| 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 |
| 8.0.33554432.1 |
$x^{8} - 4 x^{6} + 6 x^{4} - 4 x^{2} + 2$ |
$8$ |
[0,4] |
$2^{25}$ |
$1$ |
$8.72406186132$ |
$14.050017282986396$ |
|
|
✓ |
$C_2^3: C_4$ (as 8T21) |
trivial |
$8$ |
$3$ |
$15.2489763542$ |
| 8.0.115200000.1 |
$x^{8} - 2 x^{7} + 4 x^{6} + 4 x^{5} - 11 x^{4} + 8 x^{3} + 6 x^{2} - 10 x + 5$ |
$8$ |
[0,4] |
$2^{12}\cdot 3^{2}\cdot 5^{5}$ |
$3$ |
$10.1784479448$ |
$19.480074928505935$ |
|
|
? |
$C_2^3: C_4$ (as 8T21) |
trivial |
$4$ |
$3$ |
$14.0366805636$ |
| 8.0.115200000.2 |
$x^{8} - 2 x^{7} - 2 x^{6} + 10 x^{5} + 6 x^{4} - 10 x^{3} - 2 x^{2} + 2 x + 1$ |
$8$ |
[0,4] |
$2^{12}\cdot 3^{2}\cdot 5^{5}$ |
$3$ |
$10.1784479448$ |
$19.480074928505935$ |
|
|
? |
$C_2^3: C_4$ (as 8T21) |
trivial |
$4$ |
$3$ |
$11.8801003247$ |
| 8.0.204800000.2 |
$x^{8} - 4 x^{6} + 9 x^{4} - 10 x^{2} + 5$ |
$8$ |
[0,4] |
$2^{16}\cdot 5^{5}$ |
$2$ |
$10.9374541141$ |
$18.914832180063517$ |
|
|
✓ |
$C_2^3: C_4$ (as 8T21) |
trivial |
$4$ |
$3$ |
$15.0857493017$ |
| 8.0.204800000.3 |
$x^{8} - 2 x^{6} + x^{4} + 5$ |
$8$ |
[0,4] |
$2^{16}\cdot 5^{5}$ |
$2$ |
$10.9374541141$ |
$18.914832180063517$ |
|
|
? |
$C_2^3: C_4$ (as 8T21) |
trivial |
$4$ |
$3$ |
$20.3437096132$ |
| 8.0.301989888.1 |
$x^{8} - 8 x^{6} + 26 x^{4} - 36 x^{2} + 18$ |
$8$ |
[0,4] |
$2^{25}\cdot 3^{2}$ |
$2$ |
$11.4815111031$ |
$24.33534378135327$ |
|
|
? |
$C_2^3: C_4$ (as 8T21) |
trivial |
$8$ |
$3$ |
$46.2536410318$ |
| 8.0.301989888.2 |
$x^{8} - 4 x^{6} - 2 x^{4} + 12 x^{2} + 18$ |
$8$ |
[0,4] |
$2^{25}\cdot 3^{2}$ |
$2$ |
$11.4815111031$ |
$24.33534378135327$ |
|
|
? |
$C_2^3: C_4$ (as 8T21) |
trivial |
$8$ |
$3$ |
$53.8244876865$ |
| 8.0.627200000.1 |
$x^{8} - 2 x^{7} + 6 x^{5} + 10 x^{4} + 14 x^{3} + 32 x^{2} + 30 x + 9$ |
$8$ |
[0,4] |
$2^{12}\cdot 5^{5}\cdot 7^{2}$ |
$3$ |
$12.5798585022$ |
$29.756305967763307$ |
|
|
? |
$C_2^3: C_4$ (as 8T21) |
trivial |
$4$ |
$3$ |
$37.2578211063$ |
| 8.0.627200000.2 |
$x^{8} - 2 x^{7} - 2 x^{6} + 12 x^{5} + 16 x^{4} - 20 x^{3} - 12 x^{2} + 8 x + 4$ |
