| 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 |
| 8.0.9453125.1 |
$x^{8} - 2 x^{7} + 8 x^{6} - 9 x^{5} + 15 x^{4} - 9 x^{3} + 8 x^{2} - 2 x + 1$ |
$8$ |
[0,4] |
$5^{7}\cdot 11^{2}$ |
$2$ |
$7.44640966136$ |
$13.561105554803268$ |
|
|
✓ |
$(C_8:C_2):C_2$ (as 8T16) |
trivial |
$10$ |
$3$ |
$6.01390136566$ |
| 8.0.20000000.1 |
$x^{8} - 5 x^{6} + 10 x^{4} - 10 x^{2} + 5$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{7}$ |
$2$ |
$8.17765433958$ |
$13.753120438672642$ |
|
|
✓ |
$(C_8:C_2):C_2$ (as 8T16) |
trivial |
$10$ |
$3$ |
$9.319417497$ |
| 8.0.75078125.1 |
$x^{8} - 2 x^{7} - 7 x^{6} + 11 x^{5} + 20 x^{4} - 14 x^{3} - 22 x^{2} + 3 x + 11$ |
$8$ |
[0,4] |
$5^{7}\cdot 31^{2}$ |
$2$ |
$9.6480418195$ |
$22.7656262017263$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
trivial |
$10$ |
$3$ |
$18.8167167844$ |
| 8.0.320000000.1 |
$x^{8} - 10 x^{6} + 40 x^{4} - 80 x^{2} + 80$ |
$8$ |
[0,4] |
$2^{12}\cdot 5^{7}$ |
$2$ |
$11.5649496754$ |
$19.449849449321462$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
trivial |
$10$ |
$3$ |
$40.4008943246$ |
| 8.4.320000000.1 |
$x^{8} - 2 x^{7} - 2 x^{6} + 6 x^{5} - 10 x^{4} + 6 x^{3} - 2 x^{2} - 2 x + 1$ |
$8$ |
[4,2] |
$2^{12}\cdot 5^{7}$ |
$2$ |
$11.5649496754$ |
$13.753120438672642$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
trivial |
$2$ |
$5$ |
$17.9412831204$ |
| 8.0.393828125.1 |
$x^{8} - 2 x^{7} + 3 x^{6} + 11 x^{5} - 30 x^{4} + 36 x^{3} + 13 x^{2} - 142 x + 121$ |
$8$ |
[0,4] |
$5^{7}\cdot 71^{2}$ |
$2$ |
$11.8689784408$ |
$34.45307012928092$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
trivial |
$10$ |
$3$ |
$43.0915817584$ |
| 8.0.564736653.1 |
$x^{8} - 4 x^{7} + 7 x^{6} - 7 x^{5} + 6 x^{4} - 5 x^{3} - 2 x^{2} + 4 x + 3$ |
$8$ |
[0,4] |
$3^{2}\cdot 13^{7}$ |
$2$ |
$12.4159726414$ |
$16.340338938923477$ |
|
|
|
$(C_8:C_2):C_2$ (as 8T16) |
trivial |
$2$ |
$3$ |
$31.1669523778$ |
| 8.0.765703125.1 |
$x^{8} - 2 x^{7} - 12 x^{6} + 16 x^{5} + 75 x^{4} - 59 x^{3} - 217 x^{2} + 78 x + 241$ |
$8$ |
[0,4] |
$3^{4}\cdot 5^{7}\cdot 11^{2}$ |
$3$ |
$12.8975598675$ |
$23.48852382772379$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
$[2]$ |
$10$ |
$3$ |
$30.3135260287$ |
| 8.4.1143828125.1 |
$x^{8} - x^{7} - 8 x^{6} + 7 x^{5} + 15 x^{4} - 12 x^{3} - 18 x^{2} - 4 x + 1$ |
$8$ |
[4,2] |
$5^{7}\cdot 11^{4}$ |
$2$ |
$13.5611055548$ |
$13.561105554803268$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
trivial |
$2$ |
$5$ |
$33.0834922285$ |
| 8.0.1340703125.1 |
$x^{8} - 2 x^{7} - 7 x^{6} - 4 x^{5} + 70 x^{4} + 41 x^{3} - 287 x^{2} - 62 x + 401$ |
$8$ |
[0,4] |
$5^{7}\cdot 131^{2}$ |
$2$ |
$13.8330063948$ |
$46.79876599652796$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
trivial |
$10$ |
$3$ |
$50.8310364801$ |
| 8.0.1620000000.1 |
