Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
8.0.1257728.1 |
x8 - 2x7 + 4x5 - 4x4 + 3x2 - 2x + 1 |
$8$ |
[0,4] |
$2^{8}\cdot 17^{3}$ |
$2$ |
$5.78693149384$ |
|
|
✓ |
$C_4\wr C_2$ (as 8T17) |
trivial |
$4$ |
$3$ |
$0.618886617067$ |
8.0.1265625.1 |
x8 - x7 + x5 - x4 + x3 - x + 1 |
$8$ |
[0,4] |
$3^{4}\cdot 5^{6}$ |
$2$ |
$5.79146092644$ |
✓ |
✓ |
✓ |
$C_4\times C_2$ (as 8T2) |
trivial |
$30$ |
$3$ |
$4.6618207773$ |
8.0.1282789.1 |
x8 - x7 + 2x6 - 3x5 + 3x4 - 3x3 + 3x2 - 2x + 1 |
$8$ |
[0,4] |
$1103\cdot 1163$ |
$2$ |
$5.80122090621$ |
|
|
✓ |
$S_8$ (as 8T50) |
trivial |
$2$ |
$3$ |
$0.313539838403$ |
8.0.1327833.1 |
x8 - x7 + x6 - 2x5 + 3x4 - 4x3 + 4x2 - 2x + 1 |
$8$ |
[0,4] |
$3^{4}\cdot 13^{2}\cdot 97$ |
$3$ |
$5.82630119728$ |
|
|
✓ |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$6$ |
$3$ |
$0.963083858701$ |
8.0.1342413.1 |
x8 - x7 + x6 + x4 - 2x3 + 3x2 - 3x + 1 |
$8$ |
[0,4] |
$3^{4}\cdot 16573$ |
$2$ |
$5.83425985742$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$0.970727427757$ |
8.0.1361513.1 |
x8 - x7 + 2x6 - 3x5 + 3x4 - 3x3 + 2x2 - x + 1 |
$8$ |
[0,4] |
$17\cdot 283^{2}$ |
$2$ |
$5.84457214701$ |
|
|
✓ |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$2$ |
$3$ |
$0.32641205382$ |
8.0.1385533.1 |
x8 - 2x7 + 3x6 - 3x5 + x4 + 1 |
$8$ |
[0,4] |
$29\cdot 47777$ |
$2$ |
$5.85736259192$ |
|
|
✓ |
$S_8$ (as 8T50) |
trivial |
$2$ |
$3$ |
$0.331112529152$ |
8.0.1424293.1 |
x8 - 2x7 + 2x6 - x5 + x4 - x3 + 2x2 - 2x + 1 |
$8$ |
[0,4] |
$13\cdot 331^{2}$ |
$2$ |
$5.87759852004$ |
|
|
✓ |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$2$ |
$3$ |
$0.336709575883$ |
8.0.1474013.1 |
x8 - x7 + x6 - x4 + x3 - x2 + 1 |
$8$ |
[0,4] |
$617\cdot 2389$ |
$2$ |
$5.90286246256$ |
|
|
✓ |
$S_8$ (as 8T50) |
trivial |
$2$ |
$3$ |
$0.345105135911$ |
8.0.1492101.1 |
x8 - x7 + x6 - 3x5 + x4 - 2x3 + 3x2 + 1 |
$8$ |
[0,4] |
$3^{4}\cdot 13^{2}\cdot 109$ |
$3$ |
$5.91186866834$ |
|
|
✓ |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$6$ |
$3$ |
$1.04325557006$ |
8.0.1513728.1 |
x8 - 2x7 + x6 + 2x5 - 3x4 - 2x3 + x2 + 2x + 1 |
$8$ |
[0,4] |
$2^{8}\cdot 3^{4}\cdot 73$ |
$3$ |
$5.92251242534$ |
|
|
✓ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
trivial |
$12$ |
$3$ |
$2.10694405423$ |
8.0.1520789.1 |
x8 - x7 - x6 + x4 - x2 + x + 1 |
$8$ |
[0,4] |
$29\cdot 229^{2}$ |
$2$ |
$5.9259586988$ |
|
|
✓ |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$2$ |
$3$ |
$0.353845256559$ |
8.0.1578125.1 |
x8 - 2x7 + 3x5 - x4 - 3x3 + 2x + 1 |
$8$ |
[0,4] |
