| 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 |
| 8.0.305677387911424.1 |
$x^{8} - 4 x^{7} + 8 x^{6} - 10 x^{5} - 43 x^{4} + 98 x^{3} + 2 x^{2} - 52 x + 676$ |
$8$ |
[0,4] |
$2^{8}\cdot 103^{6}$ |
$2$ |
$64.663307407$ |
$64.66330740704495$ |
|
✓ |
|
$D_4$ (as 8T4) |
$[5]$ |
$4$ |
$3$ |
$11035.7757165$ |
| 8.0.305677387911424.2 |
$x^{8} + 49 x^{6} + 1145 x^{4} + 11840 x^{2} + 43264$ |
$8$ |
[0,4] |
$2^{8}\cdot 103^{6}$ |
$2$ |
$64.663307407$ |
$129.3266148140899$ |
|
|
|
$C_2^2 \wr C_2$ (as 8T18) |
$[15]$ |
$2$ |
$3$ |
$3649.32311553$ |
| 8.0.746282685330625.1 |
$x^{8} + 56 x^{6} + 764 x^{4} - 45 x^{2} + 100$ |
$8$ |
[0,4] |
$5^{4}\cdot 103^{6}$ |
$2$ |
$72.2957755061$ |
$72.29577550605909$ |
|
|
|
$S_4$ (as 8T14) |
$[6]$ |
$2$ |
$3$ |
$11806.4782623$ |
| 8.4.746282685330625.1 |
$x^{8} - 3 x^{7} - 35 x^{6} + 178 x^{5} - 27 x^{4} - 2757 x^{3} - 6191 x^{2} - 28930 x - 43580$ |
$8$ |
[4,2] |
$5^{4}\cdot 103^{6}$ |
$2$ |
$72.2957755061$ |
$72.29577550605909$ |
|
|
|
$S_4\times C_2$ (as 8T24) |
trivial |
$2$ |
$5$ |
$103855.239392$ |
| 8.0.1222709551645696.2 |
$x^{8} - 10 x^{6} - 323 x^{4} + 3800 x^{2} + 56644$ |
$8$ |
[0,4] |
$2^{10}\cdot 103^{6}$ |
$2$ |
$76.8980652481$ |
$129.3266148140899$ |
|
|
|
$C_2^2 \wr C_2$ (as 8T18) |
$[5]$ |
$2$ |
$3$ |
$8788.69574151$ |
| 8.0.2866919563966129.1 |
$x^{8} - 2 x^{7} + 86 x^{6} - 50 x^{5} + 1740 x^{4} + 978 x^{3} + 8261 x^{2} + 4410 x + 1044$ |
$8$ |
[0,4] |
$7^{4}\cdot 103^{6}$ |
$2$ |
$85.541515175$ |
$85.54151517498092$ |
|
✓ |
|
$D_4$ (as 8T4) |
$[5]$ |
$2$ |
$3$ |
$34099.5465681$ |
| 8.0.2866919563966129.2 |
$x^{8} - 3 x^{7} + 5 x^{6} - 118 x^{5} + 236 x^{4} - 505 x^{3} + 3550 x^{2} - 125 x + 20000$ |
$8$ |
[0,4] |
$7^{4}\cdot 103^{6}$ |
$2$ |
$85.541515175$ |
$85.54151517498092$ |
|
|
? |
$\PSL(2,7)$ (as 8T37) |
$[2, 12]$ |
$2$ |
$3$ |
$1819.4908361$ |
| 8.0.4890838206582784.1 |
$x^{8} - 2 x^{7} + 87 x^{6} + 1753 x^{4} + 2678 x^{3} + 11513 x^{2} + 12548 x + 4454$ |
$8$ |
[0,4] |
$2^{12}\cdot 103^{6}$ |
$2$ |
$91.4477263229$ |
$91.44772632294358$ |
|
✓ |
|
$D_4$ (as 8T4) |
$[3, 15]$ |
$2$ |
$3$ |
$14017.7180273$ |
| 8.0.4890838206582784.2 |
$x^{8} - 77 x^{6} + 1747 x^{4} - 3279 x^{2} + 4624$ |
$8$ |
[0,4] |
$2^{12}\cdot 103^{6}$ |
$2$ |
$91.4477263229$ |
$129.3266148140899$ |
|
|
|
$D_4\times C_2$ (as 8T9) |
$[30]$ |
$4$ |
$3$ |
$18815.798496$ |
| 8.0.4890838206582784.3 |
$x^{8} - 4 x^{7} + 56 x^{6} - 154 x^{5} + 1140 x^{4} - 2028 x^{3} + 11737 x^{2} - 10748 x + 60316$ |
$8$ |
[0,4] |
$2^{12}\cdot 103^{6}$ |
$2$ |
$91.4477263229$ |
$129.3266148140899$ |
|
|
? |
