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 |
8.8.410338673.1 |
$x^{8} - x^{7} - 7 x^{6} + 6 x^{5} + 15 x^{4} - 10 x^{3} - 10 x^{2} + 4 x + 1$ |
$8$ |
[8,0] |
$17^{7}$ |
$1$ |
$11.9300648987$ |
$11.93006489865314$ |
|
✓ |
✓ |
$C_8$ (as 8T1) |
trivial |
$2$ |
$7$ |
$28.437595417$ |
8.8.2147483648.1 |
$x^{8} - 8 x^{6} + 20 x^{4} - 16 x^{2} + 2$ |
$8$ |
[8,0] |
$2^{31}$ |
$1$ |
$14.6720646913$ |
$14.67206469127474$ |
|
✓ |
✓ |
$C_8$ (as 8T1) |
trivial |
$2$ |
$7$ |
$123.0777333$ |
8.0.2147483648.1 |
$x^{8} + 8 x^{6} + 20 x^{4} + 16 x^{2} + 2$ |
$8$ |
[0,4] |
$2^{31}$ |
$1$ |
$14.6720646913$ |
$14.67206469127474$ |
✓ |
✓ |
✓ |
$C_8$ (as 8T1) |
trivial |
$2$ |
$3$ |
$19.534360053$ |
8.0.33237432513.1 |
$x^{8} - x^{7} + 10 x^{6} - 11 x^{5} + 15 x^{4} - 61 x^{3} + 58 x^{2} - 47 x + 103$ |
$8$ |
[0,4] |
$3^{4}\cdot 17^{7}$ |
$2$ |
$20.6634785421$ |
$20.663478542061284$ |
✓ |
✓ |
? |
$C_8$ (as 8T1) |
$[2]$ |
$2$ |
$3$ |
$27.6959098582$ |
8.0.105046700288.1 |
$x^{8} + 17 x^{6} + 68 x^{4} + 85 x^{2} + 17$ |
$8$ |
[0,4] |
$2^{8}\cdot 17^{7}$ |
$2$ |
$23.8601297973$ |
$23.86012979730628$ |
✓ |
✓ |
|
$C_8$ (as 8T1) |
$[2, 2]$ |
$2$ |
$3$ |
$27.6959098582$ |
8.8.173946175488.1 |
$x^{8} - 24 x^{6} + 180 x^{4} - 432 x^{2} + 162$ |
$8$ |
[8,0] |
$2^{31}\cdot 3^{4}$ |
$2$ |
$25.4127614972$ |
$25.412761497225222$ |
|
✓ |
? |
$C_8$ (as 8T1) |
trivial |
$2$ |
$7$ |
$1494.12984141$ |
8.0.173946175488.1 |
$x^{8} + 24 x^{6} + 180 x^{4} + 432 x^{2} + 162$ |
$8$ |
[0,4] |
$2^{31}\cdot 3^{4}$ |
$2$ |
$25.4127614972$ |
$25.412761497225222$ |
✓ |
✓ |
? |
$C_8$ (as 8T1) |
$[3, 6]$ |
$2$ |
$3$ |
$19.534360053$ |
8.0.194754273881.1 |
$x^{8} - x^{7} + 3 x^{6} - 11 x^{5} + 44 x^{4} + 53 x^{3} + 153 x^{2} + 160 x + 59$ |
$8$ |
[0,4] |
$41^{7}$ |
$1$ |
$25.7742403823$ |
$25.774240382333762$ |
✓ |
✓ |
? |
$C_8$ (as 8T1) |
trivial |
$2$ |
$3$ |
$108.197795509$ |
8.8.256461670625.1 |
$x^{8} - x^{7} - 24 x^{6} + 23 x^{5} + 151 x^{4} - 197 x^{3} - 214 x^{2} + 429 x - 169$ |
$8$ |
[8,0] |
$5^{4}\cdot 17^{7}$ |