$5^{6}\cdot 101$ |
$2$ |
$5.95343580388$ |
|
|
✓ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
trivial |
$10$ |
$3$ |
$1.81195906066$ |
8.0.1590773.1 |
x8 - x7 + 2x5 - 2x4 + x3 + x2 - 2x + 1 |
$8$ |
[0,4] |
$179\cdot 8887$ |
$2$ |
$5.95937927669$ |
|
|
✓ |
$S_8$ (as 8T50) |
trivial |
$2$ |
$3$ |
$0.363609073488$ |
8.0.1601613.1 |
x8 - 2x6 - 3x5 + 3x4 + 3x3 - 2x2 + 1 |
$8$ |
[0,4] |
$3^{6}\cdot 13^{3}$ |
$2$ |
$5.9644403303$ |
|
|
✓ |
$C_4\wr C_2$ (as 8T17) |
trivial |
$6$ |
$3$ |
$1.10095849199$ |
8.0.1740113.1 |
x8 - 2x7 + 3x6 - 4x5 + 4x4 - 4x3 + 3x2 - x + 1 |
$8$ |
[0,4] |
$1740113$ |
$1$ |
$6.0265974216$ |
|
|
✓ |
$S_8$ (as 8T50) |
trivial |
$2$ |
$3$ |
$0.38876666774366264$ |
8.0.1750329.1 |
x8 - 3x7 + 4x6 - 3x5 + 3x4 - 3x3 + 4x2 - 3x + 1 |
$8$ |
[0,4] |
$3^{6}\cdot 7^{4}$ |
$2$ |
$6.03100878452$ |
|
✓ |
not computed |
$D_4$ (as 8T4) |
trivial |
$6$ |
$3$ |
$1.1656993933$ |
8.0.1763584.1 |
x8 - 2x7 + x6 + 2x5 - 3x4 + 2x3 + x2 - 2x + 1 |
$8$ |
[0,4] |
$2^{8}\cdot 83^{2}$ |
$2$ |
$6.03669895858$ |
|
|
✓ |
$S_4\times C_2$ (as 8T24) |
trivial |
$4$ |
$3$ |
$0.781195313952$ |
8.0.1797309.1 |
x8 - 3x7 + 6x6 - 8x5 + 10x4 - 9x3 + 7x2 - 4x + 1 |
$8$ |
[0,4] |
$3^{4}\cdot 22189$ |
$2$ |
$6.05100962346$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$1.20014144807$ |
8.0.1820637.1 |
x8 - x7 + x5 - x4 - 2x3 + 2x + 1 |
$8$ |
[0,4] |
$3^{4}\cdot 7\cdot 13^{2}\cdot 19$ |
$4$ |
$6.06077163648$ |
|
|
✓ |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$6$ |
$3$ |
$1.21081359453$ |
8.0.1867553.1 |
x8 - x7 + x5 - 2x4 + x3 + x2 - x + 1 |
$8$ |
[0,4] |
$1867553$ |
$1$ |
$6.08007752654$ |
|
|
✓ |
$S_8$ (as 8T50) |
trivial |
$2$ |
$3$ |
$0.40885972396034426$ |
8.0.1890625.1 |
x8 - 3x7 + 6x6 - 9x5 + 9x4 - 7x3 + 4x2 - x + 1 |
$8$ |
[0,4] |
$5^{6}\cdot 11^{2}$ |
$2$ |
$6.08941642815$ |
|
|
✓ |
$C_2^2:C_4$ (as 8T10) |
trivial |
$10$ |
$3$ |
$2.04169489066$ |
8.0.2067245.1 |
x8 - x7 + x6 - x4 + x2 - x + 1 |
$8$ |
[0,4] |
$5\cdot 643^{2}$ |
$2$ |
$6.15777751924$ |
|
|
✓ |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$2$ |
$3$ |
$0.453534943932$ |
8.0.2105893.1 |
x8 - x7 + 2x6 - x5 + x4 - x3 + x2 - 2x + 1 |
$8$ |
[0,4] |
$29\cdot 72617$ |
$2$ |
$6.17205144936$ |
|
|
✓ |
$S_8$ (as 8T50) |
trivial |
$2$ |
$3$ |
$0.44069755405256955$ |
8.0.2118069.1 |
x8 - x7 - x3 + 2x2 - x + 1 |
$8$ |
[0,4] |
$3^{4}\cdot 79\cdot 331$ |
$3$ |
$6.17650095624$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$1.33864883478$ |
8.0.2149173.1 |
x8 - x7 - 2x6 + 2x5 + x3 + x2 - 2x + 1 |
$8$ |
[0,4] |