$8$ |
[0,4] |
$2^{12}\cdot 5^{5}\cdot 7^{2}$ |
$3$ |
$12.5798585022$ |
$29.756305967763307$ |
|
|
? |
$C_2^3: C_4$ (as 8T21) |
trivial |
$4$ |
$3$ |
$26.6650301087$ |
| 8.0.819200000.2 |
$x^{8} - 2 x^{6} + 6 x^{4} - 20 x^{2} + 20$ |
$8$ |
[0,4] |
$2^{18}\cdot 5^{5}$ |
$2$ |
$13.0068982525$ |
$24.529502540692157$ |
|
|
? |
$C_2^3: C_4$ (as 8T21) |
trivial |
$4$ |
$3$ |
$43.0186249045$ |
| 8.0.819200000.3 |
$x^{8} - 6 x^{6} + 14 x^{4} - 20 x^{2} + 20$ |
$8$ |
[0,4] |
$2^{18}\cdot 5^{5}$ |
$2$ |
$13.0068982525$ |
$24.529502540692157$ |
|
|
? |
$C_2^3: C_4$ (as 8T21) |
trivial |
$4$ |
$3$ |
$30.4030946118$ |
| 8.0.838860800.3 |
$x^{8} - 4 x^{6} + 22 x^{4} - 60 x^{2} + 50$ |
$8$ |
[0,4] |
$2^{25}\cdot 5^{2}$ |
$2$ |
$13.0455152716$ |
$31.416793729804482$ |
|
|
? |
$C_2^3: C_4$ (as 8T21) |
trivial |
$8$ |
$3$ |
$83.1517796626$ |
| 8.0.838860800.4 |
$x^{8} - 8 x^{6} + 34 x^{4} - 60 x^{2} + 50$ |
$8$ |
[0,4] |
$2^{25}\cdot 5^{2}$ |
$2$ |
$13.0455152716$ |
$31.416793729804482$ |
|
|
? |
$C_2^3: C_4$ (as 8T21) |
trivial |
$8$ |
$3$ |
$86.5167920166$ |
| 8.0.1644167168.1 |
$x^{8} - 8 x^{6} + 66 x^{4} - 140 x^{2} + 98$ |
$8$ |
[0,4] |
$2^{25}\cdot 7^{2}$ |
$2$ |
$14.1903545464$ |
$37.17285164694141$ |
|
|
? |
$C_2^3: C_4$ (as 8T21) |
$[2]$ |
$8$ |
$3$ |
$68.4510242492$ |
| 8.0.1644167168.2 |
$x^{8} - 8 x^{6} + 34 x^{4} - 84 x^{2} + 98$ |
$8$ |
[0,4] |
$2^{25}\cdot 7^{2}$ |
$2$ |
$14.1903545464$ |
$37.17285164694141$ |
|
|
? |
$C_2^3: C_4$ (as 8T21) |
$[2]$ |
$8$ |
$3$ |
$48.8145003772$ |
| 8.0.1843200000.1 |
$x^{8} - 8 x^{6} + 31 x^{4} - 60 x^{2} + 45$ |
$8$ |
[0,4] |
$2^{16}\cdot 3^{2}\cdot 5^{5}$ |
$3$ |
$14.3944991274$ |
$27.548986159937193$ |
|
|
? |
$C_2^3: C_4$ (as 8T21) |
trivial |
$4$ |
$3$ |
$71.1984988503$ |
| 8.0.1843200000.2 |
$x^{8} - 4 x^{6} - x^{4} + 45$ |
$8$ |
[0,4] |
$2^{16}\cdot 3^{2}\cdot 5^{5}$ |
$3$ |
$14.3944991274$ |
$27.548986159937193$ |
|
|
? |
$C_2^3: C_4$ (as 8T21) |
trivial |
$4$ |
$3$ |
$40.894001743$ |
| 8.0.1924782912.1 |
