| 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 |
| 28.0.941...672.1 |
$x^{28} - 3 x^{14} + 3$ |
$28$ |
[0,14] |
$2^{28}\cdot 3^{27}\cdot 7^{28}$ |
$3$ |
$40.3839918504$ |
$71.99977726879091$ |
|
|
✓ |
$D_4\times F_7$ (as 28T41) |
trivial |
$6$ |
$13$ |
$647468634170.5619$ |
| 28.2.444...808.1 |
$x^{28} - 2$ |
$28$ |
[2,13] |
$-\,2^{83}\cdot 7^{28}$ |
$2$ |
$54.6307239549$ |
$76.04105792041854$ |
|
|
✓ |
$D_4\times F_7$ (as 28T41) |
trivial |
$2$ |
$14$ |
$23978441188016.812$ |
| 28.0.444...808.1 |
$x^{28} + 2$ |
$28$ |
[0,14] |
$2^{83}\cdot 7^{28}$ |
$2$ |
$54.6307239549$ |
$76.04105792041854$ |
|
|
✓ |
$D_4\times F_7$ (as 28T41) |
trivial |
$2$ |
$13$ |
$26773418571562.227$ |
| 28.0.154...048.1 |
$x^{28} - 384 x^{14} + 49152$ |
$28$ |
[0,14] |
$2^{42}\cdot 3^{27}\cdot 7^{28}$ |
$3$ |
$57.11158897763544$ |
$101.82306150136618$ |
|
|
? |
$D_4\times F_7$ (as 28T41) |
trivial |
$6$ |
$13$ |
$103320259652055.95$ |
| 28.2.919...000.1 |
$x^{28} - 5$ |
$28$ |
[2,13] |
$-\,2^{28}\cdot 5^{27}\cdot 7^{28}$ |
$3$ |
$66.0898590383$ |
$117.83023204115541$ |
|
|
? |
$D_4\times F_7$ (as 28T41) |
trivial |
$2$ |
$14$ |
$329491969938806.1$ |
| 28.2.252...432.1 |
$x^{28} - 3$ |
$28$ |
[2,13] |
$-\,2^{56}\cdot 3^{27}\cdot 7^{28}$ |
$3$ |
$80.7679837008$ |
$101.82306150136618$ |
|
|
✓ |
$D_4\times F_7$ (as 28T41) |
trivial |
$2$ |
$14$ |
$11582345197990588$ |
| 28.2.150...000.1 |
$x^{28} - 81920$ |
$28$ |
[2,13] |
$-\,2^{42}\cdot 5^{27}\cdot 7^{28}$ |
$3$ |
$93.46517498729598$ |
$166.6371122101708$ |
|
|
? |
$D_4\times F_7$ (as 28T41) |
trivial |
$2$ |
$14$ |
$39664645753321230$ |
| 28.0.246...000.1 |
$x^{28} + 5$ |
$28$ |
[0,14] |
$2^{56}\cdot 5^{27}\cdot 7^{28}$ |
$3$ |
$132.179718077$ |
$166.6371122101708$ |
|
|
✓ |
$D_4\times F_7$ (as 28T41) |
$[4]$ |
$2$ |
$13$ |
$2784084912517084000$ |