$3^{4}\cdot 13^{2}\cdot 157$ |
$3$ |
$6.18776657236$ |
|
|
✓ |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$6$ |
$3$ |
$1.34468819349$ |
8.0.2178981.1 |
x8 - x7 - x6 + 2x5 + x4 - 2x3 - x2 + x + 1 |
$8$ |
[0,4] |
$3^{6}\cdot 7^{2}\cdot 61$ |
$3$ |
$6.19842970625$ |
|
|
✓ |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$6$ |
$3$ |
$1.34805397566$ |
8.0.2193125.1 |
x8 - 2x7 + 4x6 - 5x5 + 5x4 - 5x3 + 4x2 - 2x + 1 |
$8$ |
[0,4] |
$5^{4}\cdot 11^{2}\cdot 29$ |
$3$ |
$6.20344481555$ |
|
|
✓ |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$2$ |
$3$ |
$0.454073872008$ |
8.0.2217213.1 |
x8 - x7 - x6 - x5 + 3x4 - x + 1 |
$8$ |
[0,4] |
$3^{4}\cdot 31\cdot 883$ |
$3$ |
$6.21192104402$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$1.37910404568$ |
8.0.2313441.1 |
x8 - x7 + 2x6 + 3x5 - x4 + 3x3 + 2x2 - x + 1 |
$8$ |
[0,4] |
$3^{4}\cdot 13^{4}$ |
$2$ |
$6.2449979984$ |
|
✓ |
not computed |
$D_4$ (as 8T4) |
trivial |
$6$ |
$3$ |
$1.41187738145$ |
8.0.2314413.1 |
x8 - x6 - x5 - x3 + 2x + 1 |
$8$ |
[0,4] |
$3^{4}\cdot 28573$ |
$2$ |
$6.24532592023$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$1.42029894182$ |
8.0.2477709.1 |
x8 - x7 + 3x5 - x3 + 2x2 + 2x + 1 |
$8$ |
[0,4] |
$3^{4}\cdot 13^{2}\cdot 181$ |
$3$ |
$6.2987777876$ |
|
|
✓ |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$6$ |
$3$ |
$1.51551812359$ |
8.0.2560000.1 |
x8 - 2x7 + 2x6 + 2x5 - 2x4 + 2x3 + 2x2 - 2x + 1 |
$8$ |
[0,4] |
$2^{12}\cdot 5^{4}$ |
$2$ |
$6.32455532034$ |
|
✓ |
not computed |
$D_4$ (as 8T4) |
trivial |
$4$ |
$3$ |
$1.0839823354$ |
8.0.2671805.1 |
x8 - x5 + x4 - x3 + 1 |
$8$ |
[0,4] |
$5\cdot 17^{2}\cdot 43^{2}$ |
$3$ |
$6.35844025272$ |
|
|
✓ |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$2$ |
$3$ |
$0.542256876594$ |
8.0.2708009.1 |
x8 - x7 - x6 + x5 + x4 - x3 - x2 + x + 1 |
$8$ |
[0,4] |
$41\cdot 257^{2}$ |
$2$ |
$6.36914685919$ |
|
|
✓ |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$2$ |
$3$ |
$0.563263410972$ |
8.0.2712933.1 |
x8 - 3x7 + 3x6 - x5 + x4 - 2x2 + x + 1 |
$8$ |
[0,4] |
$3^{4}\cdot 33493$ |
$2$ |
$6.37059334437$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$1.57666375612$ |
8.0.2824713.1 |
x8 - 3x7 + 2x6 + 3x5 - 4x4 + x2 + 1 |
$8$ |
[0,4] |
$3^{4}\cdot 43\cdot 811$ |
$3$ |
$6.40282734558$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$1.7400253268$ |
8.0.2828125.1 |
x8 - x7 - x6 - 2x5 + 4x4 + x3 + x2 - 3x + 1 |
$8$ |
[0,4] |
$5^{6}\cdot 181$ |
$2$ |
$6.40379359023$ |
|
|
✓ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