$x^{8} - 3 x^{7} + 2 x^{6} - 8 x^{5} + 37 x^{4} - 56 x^{3} + 40 x^{2} - 24 x + 12$ |
$8$ |
[0,4] |
$2^{6}\cdot 3^{4}\cdot 13^{5}$ |
$3$ |
$14.4726386645$ |
$33.54000593239012$ |
|
|
? |
$C_2^3: C_4$ (as 8T21) |
$[2]$ |
$6$ |
$3$ |
$64.7385702926$ |
| 8.0.1924782912.2 |
$x^{8} + 12 x^{6} + 49 x^{4} + 78 x^{2} + 52$ |
$8$ |
[0,4] |
$2^{6}\cdot 3^{4}\cdot 13^{5}$ |
$3$ |
$14.4726386645$ |
$33.54000593239012$ |
|
|
|
$C_2^3: C_4$ (as 8T21) |
$[2]$ |
$6$ |
$3$ |
$90.3015016638$ |
| 8.0.2241903125.1 |
$x^{8} - 2 x^{7} - 4 x^{6} + 9 x^{5} + 11 x^{4} - 5 x^{3} - 11 x^{2} - 10 x + 20$ |
$8$ |
[0,4] |
$5^{5}\cdot 7^{2}\cdot 11^{4}$ |
$3$ |
$14.7511916438$ |
$29.34086180290925$ |
|
|
|
$C_2^3: C_4$ (as 8T21) |
$[2]$ |
$2$ |
$3$ |
$25.4706381476$ |
| 8.0.2241903125.2 |
$x^{8} - 2 x^{7} + x^{6} + 3 x^{5} - x^{4} - 2 x^{3} + 16 x^{2} + 3 x + 1$ |
$8$ |
[0,4] |
$5^{5}\cdot 7^{2}\cdot 11^{4}$ |
$3$ |
$14.7511916438$ |
$29.34086180290925$ |
|
|
|
$C_2^3: C_4$ (as 8T21) |
$[2]$ |
$2$ |
$3$ |
$18.7719162165$ |
| 8.0.2717908992.1 |
$x^{8} - 12 x^{6} + 54 x^{4} - 108 x^{2} + 162$ |
$8$ |
[0,4] |
$2^{25}\cdot 3^{4}$ |
$2$ |
$15.1105183922$ |
$24.33534378135327$ |
|
|
? |
$C_2^3: C_4$ (as 8T21) |
$[2]$ |
$8$ |
$3$ |
$74.4480757518$ |
| 8.0.2832334848.3 |
$x^{8} - 2 x^{6} + 11 x^{4} - 24 x^{2} + 18$ |
$8$ |
[0,4] |
$2^{17}\cdot 3^{2}\cdot 7^{4}$ |
$3$ |
$15.188611527$ |
$30.827771796137323$ |
|
|
|
$C_2^3: C_4$ (as 8T21) |
$[2]$ |
$2$ |
$3$ |
$74.316276522$ |
| 8.0.2832334848.4 |
$x^{8} - 4 x^{5} - 3 x^{4} + 32 x^{2} + 48 x + 18$ |
$8$ |
[0,4] |
$2^{17}\cdot 3^{2}\cdot 7^{4}$ |
$3$ |
$15.188611527$ |
$30.827771796137323$ |
|
|
? |
$C_2^3: C_4$ (as 8T21) |
$[2]$ |
$2$ |
$3$ |
$31.6355229678$ |
| 8.0.2928200000.1 |
$x^{8} - 4 x^{6} + 9 x^{4} - 10 x^{2} + 20$ |
$8$ |
[0,4] |
$2^{6}\cdot 5^{5}\cdot 11^{4}$ |
$3$ |
$15.2519401375$ |
$31.366700656905365$ |
|
|
|
$C_2^3: C_4$ (as 8T21) |
$[2]$ |
$2$ |
$3$ |
$26.3711079283$ |
| 8.0.2928200000.2 |
$x^{8} - 3 x^{7} + 7 x^{6} - 11 x^{5} + 4 x^{4} + 11 x^{3} + 7 x^{2} + 3 x + 1$ |
$8$ |
[0,4] |
