351061$ |
| 12.0.10240000000000.1 |
$x^{12} - x^{10} + 5 x^{6} - x^{2} + 1$ |
$12$ |
[0,6] |
$2^{20}\cdot 5^{10}$ |
$2$ |
$12.1392446201$ |
$25.722163336702884$ |
|
|
|
$C_2^2\times S_4$ (as 12T48) |
trivial |
$2$ |
$5$ |
$57.929718633$ |
| 12.0.15494111297536.1 |
$x^{12} - 2 x^{8} + x^{4} + 1$ |
$12$ |
[0,6] |
$2^{24}\cdot 31^{4}$ |
$2$ |
$12.5655226096$ |
$28.881988226776993$ |
|
|
✓ |
$C_2^2\times S_4$ (as 12T48) |
trivial |
$4$ |
$5$ |
$81.4263748057$ |
| 12.0.15494111297536.10 |
$x^{12} + 2 x^{10} + x^{8} - 4 x^{6} - 6 x^{4} - 2 x^{2} + 9$ |
$12$ |
[0,6] |
$2^{24}\cdot 31^{4}$ |
$2$ |
$12.5655226096$ |
$28.881988226776993$ |
|
|
? |
$C_2^2\times S_4$ (as 12T48) |
trivial |
$2$ |
$5$ |
$37.8452818699$ |
| 12.0.15494111297536.11 |
$x^{12} - 2 x^{10} + x^{8} + 4 x^{6} - 6 x^{4} + 2 x^{2} + 9$ |
$12$ |
[0,6] |
$2^{24}\cdot 31^{4}$ |
$2$ |
$12.5655226096$ |
$28.881988226776993$ |
|
|
|
$C_2^2\times S_4$ (as 12T48) |
trivial |
$2$ |
$5$ |
$109.020157931$ |
| 12.0.20061226008576.6 |
$x^{12} - 3 x^{10} + 3 x^{8} - 14 x^{6} + 30 x^{4} - 12 x^{2} + 4$ |
$12$ |
[0,6] |
$2^{22}\cdot 3^{14}$ |
$2$ |
$12.8389583272$ |
$28.822486924224066$ |
|
|
|
$C_2^2\times S_4$ (as 12T48) |
trivial |
$6$ |
$5$ |
$348.839569983$ |
| 12.4.20245104295936.2 |
$x^{12} - 6 x^{10} + 8 x^{8} - 4 x^{7} - 10 x^{6} - 12 x^{5} + 8 x^{4} + 16 x^{3} - 4 x - 1$ |
$12$ |
[4,4] |
$2^{22}\cdot 13^{6}$ |
$2$ |
$12.848724038$ |
$27.385300168092183$ |
|
|
|
$C_2^2\times S_4$ (as 12T48) |
trivial |
$2$ |
$7$ |
$105.933496786$ |
| 12.4.20245104295936.3 |
$x^{12} - 7 x^{10} + 7 x^{8} - 10 x^{6} + 2 x^{4} + 4 x^{2} + 4$ |
$12$ |
[4,4] |
$2^{22}\cdot 13^{6}$ |
$2$ |
$12.848724038$ |
$28.844410203711913$ |
|
|
|
$C_2^2\times S_4$ (as 12T48) |
trivial |
$2$ |
$7$ |
$123.945383669$ |
| 12.0.26646078816256.1 |
$x^{12} + 4 x^{10} - 2 x^{6} + 4 x^{2} + 1$ |
$12$ |
[0,6] |
$2^{20}\cdot 71^{4}$ |
$2$ |
$13.146276902884859$ |
$33.704599092705436$ |
|
|
|
$C_2^2\times S_4$ (as 12T48) |
trivial |
$2$ |
$5$ |
$128.19042236848307$ |
| 12.0.30667140235264.4 |
$x^{12} - 9 x^{8} + 23 x^{4} + 1$ |
$12$ |
[0,6] |
$2^{30}\cdot 13^{4}$ |
$2$ |
$13.3011576202$ |
$24.255161140409015$ |
|
|
? |
$C_2^2\times S_4$ (as 12T48) |
$[2]$ |
$4$ |
$5$ |
$159.454020061$ |
| 12.0.30667140235264.5 |
$x^{12} + 2 x^{10} - 3 x^{8} + 8 x^{6} - 3 x^{4} + 2 x^{2} + 1$ |
$12$ |
[0,6] |
$2^{30}\cdot 13^{4}$ |
$2$ |
$13.3011576202$ |
$28.844410203711913$ |
|
|
|
$C_2^2\times S_4$ (as 12T48) |
trivial |
$2$ |
$5$ |
$253.213783535$ |
| 12.0.30667140235264.8 |
$x^{12} + 2 x^{10} + 11 x^{8} + 24 x^{6} + 30 x^{4} + 16 x^{2} + 4$ |