$x^{8} - 15 x^{6} + 90 x^{4} - 270 x^{2} + 405$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{4}\cdot 5^{7}$ |
$3$ |
$14.1641128029$ |
$23.821103362394982$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
$[2]$ |
$10$ |
$3$ |
$46.0046542753$ |
| 8.0.1781328125.1 |
$x^{8} - 2 x^{7} + 18 x^{6} - 39 x^{5} + 140 x^{4} - 219 x^{3} + 453 x^{2} - 382 x + 451$ |
$8$ |
[0,4] |
$5^{7}\cdot 151^{2}$ |
$2$ |
$14.3331943803$ |
$50.244349446340664$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
trivial |
$10$ |
$3$ |
$122.543627005$ |
| 8.4.2147483648.2 |
$x^{8} - 4 x^{4} + 2$ |
$8$ |
[4,2] |
$2^{31}$ |
$1$ |
$14.6720646913$ |
$18.220618156107065$ |
|
|
✓ |
$(C_8:C_2):C_2$ (as 8T16) |
trivial |
$2$ |
$5$ |
$65.1364334631$ |
| 8.0.2147483648.3 |
$x^{8} + 4 x^{4} + 2$ |
$8$ |
[0,4] |
$2^{31}$ |
$1$ |
$14.6720646913$ |
$18.220618156107065$ |
|
|
✓ |
$(C_8:C_2):C_2$ (as 8T16) |
trivial |
$2$ |
$3$ |
$47.0224010217$ |
| 8.0.2420000000.1 |
$x^{8} - 20 x^{6} + 150 x^{4} - 495 x^{2} + 605$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{7}\cdot 11^{2}$ |
$3$ |
$14.8928193227$ |
$27.122211109606535$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
$[2]$ |
$10$ |
$3$ |
$56.7492886583$ |
| 8.0.2420000000.2 |
$x^{8} - 15 x^{6} + 120 x^{4} - 440 x^{2} + 605$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{7}\cdot 11^{2}$ |
$3$ |
$14.8928193227$ |
$45.61394019164521$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
$[2]$ |
$10$ |
$3$ |
$53.8489996117$ |
| 8.0.2420000000.3 |
$x^{8} + 5 x^{6} - 40 x^{4} - 110 x^{2} + 605$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{7}\cdot 11^{2}$ |
$3$ |
$14.8928193227$ |
$38.3565987927518$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
$[2]$ |
$10$ |
$3$ |
$41.2376928653$ |
| 8.0.2420000000.4 |
$x^{8} + 50 x^{4} + 605$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{7}\cdot 11^{2}$ |
$3$ |
$14.8928193227$ |
$45.61394019164521$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
$[2]$ |
$10$ |
$3$ |
$57.1742004281$ |
| 8.0.2420000000.5 |
$x^{8} - 5 x^{6} - 40 x^{4} + 110 x^{2} + 605$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{7}\cdot 11^{2}$ |
$3$ |
$14.8928193227$ |
$38.3565987927518$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
$[2]$ |
$10$ |
$3$ |
$69.9854392908$ |
| 8.0.2850078125.1 |
$x^{8} - 2 x^{7} - 7 x^{6} - 9 x^{5} + 95 x^{4} + 46 x^{3} - 372 x^{2} - 232 x + 841$ |
$8$ |
[0,4] |
$5^{7}\cdot 191^{2}$ |
$2$ |
$15.2004727659$ |
$56.508715754849845$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
trivial |
$10$ |
$3$ |
$113.995633666$ |
| 8.0.3412578125.1 |
$x^{8} - 2 x^{7} + 18 x^{6} - 9 x^{5} + 115 x^{4} + 31 x^{3} + 408 x^{2} + 238 x + 671$ |
$8$ |
[0,4] |
$5^{7}\cdot 11^{2}\cdot 19^{2}$ |
$3$ |
$15.5465964425$ |