$2^{6}\cdot 5^{5}\cdot 11^{4}$ |
$3$ |
$15.2519401375$ |
$31.366700656905365$ |
|
|
? |
$C_2^3: C_4$ (as 8T21) |
$[2]$ |
$2$ |
$3$ |
$23.7914996481$ |
| 8.0.3639042693.1 |
$x^{8} - x^{7} - 3 x^{6} + x^{5} + 6 x^{4} - 13 x^{3} + 49 x^{2} - 78 x + 39$ |
$8$ |
[0,4] |
$3^{4}\cdot 11^{2}\cdot 13^{5}$ |
$3$ |
$15.6719628622$ |
$39.32914310246349$ |
|
|
|
$C_2^3: C_4$ (as 8T21) |
$[2]$ |
$6$ |
$3$ |
$114.081966573$ |
| 8.0.3639042693.2 |
$x^{8} - 2 x^{7} + 12 x^{6} - 17 x^{5} + 50 x^{4} - 37 x^{3} + 70 x^{2} - 12 x + 43$ |
$8$ |
[0,4] |
$3^{4}\cdot 11^{2}\cdot 13^{5}$ |
$3$ |
$15.6719628622$ |
$39.32914310246349$ |
|
|
|
$C_2^3: C_4$ (as 8T21) |
$[2]$ |
$6$ |
$3$ |
$104.005391697$ |
| 8.0.4060086272.4 |
$x^{8} - 16 x^{6} + 90 x^{4} - 220 x^{2} + 242$ |
$8$ |
[0,4] |
$2^{25}\cdot 11^{2}$ |
$2$ |
$15.8879150018$ |
$46.5986356256745$ |
|
|
? |
$C_2^3: C_4$ (as 8T21) |
trivial |
$8$ |
$3$ |
$186.233025776$ |
| 8.0.4060086272.5 |
$x^{8} - 4 x^{6} - 2 x^{4} + 132 x^{2} + 242$ |
$8$ |
[0,4] |
$2^{25}\cdot 11^{2}$ |
$2$ |
$15.8879150018$ |
$46.5986356256745$ |
|
|
? |
$C_2^3: C_4$ (as 8T21) |
trivial |
$8$ |
$3$ |
$179.028035293$ |
| 8.0.5670699008.3 |
$x^{8} - 8 x^{6} + 66 x^{4} - 260 x^{2} + 338$ |
$8$ |
[0,4] |
$2^{25}\cdot 13^{2}$ |
$2$ |
$16.5655009806$ |
$50.658057734962696$ |
|
|
? |
$C_2^3: C_4$ (as 8T21) |
trivial |
$8$ |
$3$ |
$213.809060634$ |
| 8.0.5670699008.4 |
$x^{8} - 12 x^{6} + 86 x^{4} - 260 x^{2} + 338$ |
$8$ |
[0,4] |
$2^{25}\cdot 13^{2}$ |
$2$ |
$16.5655009806$ |
$50.658057734962696$ |
|
|
? |
$C_2^3: C_4$ (as 8T21) |
trivial |
$8$ |
$3$ |
$238.553600003$ |
| 8.0.5815734272.3 |
$x^{8} - 2 x^{6} + x^{4} + 68$ |
$8$ |
[0,4] |
$2^{12}\cdot 17^{5}$ |
$2$ |
$16.6178781179$ |
$23.679999262753405$ |
|
|
? |
$C_2^3: C_4$ (as 8T21) |
$[4]$ |
$4$ |
$3$ |
$62.9139633346$ |
| 8.0.6516050000.1 |
$x^{8} - 3 x^{7} + 11 x^{6} - 18 x^{5} + 24 x^{4} - 8 x^{3} + 21 x^{2} + 7 x + 1$ |
$8$ |
[0,4] |
$2^{4}\cdot 5^{5}\cdot 19^{4}$ |
$3$ |
$16.8557488244$ |
$29.149714088647936$ |
|
|
|
$C_2^3: C_4$ (as 8T21) |
$[4]$ |