trivial |
$10$ |
$3$ |
$2.66425859071$ |
8.0.2844928.1 |
x8 - 2x7 + 2x6 - 2x4 + 2x3 + x2 - 2x + 1 |
$8$ |
[0,4] |
$2^{8}\cdot 11113$ |
$2$ |
$6.40853720479$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$4$ |
$3$ |
$1.11974748455$ |
8.0.2963293.1 |
x8 - 3x7 + 5x6 - 6x5 + 7x4 - 6x3 + 5x2 - 3x + 1 |
$8$ |
[0,4] |
$37\cdot 283^{2}$ |
$2$ |
$6.44127475268$ |
|
|
✓ |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$2$ |
$3$ |
$0.545793348928$ |
8.0.2970513.1 |
x8 - 2x7 + 2x6 - 2x5 + 3x4 - 3x2 + x + 1 |
$8$ |
[0,4] |
$3^{4}\cdot 7\cdot 13^{2}\cdot 31$ |
$4$ |
$6.44323441823$ |
|
|
✓ |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$6$ |
$3$ |
$1.66725651269$ |
8.0.2985984.1 |
x8 - 2x7 + 2x6 - 2x5 + 7x4 - 10x3 + 8x2 - 4x + 1 |
$8$ |
[0,4] |
$2^{12}\cdot 3^{6}$ |
$2$ |
$6.44741959094$ |
|
✓ |
not computed |
$D_4$ (as 8T4) |
trivial |
$12$ |
$3$ |
$3.64163813098$ |
8.0.3057993.1 |
x8 - 2x7 + 3x6 - 2x5 + x3 + 2x2 - 3x + 1 |
$8$ |
[0,4] |
$3^{4}\cdot 19\cdot 1987$ |
$3$ |
$6.46665305207$ |
|
|
not computed |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$1.83028307754$ |
8.0.3134053.1 |
x8 - x7 + x6 - 2x5 + 3x4 - 2x3 + x2 - x + 1 |
$8$ |
[0,4] |
$13\cdot 491^{2}$ |
$2$ |
$6.48654286035$ |
|
|
✓ |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$2$ |
$3$ |
$0.570147165225$ |
8.0.3167829.1 |
x8 - 3x7 + 4x6 - 4x4 + 3x3 + 2x2 - 3x + 1 |
$8$ |
[0,4] |
$3^{4}\cdot 7\cdot 37\cdot 151$ |
$4$ |
$6.49524019945$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$1.77871765724$ |
8.0.3198933.1 |
x8 - x7 - x6 + 4x4 - x3 - 3x2 + x + 1 |
$8$ |
[0,4] |
$3^{4}\cdot 73\cdot 541$ |
$3$ |
$6.50317802496$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$2.04684730841$ |
8.0.3203125.1 |
x8 - x7 + 2x6 + 2x5 + 3x3 + 2x2 + x + 1 |
$8$ |
[0,4] |
$5^{7}\cdot 41$ |
$2$ |
$6.50424266534$ |
|
|
✓ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
trivial |
$10$ |
$3$ |
$3.04388544877$ |
8.0.3207681.1 |
x8 - 3x7 + 4x6 - 3x5 + 2x4 - x2 + 1 |
$8$ |
[0,4] |
$3^{4}\cdot 199^{2}$ |
$2$ |
$6.50539836897$ |
|
|
✓ |
$S_4\times C_2$ (as 8T24) |
trivial |
$6$ |
$3$ |
$1.89392987116$ |
8.0.3211264.1 |
x8 - 4x7 + 8x6 - 8x5 + 7x4 - 8x3 + 8x2 - 4x + 1 |
$8$ |
[0,4] |
$2^{16}\cdot 7^{2}$ |
$2$ |
$6.50630624679$ |
|
|
not computed |
$D_4\times C_2$ (as 8T9) |
trivial |
$8$ |
$3$ |
$2.5180422861$ |
8.0.3240000.1 |
x8 - 3x7 + 3x6 + x5 - 2x4 - 3x3 + 7x2 - 4x + 1 |
$8$ |
[0,4] |
$2^{6}\cdot 3^{4}\cdot 5^{4}$ |
$3$ |
$6.51355562433$ |
|
|
✓ |
$Q_8:C_2$ (as 8T11) |
trivial |
$6$ |
$3$ |
$1.89812936734$ |