$59.111488676075524$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
$[2]$ |
$10$ |
$3$ |
$55.7602062393$ |
| 8.0.3412578125.2 |
$x^{8} - x^{7} - 18 x^{6} + 7 x^{5} + 130 x^{4} - 52 x^{3} - 378 x^{2} + 431 x + 991$ |
$8$ |
[0,4] |
$5^{7}\cdot 11^{2}\cdot 19^{2}$ |
$3$ |
$15.5465964425$ |
$59.111488676075524$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
$[2]$ |
$10$ |
$3$ |
$68.3947030124$ |
| 8.0.3478203125.1 |
$x^{8} - 3 x^{7} + 23 x^{6} - 36 x^{5} + 185 x^{4} - 141 x^{3} + 633 x^{2} - 188 x + 781$ |
$8$ |
[0,4] |
$5^{7}\cdot 211^{2}$ |
$2$ |
$15.5836565301$ |
$59.393645356642544$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
trivial |
$10$ |
$3$ |
$172.661459531$ |
| 8.0.4921953125.1 |
$x^{8} - 2 x^{7} - 17 x^{6} + 26 x^{5} + 140 x^{4} - 119 x^{3} - 597 x^{2} + 158 x + 1441$ |
$8$ |
[0,4] |
$5^{7}\cdot 251^{2}$ |
$2$ |
$16.2748571072$ |
$64.779205102618$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
trivial |
$10$ |
$3$ |
$122.087114428$ |
| 8.4.5082629877.1 |
$x^{8} - 4 x^{7} + 7 x^{6} - 7 x^{5} - 7 x^{4} + 21 x^{3} - 2 x^{2} - 9 x + 3$ |
$8$ |
[4,2] |
$3^{4}\cdot 13^{7}$ |
$2$ |
$16.3403389389$ |
$16.340338938923477$ |
|
|
✓ |
$(C_8:C_2):C_2$ (as 8T16) |
trivial |
$2$ |
$5$ |
$123.222850641$ |
| 8.4.5120000000.3 |
$x^{8} - 5 x^{4} + 5$ |
$8$ |
[4,2] |
$2^{16}\cdot 5^{7}$ |
$2$ |
$16.3553086792$ |
$19.449849449321462$ |
|
|
✓ |
$(C_8:C_2):C_2$ (as 8T16) |
trivial |
$2$ |
$5$ |
$77.7778100001$ |
| 8.0.5737578125.1 |
$x^{8} - 3 x^{7} - 17 x^{6} + 54 x^{5} + 140 x^{4} - 326 x^{3} - 612 x^{2} + 747 x + 1271$ |
$8$ |
[0,4] |
$5^{7}\cdot 271^{2}$ |
$2$ |
$16.5897971785$ |
$67.31059029762893$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
trivial |
$10$ |
$3$ |
$123.081872248$ |
| 8.0.6081328125.1 |
$x^{8} - 2 x^{7} + 23 x^{6} - 29 x^{5} + 220 x^{4} - 124 x^{3} + 1013 x^{2} - 142 x + 1801$ |
$8$ |
[0,4] |
$3^{4}\cdot 5^{7}\cdot 31^{2}$ |
$3$ |
$16.7108986249$ |
$39.43122124751123$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
$[2]$ |
$10$ |
$3$ |
$77.0442623514$ |
| 8.0.7220000000.1 |
$x^{8} - 20 x^{6} + 220 x^{4} - 1045 x^{2} + 1805$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{7}\cdot 19^{2}$ |
$3$ |
$17.0732873486$ |
$59.94846215051783$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
$[4]$ |
$10$ |
$3$ |
$52.3346850559$ |
| 8.0.7220000000.2 |
$x^{8} + 85 x^{4} + 1805$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{7}\cdot 19^{2}$ |
$3$ |
$17.0732873486$ |
$59.94846215051783$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
$[2]$ |
$10$ |
$3$ |
$90.2043462886$ |
| 8.0.7556328125.1 |
$x^{8} - 2 x^{7} + 23 x^{6} - 29 x^{5} + 230 x^{4} - 124 x^{3} + 1133 x^{2} - 162 x + 2201$ |
$8$ |
[0,4] |
$5^{7}\cdot 311^{2}$ |
$2$ |
$17.1707336299$ |