$12$ |
[0,6] |
$2^{30}\cdot 13^{4}$ |
$2$ |
$13.3011576202$ |
$28.844410203711913$ |
|
|
? |
$C_2^2\times S_4$ (as 12T48) |
trivial |
$2$ |
$5$ |
$117.94391831$ |
| 12.0.34982777061376.1 |
$x^{12} - 6 x^{11} + 21 x^{10} - 50 x^{9} + 96 x^{8} - 150 x^{7} + 201 x^{6} - 222 x^{5} + 194 x^{4} - 126 x^{3} + 51 x^{2} - 10 x + 1$ |
$12$ |
[0,6] |
$2^{28}\cdot 19^{4}$ |
$2$ |
$13.4479016272$ |
$34.87119154832539$ |
|
|
|
$C_2^2\times S_4$ (as 12T48) |
trivial |
$2$ |
$5$ |
$69.182765343$ |
| 12.0.34982777061376.3 |
$x^{12} - 2 x^{10} + 9 x^{8} + 16 x^{6} + 9 x^{4} - 2 x^{2} + 1$ |
$12$ |
[0,6] |
$2^{28}\cdot 19^{4}$ |
$2$ |
$13.4479016272$ |
$34.87119154832539$ |
|
|
? |
$C_2^2\times S_4$ (as 12T48) |
trivial |
$4$ |
$5$ |
$209.605609982$ |
| 12.0.34982777061376.6 |
$x^{12} + 6 x^{10} + 17 x^{8} + 28 x^{6} + 20 x^{4} + 4$ |
$12$ |
[0,6] |
$2^{28}\cdot 19^{4}$ |
$2$ |
$13.4479016272$ |
$29.323059968612448$ |
|
|
|
$C_2^2\times S_4$ (as 12T48) |
trivial |
$2$ |
$5$ |
$286.273150127$ |
| 12.0.34982777061376.7 |
$x^{12} + 6 x^{10} + 15 x^{8} + 20 x^{6} + 7 x^{4} - 10 x^{2} + 9$ |
$12$ |
[0,6] |
$2^{28}\cdot 19^{4}$ |
$2$ |
$13.4479016272$ |
$27.677283073598154$ |
|
|
|
$C_2^2\times S_4$ (as 12T48) |
trivial |
$2$ |
$5$ |
$280.948871557$ |
| 12.0.34982777061376.8 |
$x^{12} - 6 x^{10} + 15 x^{8} - 20 x^{6} + 7 x^{4} + 10 x^{2} + 9$ |
$12$ |
[0,6] |
$2^{28}\cdot 19^{4}$ |
$2$ |
$13.4479016272$ |
$27.677283073598154$ |
|
|
? |
$C_2^2\times S_4$ (as 12T48) |
trivial |
$2$ |
$5$ |
$101.388526662$ |
| 12.0.34982777061376.9 |
$x^{12} - 2 x^{10} + x^{8} - 8 x^{6} + 9 x^{4} + 14 x^{2} + 25$ |
$12$ |
[0,6] |
$2^{28}\cdot 19^{4}$ |
$2$ |
$13.4479016272$ |
$34.87119154832539$ |
|
|
? |
$C_2^2\times S_4$ (as 12T48) |
trivial |
$4$ |
$5$ |
$361.288536049$ |
| 12.0.35664401793024.3 |
$x^{12} + 3 x^{8} + 15 x^{4} + 1$ |
$12$ |
[0,6] |
$2^{26}\cdot 3^{12}$ |
$2$ |
$13.4695445797$ |
$22.87642303192648$ |
|
|
? |
$C_2^2\times S_4$ (as 12T48) |
trivial |
$4$ |
$5$ |
$336.294660956$ |
| 12.0.35664401793024.8 |
$x^{12} + 6 x^{10} + 9 x^{8} - 6 x^{6} - 3 x^{4} + 12 x^{2} + 4$ |
$12$ |
[0,6] |
$2^{26}\cdot 3^{12}$ |
$2$ |
$13.4695445797$ |
$24.23672593327708$ |
|
|
? |
$C_2^2\times S_4$ (as 12T48) |
trivial |
$2$ |
$5$ |
$212.503920608$ |
| 12.0.38982341165056.3 |
$x^{12} - 4 x^{11} + 9 x^{10} - 4 x^{9} - 8 x^{8} + 30 x^{7} - 21 x^{6} + 4 x^{5} + 35 x^{4} - 34 x^{3} + 34 x^{2} - 12 x + 4$ |
$12$ |
[0,6] |
$2^{16}\cdot 29^{6}$ |
$2$ |
$13.5697649953$ |
$49.987163057233104$ |
|
|
|
$C_2^2\times S_4$ (as 12T48) |
trivial |
$4$ |
$5$ |
$293.235712897$ |