$2$ |
$26.6764360894$ |
$26.676436089372558$ |
|
✓ |
? |
$C_8$ (as 8T1) |
$[2]$ |
$2$ |
$7$ |
$636.601883042$ |
8.0.985223153873.1 |
$x^{8} - x^{7} + 27 x^{6} - 28 x^{5} + 151 x^{4} - 350 x^{3} + 500 x^{2} - 846 x + 1157$ |
$8$ |
[0,4] |
$7^{4}\cdot 17^{7}$ |
$2$ |
$31.5639848467$ |
$31.563984846697192$ |
✓ |
✓ |
? |
$C_8$ (as 8T1) |
$[3, 6]$ |
$2$ |
$3$ |
$27.6959098582$ |
8.0.1342177280000.1 |
$x^{8} + 40 x^{6} + 500 x^{4} + 2000 x^{2} + 1250$ |
$8$ |
[0,4] |
$2^{31}\cdot 5^{4}$ |
$2$ |
$32.80773402$ |
$32.807734019964784$ |
✓ |
✓ |
? |
$C_8$ (as 8T1) |
$[34]$ |
$2$ |
$3$ |
$19.534360053$ |
8.8.1342177280000.1 |
$x^{8} - 40 x^{6} + 500 x^{4} - 2000 x^{2} + 1250$ |
$8$ |
[8,0] |
$2^{31}\cdot 5^{4}$ |
$2$ |
$32.80773402$ |
$32.807734019964784$ |
|
✓ |
? |
$C_8$ (as 8T1) |
$[2]$ |
$2$ |
$7$ |
$2507.3594667$ |
8.0.1680747204608.1 |
$x^{8} + 34 x^{6} + 272 x^{4} + 680 x^{2} + 272$ |
$8$ |
[0,4] |
$2^{12}\cdot 17^{7}$ |
$2$ |
$33.7433191593$ |
$33.74331915933294$ |
✓ |
✓ |
|
$C_8$ (as 8T1) |
$[6, 6]$ |
$2$ |
$3$ |
$27.6959098582$ |
8.8.1680747204608.1 |
$x^{8} - 34 x^{6} + 272 x^{4} - 680 x^{2} + 272$ |
$8$ |
[8,0] |
$2^{12}\cdot 17^{7}$ |
$2$ |
$33.7433191593$ |
$33.74331915933294$ |
|
✓ |
|
$C_8$ (as 8T1) |
$[2]$ |
$2$ |
$7$ |
$2413.01102399$ |
8.8.5156108238848.1 |
$x^{8} - 56 x^{6} + 980 x^{4} - 5488 x^{2} + 4802$ |
$8$ |
[8,0] |
$2^{31}\cdot 7^{4}$ |
$2$ |
$38.818634393$ |
$38.81863439296463$ |
|
✓ |
? |
$C_8$ (as 8T1) |
trivial |
$2$ |
$7$ |
$9687.95863021$ |
8.0.5156108238848.1 |
$x^{8} + 56 x^{6} + 980 x^{4} + 5488 x^{2} + 4802$ |
$8$ |
[0,4] |
$2^{31}\cdot 7^{4}$ |
$2$ |
$38.818634393$ |
$38.81863439296463$ |
✓ |
✓ |
? |
$C_8$ (as 8T1) |
$[2, 34]$ |
$2$ |
$3$ |
$19.534360053$ |
8.0.6007768511393.1 |
$x^{8} - x^{7} + 44 x^{6} - 45 x^{5} + 423 x^{4} - 877 x^{3} + 1826 x^{2} - 3515 x + 4591$ |
$8$ |
[0,4] |
$11^{4}\cdot 17^{7}$ |
$2$ |
$39.5675489934$ |
$39.56754899342178$ |
✓ |
✓ |
? |
$C_8$ (as 8T1) |
$[34]$ |
$2$ |
$3$ |
$27.6959098582$ |
8.0.6411541765625.1 |