$72.10725255611727$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
trivial |
$10$ |
$3$ |
$183.907254117$ |
| 8.0.7950078125.1 |
$x^{8} - x^{7} + 27 x^{6} - 23 x^{5} + 275 x^{4} - 172 x^{3} + 1207 x^{2} - 404 x + 1891$ |
$8$ |
[0,4] |
$5^{7}\cdot 11^{2}\cdot 29^{2}$ |
$3$ |
$17.2801068892$ |
$73.0287883795628$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
$[2]$ |
$10$ |
$3$ |
$92.1870538363$ |
| 8.0.7950078125.2 |
$x^{8} - 3 x^{7} + 33 x^{6} - 71 x^{5} + 370 x^{4} - 546 x^{3} + 1653 x^{2} - 1313 x + 2131$ |
$8$ |
[0,4] |
$5^{7}\cdot 11^{2}\cdot 29^{2}$ |
$3$ |
$17.2801068892$ |
$73.0287883795628$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
$[2]$ |
$10$ |
$3$ |
$103.938638348$ |
| 8.0.8559453125.1 |
$x^{8} - 3 x^{7} - 22 x^{6} + 59 x^{5} + 215 x^{4} - 386 x^{3} - 1042 x^{2} + 842 x + 1991$ |
$8$ |
[0,4] |
$5^{7}\cdot 331^{2}$ |
$2$ |
$17.4403723261$ |
$74.38969030504087$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
trivial |
$10$ |
$3$ |
$165.461592604$ |
| 8.0.9084453125.1 |
$x^{8} - 2 x^{7} + 28 x^{6} - 39 x^{5} + 305 x^{4} - 239 x^{3} + 1338 x^{2} - 132 x + 1721$ |
$8$ |
[0,4] |
$5^{7}\cdot 11^{2}\cdot 31^{2}$ |
$3$ |
$17.5706306074$ |
$75.50504022860989$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
$[2, 2]$ |
$10$ |
$3$ |
$49.768417966$ |
| 8.0.9084453125.2 |
$x^{8} - 3 x^{7} + 23 x^{6} - 31 x^{5} + 200 x^{4} - 176 x^{3} + 1073 x^{2} - 373 x + 2141$ |
$8$ |
[0,4] |
$5^{7}\cdot 11^{2}\cdot 31^{2}$ |
$3$ |
$17.5706306074$ |
$75.50504022860989$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
$[2, 2]$ |
$10$ |
$3$ |
$39.755876686$ |
| 8.0.9084453125.3 |
$x^{8} - x^{7} - 23 x^{6} + 27 x^{5} + 225 x^{4} - 212 x^{3} - 1048 x^{2} + 701 x + 2321$ |
$8$ |
[0,4] |
$5^{7}\cdot 11^{2}\cdot 31^{2}$ |
$3$ |
$17.5706306074$ |
$75.50504022860989$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
$[2, 2]$ |
$10$ |
$3$ |
$50.8744417039$ |
| 8.0.9084453125.4 |
$x^{8} - x^{7} - 8 x^{6} + 27 x^{5} - 80 x^{4} - 12 x^{3} + 622 x^{2} - 789 x + 2441$ |
$8$ |
[0,4] |
$5^{7}\cdot 11^{2}\cdot 31^{2}$ |
$3$ |
$17.5706306074$ |
$75.50504022860989$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
$[2, 2]$ |
$10$ |
$3$ |
$65.3892426207$ |
| 8.0.14512578125.1 |
$x^{8} - 3 x^{7} + 33 x^{6} - 56 x^{5} + 350 x^{4} - 306 x^{3} + 1678 x^{2} - 633 x + 3641$ |
$8$ |
[0,4] |
$5^{7}\cdot 431^{2}$ |
$2$ |
$18.6302237717$ |
$84.88625793449107$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
$[3]$ |
$10$ |
$3$ |
$76.8982230396$ |
| 8.4.14580000000.3 |
$x^{8} - 60 x^{4} - 45 x^{2} + 45$ |
$8$ |
[4,2] |
$2^{8}\cdot 3^{6}\cdot 5^{7}$ |
$3$ |
$18.6410207764$ |
$31.350335095103276$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
trivial |
$2$ |
$5$ |
$101.763987245$ |
| 8.4.14580000000.4 |