$C_2^2 \wr C_2$ (as 8T18) |
$[15]$ |
$2$ |
$3$ |
$19174.0843424$ |
| 8.0.9781676413165568.1 |
$x^{8} + 13 x^{6} + 102 x^{4} + 324 x^{2} + 392$ |
$8$ |
[0,4] |
$2^{13}\cdot 103^{6}$ |
$2$ |
$99.7244526898$ |
$217.50057358813226$ |
|
|
|
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[15]$ |
$2$ |
$3$ |
$62904.1882138$ |
| 8.0.9781676413165568.2 |
$x^{8} - 21 x^{6} + 204 x^{4} - 920 x^{2} + 1568$ |
$8$ |
[0,4] |
$2^{13}\cdot 103^{6}$ |
$2$ |
$99.7244526898$ |
$258.6532296281798$ |
|
|
|
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[15]$ |
$2$ |
$3$ |
$58264.4440232$ |
| 8.0.9781676413165568.6 |
$x^{8} - 6 x^{6} + 65 x^{4} + 38 x^{2} + 578$ |
$8$ |
[0,4] |
$2^{13}\cdot 103^{6}$ |
$2$ |
$99.7244526898$ |
$237.18605735698713$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[5]$ |
$2$ |
$3$ |
$46294.182152$ |
| 8.0.11004385964811264.1 |
$x^{8} - 37 x^{6} + 449 x^{4} - 2580 x^{2} + 12996$ |
$8$ |
[0,4] |
$2^{10}\cdot 3^{2}\cdot 103^{6}$ |
$3$ |
$101.203545319$ |
$158.3921082279921$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[10]$ |
$2$ |
$3$ |
$29396.5682031$ |
| 8.2.14672514619748352.2 |
$x^{8} - 24 x^{6} + 10 x^{4} + 2432 x^{2} - 867$ |
$8$ |
[2,3] |
$-\,2^{12}\cdot 3\cdot 103^{6}$ |
$3$ |
$104.909077672$ |
$188.36102206500925$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$2$ |
$4$ |
$90622.0993508$ |
| 8.0.18657067133265625.2 |
$x^{8} + 4 x^{6} + 6 x^{4} + 519 x^{2} + 1$ |
$8$ |
[0,4] |
$5^{6}\cdot 103^{6}$ |
$2$ |
$108.10739979$ |
$108.10739979042843$ |
|
|
? |
$S_4$ (as 8T14) |
$[6, 12]$ |
$2$ |
$3$ |
$2297.52319977$ |
| 8.0.19563352826331136.1 |
$x^{8} + 2 x^{6} + 53 x^{4} - 154 x^{2} + 676$ |
$8$ |
[0,4] |
$2^{14}\cdot 103^{6}$ |
$2$ |
$108.750286794$ |
$129.3266148140899$ |
|
|
|
$D_4\times C_2$ (as 8T9) |
$[10]$ |
$2$ |
$3$ |
$26008.300098$ |
| 8.0.19563352826331136.6 |
$x^{8} - 10 x^{6} + 2149 x^{4} + 9980 x^{2} + 56644$ |
$8$ |
[0,4] |
$2^{14}\cdot 103^{6}$ |
$2$ |
$108.750286794$ |
$129.3266148140899$ |
|
|
? |
$C_2^2 \wr C_2$ (as 8T18) |
$[10]$ |
$2$ |
$3$ |
$23088.5547912$ |
| 8.0.19563352826331136.9 |
$x^{8} - 5 x^{6} + 48 x^{4} - 40 x^{2} + 64$ |
$8$ |
[0,4] |
$2^{14}\cdot 103^{6}$ |
$2$ |
$108.750286794$ |
$258.6532296281798$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[15]$ |
$2$ |
$3$ |
$21257.1695667$ |
| 8.0.24759868420825344.1 |
$x^{8} - 4 x^{7} + 4 x^{6} + 2 x^{5} + 357 x^{4} + 514 x^{3} + 310 x^{2} + 52 x + 676$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{4}\cdot 103^{6}$ |
$3$ |
$112.000133814$ |
$112.00013381444677$ |
|
|
? |
$D_4\times C_2$ (as 8T9) |