$x^{8} - x^{7} + 10 x^{6} - 79 x^{5} + 134 x^{4} + 41 x^{3} + 245 x^{2} - 846 x + 596$ |
$8$ |
[0,4] |
$5^{6}\cdot 17^{7}$ |
$2$ |
$39.8905761936$ |
$39.89057619356904$ |
✓ |
✓ |
|
$C_8$ (as 8T1) |
$[4]$ |
$2$ |
$3$ |
$489.802404202$ |
8.0.6411541765625.2 |
$x^{8} - x^{7} + 10 x^{6} + 6 x^{5} + 49 x^{4} - 129 x^{3} + 500 x^{2} + 2044 x + 1616$ |
$8$ |
[0,4] |
$5^{6}\cdot 17^{7}$ |
$2$ |
$39.8905761936$ |
$39.89057619356904$ |
✓ |
✓ |
|
$C_8$ (as 8T1) |
$[292]$ |
$2$ |
$3$ |
$489.802404202$ |
8.8.8508782723328.1 |
$x^{8} - 51 x^{6} + 612 x^{4} - 2295 x^{2} + 1377$ |
$8$ |
[8,0] |
$2^{8}\cdot 3^{4}\cdot 17^{7}$ |
$3$ |
$41.3269570841$ |
$41.32695708412257$ |
|
✓ |
|
$C_8$ (as 8T1) |
$[2]$ |
$2$ |
$7$ |
$2744.12339498$ |
8.0.11047398519097.1 |
$x^{8} - x^{7} + 5 x^{6} + 17 x^{5} - 46 x^{4} + 136 x^{3} + 320 x^{2} - 512 x + 4096$ |
$8$ |
[0,4] |
$73^{7}$ |
$1$ |
$42.6979970229$ |
$42.69799702286967$ |
✓ |
✓ |
|
$C_8$ (as 8T1) |
$[89]$ |
$2$ |
$3$ |
$2046.25577237$ |
8.8.11719682839553.1 |
$x^{8} - x^{7} - 58 x^{6} + 57 x^{5} + 831 x^{4} - 1285 x^{3} - 3070 x^{2} + 6889 x - 2753$ |
$8$ |
[8,0] |
$13^{4}\cdot 17^{7}$ |
$2$ |
$43.0144607117$ |
$43.014460711706995$ |
|
✓ |
? |
$C_8$ (as 8T1) |
$[2]$ |
$2$ |
$7$ |
$3630.8787207$ |
8.8.15775096184361.1 |
$x^{8} - x^{7} - 38 x^{6} + 30 x^{5} + 331 x^{4} - 152 x^{3} - 708 x^{2} - 291 x - 23$ |
$8$ |
[8,0] |
$3^{4}\cdot 41^{7}$ |
$2$ |
$44.6422938687$ |
$44.64229386869556$ |
|
✓ |
? |
$C_8$ (as 8T1) |
trivial |
$2$ |
$7$ |
$8457.57651835$ |
8.0.20773395320625.1 |
$x^{8} - x^{7} + 61 x^{6} - 62 x^{5} + 831 x^{4} - 1642 x^{3} + 4546 x^{2} - 9176 x + 12241$ |
$8$ |
[0,4] |
$3^{4}\cdot 5^{4}\cdot 17^{7}$ |
$3$ |
$46.2049426717$ |
$46.20494267165728$ |
✓ |
✓ |
? |
$C_8$ (as 8T1) |
$[2, 34]$ |
$2$ |
$3$ |
$27.6959098582$ |
8.8.31441308090368.1 |
$x^{8} - 88 x^{6} + 2420 x^{4} - 21296 x^{2} + 29282$ |
$8$ |
[8,0] |
$2^{31}\cdot 11^{4}$ |
$2$ |
$48.6617334808$ |
$48.66173348077995$ |
|
✓ |
? |
$C_8$ (as 8T1) |
trivial |
$2$ |
$7$ |
$21339.8618782$ |
8.0.31441308090368.8 |