$x^{8} - 15 x^{4} + 45$ |
$8$ |
[4,2] |
$2^{8}\cdot 3^{6}\cdot 5^{7}$ |
$3$ |
$18.6410207764$ |
$31.350335095103276$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
trivial |
$2$ |
$5$ |
$119.701462765$ |
| 8.0.15890703125.1 |
$x^{8} - 2 x^{7} - 32 x^{6} + 41 x^{5} + 380 x^{4} - 249 x^{3} - 1892 x^{2} + 483 x + 3371$ |
$8$ |
[0,4] |
$5^{7}\cdot 11^{2}\cdot 41^{2}$ |
$3$ |
$18.8426893967$ |
$86.83344366434605$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
$[2, 2]$ |
$10$ |
$3$ |
$71.039723238$ |
| 8.0.15890703125.2 |
$x^{8} - 3 x^{7} - 27 x^{6} + 64 x^{5} + 310 x^{4} - 486 x^{3} - 1722 x^{2} + 1237 x + 3931$ |
$8$ |
[0,4] |
$5^{7}\cdot 11^{2}\cdot 41^{2}$ |
$3$ |
$18.8426893967$ |
$86.83344366434605$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
$[2, 2]$ |
$10$ |
$3$ |
$53.9611950154$ |
| 8.0.15890703125.3 |
$x^{8} - x^{7} - 33 x^{6} + 37 x^{5} + 395 x^{4} - 382 x^{3} - 2018 x^{2} + 1081 x + 4051$ |
$8$ |
[0,4] |
$5^{7}\cdot 11^{2}\cdot 41^{2}$ |
$3$ |
$18.8426893967$ |
$86.83344366434605$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
$[2, 2]$ |
$10$ |
$3$ |
$78.6445211452$ |
| 8.0.15890703125.4 |
$x^{8} - 3 x^{7} - 27 x^{6} + 59 x^{5} + 315 x^{4} - 421 x^{3} - 1772 x^{2} + 1142 x + 4061$ |
$8$ |
[0,4] |
$5^{7}\cdot 11^{2}\cdot 41^{2}$ |
$3$ |
$18.8426893967$ |
$86.83344366434605$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
$[2, 2]$ |
$10$ |
$3$ |
$72.176725121$ |
| 8.0.15890703125.5 |
$x^{8} - 2 x^{7} - 27 x^{6} + 56 x^{5} + 310 x^{4} - 499 x^{3} - 1787 x^{2} + 1438 x + 4201$ |
$8$ |
[0,4] |
$5^{7}\cdot 11^{2}\cdot 41^{2}$ |
$3$ |
$18.8426893967$ |
$86.83344366434605$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
$[2, 2]$ |
$10$ |
$3$ |
$76.3631547721$ |
| 8.0.15890703125.6 |
$x^{8} - 2 x^{7} - 27 x^{6} + 41 x^{5} + 315 x^{4} - 344 x^{3} - 1747 x^{2} + 1073 x + 4331$ |
$8$ |
[0,4] |
$5^{7}\cdot 11^{2}\cdot 41^{2}$ |
$3$ |
$18.8426893967$ |
$86.83344366434605$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
$[2, 2]$ |
$10$ |
$3$ |
$45.2135282567$ |
| 8.0.16063620352.1 |
$x^{8} + 13 x^{4} + 13$ |
$8$ |
[0,4] |
$2^{8}\cdot 13^{7}$ |
$2$ |
$18.8681981701$ |
$31.732400407024496$ |
|
|
|
$(C_8:C_2):C_2$ (as 8T16) |
trivial |
$2$ |
$3$ |
$205.858731333$ |
| 8.0.16820000000.1 |
$x^{8} - 30 x^{6} + 330 x^{4} - 1595 x^{2} + 4205$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{7}\cdot 29^{2}$ |
$3$ |
$18.9770302088$ |
$74.06282017462216$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
$[2]$ |
$10$ |
$3$ |
$166.761653125$ |
| 8.0.16820000000.2 |
$x^{8} + 130 x^{4} + 4205$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{7}\cdot 29^{2}$ |
$3$ |
$18.9770302088$ |
$74.06282017462216$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
$[2]$ |
$10$ |
$3$ |
$126.906643675$ |