$[30]$ |
$2$ |
$3$ |
$17063.4513742$ |
| 8.4.24759868420825344.1 |
$x^{8} - 4 x^{7} + 4 x^{6} + 2 x^{5} - 55 x^{4} + 102 x^{3} - 308 x^{2} + 258 x + 573$ |
$8$ |
[4,2] |
$2^{8}\cdot 3^{4}\cdot 103^{6}$ |
$3$ |
$112.000133814$ |
$112.00013381444677$ |
|
|
|
$D_4\times C_2$ (as 8T9) |
trivial |
$2$ |
$5$ |
$947705.953633$ |
| 8.0.24759868420825344.3 |
$x^{8} - 4 x^{7} + 8 x^{6} - 10 x^{5} - 455 x^{4} + 922 x^{3} + 2 x^{2} - 464 x + 53824$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{4}\cdot 103^{6}$ |
$3$ |
$112.000133814$ |
$112.00013381444677$ |
|
✓ |
|
$D_4$ (as 8T4) |
$[10]$ |
$4$ |
$3$ |
$322748.581682$ |
| 8.0.24759868420825344.8 |
$x^{8} + 50 x^{6} + 577 x^{4} + 3744 x^{2} + 576$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{4}\cdot 103^{6}$ |
$3$ |
$112.000133814$ |
$112.00013381444677$ |
|
|
|
$S_4$ (as 8T14) |
$[2, 6]$ |
$2$ |
$3$ |
$127763.362989$ |
| 8.0.39126705652662272.2 |
$x^{8} + 26 x^{6} + 408 x^{4} + 2592 x^{2} + 6272$ |
$8$ |
[0,4] |
$2^{15}\cdot 103^{6}$ |
$2$ |
$118.593028678$ |
$217.50057358813226$ |
|
|
|
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[15]$ |
$2$ |
$3$ |
$63462.8504039$ |
| 8.0.39126705652662272.4 |
$x^{8} - 12 x^{6} + 260 x^{4} + 304 x^{2} + 9248$ |
$8$ |
[0,4] |
$2^{15}\cdot 103^{6}$ |
$2$ |
$118.593028678$ |
$237.18605735698713$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[85]$ |
$2$ |
$3$ |
$4048.28123007$ |
| 8.0.39126705652662272.6 |
$x^{8} + 515 x^{4} + 339488$ |
$8$ |
[0,4] |
$2^{15}\cdot 103^{6}$ |
$2$ |
$118.593028678$ |
$282.0633469883726$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$[5, 5]$ |
$2$ |
$3$ |
$16203.7992851$ |
| 8.0.44017543859245056.1 |
$x^{8} - 20 x^{6} + 356 x^{4} - 2560 x^{2} + 6084$ |
$8$ |
[0,4] |
$2^{12}\cdot 3^{2}\cdot 103^{6}$ |
$3$ |
$120.351976157$ |
$158.3921082279921$ |
|
|
|
$C_2^2 \wr C_2$ (as 8T18) |
$[3, 42]$ |
$2$ |
$3$ |
$8947.10578773$ |
| 8.4.44017543859245056.1 |
$x^{8} - 20 x^{6} - 262 x^{4} - 500 x^{2} + 625$ |
$8$ |
[4,2] |
$2^{12}\cdot 3^{2}\cdot 103^{6}$ |
$3$ |
$120.351976157$ |
$158.3921082279921$ |
|
|
? |
$C_2^2 \wr C_2$ (as 8T18) |
$[3]$ |
$2$ |
$5$ |
$322623.528957$ |
| 8.0.78253411305324544.1 |
$x^{8} + 32 x^{6} + 178 x^{4} - 1248 x^{2} + 4096$ |
$8$ |
[0,4] |
$2^{16}\cdot 103^{6}$ |
$2$ |
$129.326614814$ |
$258.6532296281798$ |
|
|
|
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[15]$ |
$2$ |
$3$ |
$134854.358867$ |
| 8.0.78253411305324544.2 |
$x^{8} + 8 x^{6} - 182 x^{4} + 2504 x^{2} + 9801$ |
$8$ |
[0,4] |
$2^{16}\cdot 103^{6}$ |
$2$ |
$129.326614814$ |
$129.3266148140899$ |