$x^{8} + 88 x^{6} + 2420 x^{4} + 21296 x^{2} + 29282$ |
$8$ |
[0,4] |
$2^{31}\cdot 11^{4}$ |
$2$ |
$48.6617334808$ |
$48.66173348077995$ |
✓ |
✓ |
? |
$C_8$ (as 8T1) |
$[226]$ |
$2$ |
$3$ |
$19.534360053$ |
8.0.33554432000000.1 |
$x^{8} + 40 x^{6} + 500 x^{4} + 2000 x^{2} + 50$ |
$8$ |
[0,4] |
$2^{31}\cdot 5^{6}$ |
$2$ |
$49.0590050814$ |
$49.05900508138431$ |
✓ |
✓ |
? |
$C_8$ (as 8T1) |
$[3, 12]$ |
$2$ |
$3$ |
$78.6242549932$ |
8.8.33554432000000.1 |
$x^{8} - 40 x^{6} + 500 x^{4} - 2000 x^{2} + 50$ |
$8$ |
[8,0] |
$2^{31}\cdot 5^{6}$ |
$2$ |
$49.0590050814$ |
$49.05900508138431$ |
|
✓ |
|
$C_8$ (as 8T1) |
$[2]$ |
$2$ |
$7$ |
$26385.2551796$ |
8.0.33554432000000.2 |
$x^{8} + 40 x^{6} + 500 x^{4} + 2000 x^{2} + 2450$ |
$8$ |
[0,4] |
$2^{31}\cdot 5^{6}$ |
$2$ |
$49.0590050814$ |
$49.05900508138431$ |
✓ |
✓ |
|
$C_8$ (as 8T1) |
$[164]$ |
$2$ |
$3$ |
$78.6242549932$ |
8.8.33554432000000.2 |
$x^{8} - 40 x^{6} + 500 x^{4} - 2000 x^{2} + 2450$ |
$8$ |
[8,0] |
$2^{31}\cdot 5^{6}$ |
$2$ |
$49.0590050814$ |
$49.05900508138431$ |
|
✓ |
? |
$C_8$ (as 8T1) |
$[2]$ |
$2$ |
$7$ |
$6237.2438059$ |
8.0.44231334895529.1 |
$x^{8} - x^{7} + 6 x^{6} - 46 x^{5} - 143 x^{4} + 575 x^{3} + 1160 x^{2} - 16 x + 512$ |
$8$ |
[0,4] |
$89^{7}$ |
$1$ |
$50.7827547495$ |
$50.78275474951909$ |
✓ |
✓ |
|
$C_8$ (as 8T1) |
$[113]$ |
$2$ |
$3$ |
$2970.52387144$ |
8.8.49857094113536.1 |
$x^{8} - 41 x^{6} + 533 x^{4} - 2296 x^{2} + 656$ |
$8$ |
[8,0] |
$2^{8}\cdot 41^{7}$ |
$2$ |
$51.5484807647$ |
$51.548480764667524$ |
|
✓ |
|
$C_8$ (as 8T1) |
trivial |
$2$ |
$7$ |
$27148.8915251$ |
8.0.53475746204033.2 |
$x^{8} - x^{7} + 78 x^{6} - 79 x^{5} + 1375 x^{4} - 2645 x^{3} + 9170 x^{2} - 18951 x + 26351$ |
$8$ |
[0,4] |
$17^{7}\cdot 19^{4}$ |
$2$ |
$52.0019472831$ |
$52.00194728311084$ |
✓ |
✓ |
? |
$C_8$ (as 8T1) |
$[10, 10]$ |
$2$ |
$3$ |
$27.6959098582$ |
8.8.61334280470528.1 |
$x^{8} - 104 x^{6} + 3380 x^{4} - 35152 x^{2} + 57122$ |
$8$ |
[8,0] |
$2^{31}\cdot 13^{4}$ |
$2$ |
$52.9008815613$ |
$52.9008815613158$ |
|