$2$ |
$3$ |
$22.5743448365$ |
| 8.0.6516050000.2 |
$x^{8} - x^{6} + 9 x^{4} - 40 x^{2} + 80$ |
$8$ |
[0,4] |
$2^{4}\cdot 5^{5}\cdot 19^{4}$ |
$3$ |
$16.8557488244$ |
$29.149714088647936$ |
|
|
? |
$C_2^3: C_4$ (as 8T21) |
$[4]$ |
$2$ |
$3$ |
$14.4364597964$ |
| 8.0.6766814925.1 |
$x^{8} - 2 x^{7} - 9 x^{6} + 25 x^{5} + 7 x^{4} - 72 x^{3} + 81 x^{2} - 42 x + 12$ |
$8$ |
[0,4] |
$3^{6}\cdot 5^{2}\cdot 13^{5}$ |
$3$ |
$16.935500551$ |
$34.89662748300597$ |
|
|
|
$C_2^3: C_4$ (as 8T21) |
$[4]$ |
$6$ |
$3$ |
$63.9321411031$ |
| 8.0.6766814925.2 |
$x^{8} - 4 x^{7} + x^{6} + 11 x^{5} - 14 x^{4} + 5 x^{3} + x^{2} - x + 103$ |
$8$ |
[0,4] |
$3^{6}\cdot 5^{2}\cdot 13^{5}$ |
$3$ |
$16.935500551$ |
$34.89662748300597$ |
|
|
|
$C_2^3: C_4$ (as 8T21) |
$[4]$ |
$6$ |
$3$ |
$74.5041555441$ |
| 8.0.6771200000.5 |
$x^{8} - 2 x^{7} - 4 x^{6} + 30 x^{5} + 19 x^{4} - 74 x^{3} - 30 x^{2} + 80 x + 89$ |
$8$ |
[0,4] |
$2^{12}\cdot 5^{5}\cdot 23^{2}$ |
$3$ |
$16.9368719938$ |
$53.937885084186505$ |
|
|
? |
$C_2^3: C_4$ (as 8T21) |
trivial |
$4$ |
$3$ |
$88.3944611471$ |
| 8.0.6771200000.6 |
$x^{8} - 2 x^{7} - 6 x^{6} + 24 x^{4} - 4 x^{3} + 20 x^{2} + 144 x + 244$ |
$8$ |
[0,4] |
$2^{12}\cdot 5^{5}\cdot 23^{2}$ |
$3$ |
$16.9368719938$ |
$53.937885084186505$ |
|
|
? |
$C_2^3: C_4$ (as 8T21) |
trivial |
$4$ |
$3$ |
$128.367925352$ |
| 8.0.7372800000.1 |
$x^{8} - 14 x^{6} + 74 x^{4} - 180 x^{2} + 180$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{2}\cdot 5^{5}$ |
$3$ |
$17.1180407792$ |
$42.486344684868676$ |
|
|
? |
$C_2^3: C_4$ (as 8T21) |
trivial |
$4$ |
$3$ |
$81.1526051599$ |
| 8.0.7372800000.2 |
$x^{8} - 2 x^{6} + 26 x^{4} - 60 x^{2} + 180$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{2}\cdot 5^{5}$ |
$3$ |
$17.1180407792$ |
$42.486344684868676$ |
|
|
? |
$C_2^3: C_4$ (as 8T21) |
trivial |
$4$ |
$3$ |
$121.493684805$ |
| 8.0.7372800000.3 |
$x^{8} - 6 x^{6} + 34 x^{4} - 60 x^{2} + 180$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{2}\cdot 5^{5}$ |
$3$ |
$17.1180407792$ |
$42.486344684868676$ |
|