|
|
|
$D_4\times C_2$ (as 8T9) |
$[20]$ |
$2$ |
$3$ |
$57983.6007043$ |
| 8.0.78253411305324544.3 |
$x^{8} + 4 x^{6} - 200 x^{4} + 1240 x^{2} + 10404$ |
$8$ |
[0,4] |
$2^{16}\cdot 103^{6}$ |
$2$ |
$129.326614814$ |
$129.3266148140899$ |
|
✓ |
|
$D_4$ (as 8T4) |
$[2, 10]$ |
$4$ |
$3$ |
$76163.6072761$ |
| 8.4.78253411305324544.3 |
$x^{8} - 12 x^{6} + 157 x^{4} - 3610 x^{2} + 81$ |
$8$ |
[4,2] |
$2^{16}\cdot 103^{6}$ |
$2$ |
$129.326614814$ |
$182.89545264588716$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
trivial |
$2$ |
$5$ |
$1245308.04706$ |
| 8.0.78253411305324544.4 |
$x^{8} - 102 x^{6} + 2305 x^{4} + 18392 x^{2} + 21904$ |
$8$ |
[0,4] |
$2^{16}\cdot 103^{6}$ |
$2$ |
$129.326614814$ |
$129.3266148140899$ |
|
|
? |
$D_4\times C_2$ (as 8T9) |
$[60]$ |
$4$ |
$3$ |
$33758.9889501$ |
| 8.0.78253411305324544.7 |
$x^{8} + 52 x^{6} + 3589 x^{4} + 112612 x^{2} + 2937796$ |
$8$ |
[0,4] |
$2^{16}\cdot 103^{6}$ |
$2$ |
$129.326614814$ |
$129.3266148140899$ |
|
✓ |
? |
$D_4$ (as 8T4) |
$[2, 10]$ |
$2$ |
$3$ |
$20325.5146935$ |
| 8.0.99728441858398609.1 |
$x^{8} - 4 x^{7} + 2 x^{6} + 8 x^{5} - 108 x^{4} + 198 x^{3} + 1856 x^{2} - 1953 x + 2988$ |
$8$ |
[0,4] |
$17^{4}\cdot 103^{6}$ |
$2$ |
$133.306823271$ |
$133.3068232705156$ |
|
|
|
$S_4$ (as 8T14) |
$[48]$ |
$2$ |
$3$ |
$24231.9025913$ |
| 8.0.155610089335955809.1 |
$x^{8} + 185 x^{6} + 9989 x^{4} + 175828 x^{2} + 992016$ |
$8$ |
[0,4] |
$19^{4}\cdot 103^{6}$ |
$2$ |
$140.930411171$ |
$140.93041117120703$ |
|
✓ |
|
$D_4$ (as 8T4) |
$[3, 3, 15]$ |
$2$ |
$3$ |
$5120.81503258$ |
| 8.4.156506822610649088.1 |
$x^{8} - 22 x^{6} + 233 x^{4} - 1232 x^{2} + 2312$ |
$8$ |
[4,2] |
$2^{17}\cdot 103^{6}$ |
$2$ |
$141.031673494$ |
$258.6532296281798$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[3]$ |
$2$ |
$5$ |
$466243.60586$ |
| 8.0.156506822610649088.3 |
$x^{8} - 42 x^{6} + 816 x^{4} - 7360 x^{2} + 25088$ |
$8$ |
[0,4] |
$2^{17}\cdot 103^{6}$ |
$2$ |
$141.031673494$ |
$258.6532296281798$ |
|
|
|
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[15]$ |
$2$ |
$3$ |
$59736.0542993$ |
| 8.0.156506822610649088.5 |
$x^{8} + 1030 x^{4} + 1357952$ |
$8$ |
[0,4] |
$2^{17}\cdot 103^{6}$ |
$2$ |
$141.031673494$ |
$282.0633469883726$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$[5]$ |
$2$ |
$3$ |
$107403.738042$ |
| 8.4.313013645221298176.1 |
$x^{8} - 114 x^{6} + 3586 x^{4} - 23844 x^{2} + 158404$ |
$8$ |
[4,2] |
$2^{18}\cdot 103^{6}$ |
$2$ |
$153.796130496$ |
$217.50057358813226$ |
|
|
|
$C_2^2 \wr C_2$ (as 8T18) |
$[3]$ |
$2$ |
$5$ |
$487918.275873$ |