✓ |
? |
$C_8$ (as 8T1) |
$[2]$ |
$2$ |
$7$ |
$8398.03205033$ |
8.0.61334280470528.11 |
$x^{8} + 104 x^{6} + 3380 x^{4} + 35152 x^{2} + 57122$ |
$8$ |
[0,4] |
$2^{31}\cdot 13^{4}$ |
$2$ |
$52.9008815613$ |
$52.9008815613158$ |
✓ |
✓ |
? |
$C_8$ (as 8T1) |
$[9, 18]$ |
$2$ |
$3$ |
$19.534360053$ |
8.0.65654187680000.2 |
$x^{8} + 85 x^{6} + 1700 x^{4} + 10625 x^{2} + 10625$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{4}\cdot 17^{7}$ |
$3$ |
$53.3528721787$ |
$53.352872178745116$ |
✓ |
✓ |
|
$C_8$ (as 8T1) |
$[2, 10, 10]$ |
$2$ |
$3$ |
$27.6959098582$ |
8.8.79803075463713.1 |
$x^{8} - x^{7} - 92 x^{6} + 91 x^{5} + 2055 x^{4} - 3325 x^{3} - 12590 x^{2} + 28309 x - 7649$ |
$8$ |
[8,0] |
$3^{4}\cdot 7^{4}\cdot 17^{7}$ |
$3$ |
$54.6704254438$ |
$54.67042544381368$ |
|
✓ |
? |
$C_8$ (as 8T1) |
$[2]$ |
$2$ |
$7$ |
$11333.9362425$ |
8.8.80798284478113.1 |
$x^{8} - x^{7} - 42 x^{6} + 59 x^{5} + 497 x^{4} - 719 x^{3} - 1792 x^{2} + 2295 x + 193$ |
$8$ |
[8,0] |
$97^{7}$ |
$1$ |
$54.7551871235$ |
$54.755187123491936$ |
|
✓ |
? |
$C_8$ (as 8T1) |
trivial |
$2$ |
$7$ |
$13092.2724361$ |
8.8.108716359680000.1 |
$x^{8} - 120 x^{6} + 4500 x^{4} - 54000 x^{2} + 101250$ |
$8$ |
[8,0] |
$2^{31}\cdot 3^{4}\cdot 5^{4}$ |
$3$ |
$56.8246622038$ |
$56.82466220378493$ |
|
✓ |
? |
$C_8$ (as 8T1) |
$[2]$ |
$2$ |
$7$ |
$12922.0093704$ |
8.0.108716359680000.13 |
$x^{8} + 120 x^{6} + 4500 x^{4} + 54000 x^{2} + 101250$ |
$8$ |
[0,4] |
$2^{31}\cdot 3^{4}\cdot 5^{4}$ |
$3$ |
$56.8246622038$ |
$56.82466220378493$ |
✓ |
✓ |
? |
$C_8$ (as 8T1) |
$[14, 14]$ |
$2$ |
$3$ |
$19.534360053$ |
8.0.114829584590993.1 |
$x^{8} - x^{7} + 95 x^{6} - 96 x^{5} + 2055 x^{4} - 3886 x^{3} + 16208 x^{2} - 33962 x + 49573$ |
$8$ |
[0,4] |
$17^{7}\cdot 23^{4}$ |
$2$ |
$57.2145813161$ |
$57.21458131612729$ |
✓ |
✓ |
? |
$C_8$ (as 8T1) |
$[7, 14]$ |
$2$ |
$3$ |
$27.6959098582$ |
8.0.121721421175625.1 |
$x^{8} - x^{7} + 44 x^{6} - 52 x^{5} + 823 x^{4} + 94 x^{3} + 6016 x^{2} + 6843 x + 4651$ |
$8$ |
[0,4] |
$5^{4}\cdot 41^{7}$ |
$2$ |