|
? |
$C_2^3: C_4$ (as 8T21) |
trivial |
$4$ |
$3$ |
$101.224116375$ |
| 8.0.7372800000.4 |
$x^{8} - 2 x^{6} - 14 x^{4} + 60 x^{2} + 180$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{2}\cdot 5^{5}$ |
$3$ |
$17.1180407792$ |
$42.486344684868676$ |
|
|
? |
$C_2^3: C_4$ (as 8T21) |
trivial |
$4$ |
$3$ |
$146.932874819$ |
| 8.0.7549747200.3 |
$x^{8} - 20 x^{6} + 142 x^{4} - 420 x^{2} + 450$ |
$8$ |
[0,4] |
$2^{25}\cdot 3^{2}\cdot 5^{2}$ |
$3$ |
$17.1688636346$ |
$54.41548295093269$ |
|
|
? |
$C_2^3: C_4$ (as 8T21) |
trivial |
$8$ |
$3$ |
$323.381354917$ |
| 8.0.7549747200.4 |
$x^{8} - 16 x^{6} + 106 x^{4} - 300 x^{2} + 450$ |
$8$ |
[0,4] |
$2^{25}\cdot 3^{2}\cdot 5^{2}$ |
$3$ |
$17.1688636346$ |
$54.41548295093269$ |
|
|
? |
$C_2^3: C_4$ (as 8T21) |
trivial |
$8$ |
$3$ |
$231.647898151$ |
| 8.0.7549747200.5 |
$x^{8} - 8 x^{6} - 22 x^{4} + 180 x^{2} + 450$ |
$8$ |
[0,4] |
$2^{25}\cdot 3^{2}\cdot 5^{2}$ |
$3$ |
$17.1688636346$ |
$54.41548295093269$ |
|
|
? |
$C_2^3: C_4$ (as 8T21) |
trivial |
$8$ |
$3$ |
$154.776891001$ |
| 8.0.7549747200.6 |
$x^{8} - 4 x^{6} + 14 x^{4} + 180 x^{2} + 450$ |
$8$ |
[0,4] |
$2^{25}\cdot 3^{2}\cdot 5^{2}$ |
$3$ |
$17.1688636346$ |
$54.41548295093269$ |
|
|
? |
$C_2^3: C_4$ (as 8T21) |
trivial |
$8$ |
$3$ |
$273.663193414$ |
| 8.0.7867596800.1 |
$x^{8} - 2 x^{7} + 3 x^{6} - 8 x^{5} + 17 x^{4} - 2 x^{3} - 23 x^{2} + 12 x + 18$ |
$8$ |
[0,4] |
$2^{17}\cdot 5^{2}\cdot 7^{4}$ |
$3$ |
$17.2575945667$ |
$39.79848225570752$ |
|
|
|
$C_2^3: C_4$ (as 8T21) |
$[4]$ |
$2$ |
$3$ |
$56.4710132415$ |
| 8.0.7867596800.2 |
$x^{8} - 2 x^{7} + x^{6} + 2 x^{5} - 4 x^{4} + 2 x^{3} + 15 x^{2} - 2 x + 1$ |
$8$ |
[0,4] |
$2^{17}\cdot 5^{2}\cdot 7^{4}$ |
$3$ |
$17.2575945667$ |
$39.79848225570752$ |
|
|
? |
$C_2^3: C_4$ (as 8T21) |
$[4]$ |
$2$ |
$3$ |
$30.610646293$ |
| 8.4.8830503125.1 |
$x^{8} - x^{6} - 36 x^{4} + 95 x^{2} + 5$ |
$8$ |
[4,2] |
$5^{5}\cdot 41^{4}$ |
$2$ |
$17.5084693834$ |
$21.410136276713814$ |
|
|
|
$C_2^3: C_4$ (as 8T21) |
trivial |
$2$ |
$5$ |
$150.778950182$ |