| 8.0.313013645221298176.2 |
$x^{8} + 58 x^{6} - 26 x^{4} - 24628 x^{2} + 195364$ |
$8$ |
[0,4] |
$2^{18}\cdot 103^{6}$ |
$2$ |
$153.796130496$ |
$217.50057358813226$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[2]$ |
$2$ |
$3$ |
$314082.381119$ |
| 8.4.313013645221298176.3 |
$x^{8} - 44 x^{6} - 2776 x^{4} - 37048 x^{2} + 324$ |
$8$ |
[4,2] |
$2^{18}\cdot 103^{6}$ |
$2$ |
$153.796130496$ |
$217.50057358813226$ |
|
|
|
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$2$ |
$5$ |
$3544085.71263$ |
| 8.0.313013645221298176.4 |
$x^{8} - 206 x^{6} + 21218 x^{4} - 1357952 x^{2} + 43454464$ |
$8$ |
[0,4] |
$2^{18}\cdot 103^{6}$ |
$2$ |
$153.796130496$ |
$217.50057358813226$ |
|
|
|
$D_4\times C_2$ (as 8T9) |
$[30]$ |
$4$ |
$3$ |
$83463.7239757$ |
| 8.0.313013645221298176.5 |
$x^{8} + 42436$ |
$8$ |
[0,4] |
$2^{18}\cdot 103^{6}$ |
$2$ |
$153.796130496$ |
$217.50057358813226$ |
|
|
? |
$Q_8:C_2$ (as 8T11) |
$[10]$ |
$4$ |
$3$ |
$126743.128837$ |
| 8.0.334144788712971889.2 |
$x^{8} + 83 x^{6} + 1180 x^{4} + 127632 x^{2} + 5494336$ |
$8$ |
[0,4] |
$23^{4}\cdot 103^{6}$ |
$2$ |
$155.057164032$ |
$155.05716403218352$ |
|
✓ |
|
$D_4$ (as 8T4) |
$[15]$ |
$2$ |
$3$ |
$3104207.7484$ |
| 8.0.396157894733205504.6 |
$x^{8} - 4 x^{7} + 16 x^{6} - 34 x^{5} - 189 x^{4} + 430 x^{3} + 3190 x^{2} + 43558 x + 200329$ |
$8$ |
[0,4] |
$2^{12}\cdot 3^{4}\cdot 103^{6}$ |
$3$ |
$158.392108228$ |
$158.3921082279921$ |
|
|
? |
$\PSL(2,7)$ (as 8T37) |
$[2, 2, 6]$ |
$2$ |
$3$ |
$16473.3582061$ |
| 8.4.626027290442596352.1 |
$x^{8} - 42 x^{6} + 713 x^{4} - 5712 x^{2} + 17672$ |
$8$ |
[4,2] |
$2^{19}\cdot 103^{6}$ |
$2$ |
$167.71586956$ |
$258.6532296281798$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[3]$ |
$2$ |
$5$ |
$2029026.34734$ |
| 8.0.1118855659102789696.1 |
$x^{8} - 2 x^{7} + 48 x^{6} - 96 x^{5} + 1776 x^{4} - 5442 x^{3} + 16452 x^{2} - 102568 x + 166615$ |
$8$ |
[0,4] |
$2^{6}\cdot 11^{4}\cdot 103^{6}$ |
$3$ |
$180.34194857$ |
$194.24505505804268$ |
|
|
? |
$\PSL(2,7)$ (as 8T37) |
$[2, 12]$ |
$2$ |
$3$ |
$138945.658398$ |
| 8.0.1252054580885192704.2 |
$x^{8} - 22 x^{6} + 130 x^{4} + 416 x^{2} + 3136$ |
$8$ |
[0,4] |
$2^{20}\cdot 103^{6}$ |
$2$ |
$182.895452646$ |
$335.43173912005403$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[20]$ |
$2$ |
$3$ |
$144710.001188$ |
| 8.4.1252054580885192704.2 |
$x^{8} - 24 x^{6} + 10 x^{4} - 26408 x^{2} + 19321$ |
$8$ |
[4,2] |
$2^{20}\cdot 103^{6}$ |
$2$ |
$182.895452646$ |
$182.89545264588716$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[2]$ |
$2$ |
$5$ |
$1600716.89493$ |