$57.6329535633$ |
$57.632953563318466$ |
✓ |
✓ |
? |
$C_8$ (as 8T1) |
$[6, 6]$ |
$2$ |
$3$ |
$108.197795509$ |
8.8.136140523573248.1 |
$x^{8} - 102 x^{6} + 2448 x^{4} - 18360 x^{2} + 22032$ |
$8$ |
[8,0] |
$2^{12}\cdot 3^{4}\cdot 17^{7}$ |
$3$ |
$58.4451432$ |
$58.445143199977$ |
|
✓ |
|
$C_8$ (as 8T1) |
$[2]$ |
$2$ |
$7$ |
$24393.5787616$ |
8.0.136140523573248.5 |
$x^{8} + 102 x^{6} + 2448 x^{4} + 18360 x^{2} + 22032$ |
$8$ |
[0,4] |
$2^{12}\cdot 3^{4}\cdot 17^{7}$ |
$3$ |
$58.4451432$ |
$58.445143199977$ |
✓ |
✓ |
|
$C_8$ (as 8T1) |
$[2, 2, 82]$ |
$2$ |
$3$ |
$27.6959098582$ |
8.8.179359981764608.1 |
$x^{8} - 136 x^{6} + 5780 x^{4} - 78608 x^{2} + 167042$ |
$8$ |
[8,0] |
$2^{31}\cdot 17^{4}$ |
$2$ |
$60.494472468$ |
$60.49447246802112$ |
|
✓ |
? |
$C_8$ (as 8T1) |
$[2]$ |
$2$ |
$7$ |
$19415.8257216$ |
8.0.179359981764608.32 |
$x^{8} + 136 x^{6} + 5780 x^{4} + 78608 x^{2} + 167042$ |
$8$ |
[0,4] |
$2^{31}\cdot 17^{4}$ |
$2$ |
$60.494472468$ |
$60.49447246802112$ |
✓ |
✓ |
? |
$C_8$ (as 8T1) |
$[2, 2, 10, 10]$ |
$2$ |
$3$ |
$19.534360053$ |
8.8.235260548044817.1 |
$x^{8} - x^{7} - 49 x^{6} - 16 x^{5} + 511 x^{4} + 367 x^{3} - 1499 x^{2} - 798 x + 1372$ |
$8$ |
[8,0] |
$113^{7}$ |
$1$ |
$62.5811641949$ |
$62.58116419486453$ |
|
✓ |
|
$C_8$ (as 8T1) |
trivial |
$2$ |
$7$ |
$172951.810041$ |
8.8.252217127391488.1 |
$x^{8} - 119 x^{6} + 3332 x^{4} - 29155 x^{2} + 40817$ |
$8$ |
[8,0] |
$2^{8}\cdot 7^{4}\cdot 17^{7}$ |
$3$ |
$63.1279696934$ |
$63.127969693394384$ |
|
✓ |
|
$C_8$ (as 8T1) |
$[2]$ |
$2$ |
$7$ |
$31560.7919293$ |
8.8.279862216491008.1 |
$x^{8} - 152 x^{6} + 7220 x^{4} - 109744 x^{2} + 260642$ |
$8$ |
[8,0] |
$2^{31}\cdot 19^{4}$ |
$2$ |
$63.9540472824$ |
$63.954047282357884$ |
|
✓ |
? |
$C_8$ (as 8T1) |
trivial |
$2$ |
$7$ |
$54291.5640611$ |
8.0.279862216491008.16 |
$x^{8} + 152 x^{6} + 7220 x^{4} + 109744 x^{2} + 260642$ |
$8$ |
[0,4] |
$2^{31}\cdot 19^{4}$ |
$2$ |
$63.9540472824$ |
$63.954047282357884$ |
✓ |
✓ |
? |
$C_8$ (as 8T1) |
$[274]$ |
$2$ |
$3$ |
$19.534360053$ |