| 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 |
| 8.0.13619760968.1 |
$x^{8} - 2 x^{7} + 4 x^{6} + 4 x^{5} + 17 x^{4} + 8 x^{3} + 5 x^{2} - 16 x + 5$ |
$8$ |
[0,4] |
$2^{3}\cdot 11^{6}\cdot 31^{2}$ |
$3$ |
$18.4829456181$ |
$95.11967424297421$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[2]$ |
$2$ |
$3$ |
$75.4419799835$ |
| 8.4.13619760968.1 |
$x^{8} - 3 x^{7} - 2 x^{6} + 8 x^{5} - 15 x^{4} + 3 x^{3} + 31 x^{2} + 58 x - 10$ |
$8$ |
[4,2] |
$2^{3}\cdot 11^{6}\cdot 31^{2}$ |
$3$ |
$18.4829456181$ |
$95.11967424297421$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$2$ |
$5$ |
$268.961507773$ |
| 8.4.22132111573.1 |
$x^{8} - 7 x^{6} - 11 x^{5} + 17 x^{4} + 11 x^{3} - 7 x^{2} + 1$ |
$8$ |
[4,2] |
$11^{6}\cdot 13\cdot 31^{2}$ |
$3$ |
$19.6393837551$ |
$121.25426877287862$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$2$ |
$5$ |
$247.882240279$ |
| 8.0.117915100160.1 |
$x^{8} + 12 x^{6} - 22 x^{5} + 32 x^{4} - 88 x^{3} + 130 x^{2} + 44 x + 4$ |
$8$ |
[0,4] |
$2^{10}\cdot 5\cdot 11^{6}\cdot 13$ |
$4$ |
$24.20729028$ |
$122.70846396322771$ |
|
|
? |
$S_4\wr C_2$ (as 8T47) |
$[2]$ |
$4$ |
$3$ |
$856.242778455$ |
| 8.4.871664701952.1 |
$x^{8} - 3 x^{7} + 7 x^{6} + 18 x^{5} - 37 x^{4} - 115 x^{3} - 86 x^{2} + 347 x - 41$ |
$8$ |
[4,2] |
$2^{9}\cdot 11^{6}\cdot 31^{2}$ |
$3$ |
$31.0844854272$ |
$95.11967424297421$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$2$ |
$5$ |
$1613.70431474$ |
| 8.0.871664701952.1 |
$x^{8} + 11 x^{6} + 88 x^{4} + 484 x^{2} + 968$ |
$8$ |
[0,4] |
$2^{9}\cdot 11^{6}\cdot 31^{2}$ |
$3$ |
$31.0844854272$ |
$95.11967424297421$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[2]$ |
$2$ |
$3$ |
$437.776659637$ |
| 8.0.1328920540101.1 |
$x^{8} - 3 x^{7} + 42 x^{5} - 12 x^{4} - 87 x^{3} + 264 x^{2} + 483 x + 273$ |
$8$ |
[0,4] |
$3^{7}\cdot 7^{3}\cdot 11^{6}$ |
$3$ |
$32.7670524831$ |
$41.79021752801406$ |
|
|
? |
$Z_8 : Z_8^\times$ (as 8T15) |
$[4]$ |
$6$ |
$3$ |
$586.574369078$ |
| 8.0.1328920540101.2 |
$x^{8} - 2 x^{7} - 14 x^{6} + 31 x^{5} + 61 x^{4} - 149 x^{3} - 71 x^{2} + 397 x + 433$ |
$8$ |
[0,4] |
$3^{7}\cdot 7^{3}\cdot 11^{6}$ |
$3$ |
$32.7670524831$ |
$41.79021752801406$ |
|
|
? |
$Z_8 : Z_8^\times$ (as 8T15) |
$[4]$ |
$6$ |
$3$ |
$586.574369078$ |
| 8.4.1973717368832.1 |
$x^{8} - 4 x^{7} - 10 x^{6} + 44 x^{5} + 16 x^{4} - 44 x^{3} - 50 x^{2} - 668 x + 1103$ |
$8$ |
[4,2] |
$2^{16}\cdot 11^{6}\cdot 17$ |
$3$ |
$34.4279069391$ |
$118.46401965741202$ |
|
|
? |
$S_4\wr C_2$ (as 8T47) |
trivial |
$2$ |
$5$ |
$1728.81982132$ |
| 8.0.2093900067072.1 |
$x^{8} - 2 x^{7} + 8 x^{6} + 20 x^{5} - 71 x^{4} + 60 x^{3} - 192 x^{2} - 450 x + 1533$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{5}\cdot 11^{6}\cdot 19$ |
$4$ |
$34.6832266406$ |
$146.92397393927368$ |
|
|
? |
$S_4\wr C_2$ (as 8T47) |
$[4]$ |
$6$ |
$3$ |
$1549.28330307$ |
| 8.2.2450026345536.1 |
$x^{8} - x^{7} + 12 x^{6} - 27 x^{5} + 32 x^{4} - 19 x^{3} - 85 x^{2} + 92 x + 86$ |
$8$ |
[2,3] |
$-\,2^{6}\cdot 3^{2}\cdot 7^{4}\cdot 11^{6}$ |
$4$ |
$35.3709190482$ |
$96.46664224648953$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$2$ |
$4$ |
$3062.70507285$ |
| 8.2.2450026345536.2 |
$x^{8} - x^{7} - 11 x^{6} + 37 x^{5} + 30 x^{4} - 120 x^{3} + 336 x + 224$ |
$8$ |
[2,3] |
$-\,2^{6}\cdot 3^{2}\cdot 7^{4}\cdot 11^{6}$ |
$4$ |
$35.3709190482$ |
$96.46664224648953$ |
|
|
|
$C_2 \wr S_4$ (as 8T44) |
trivial |
$2$ |
$4$ |
$6703.6498935$ |
| 8.0.2452634083328.1 |
$x^{8} - 4 x^{7} - x^{6} - 16 x^{5} + 162 x^{4} - 412 x^{3} + 1011 x^{2} - 2028 x + 1937$ |
$8$ |
[0,4] |
$2^{13}\cdot 11^{6}\cdot 13^{2}$ |
$3$ |
$35.3756228323$ |
$146.503728679348$ |
|
|
? |
$S_4\wr C_2$ (as 8T47) |
$[2]$ |
$4$ |
$3$ |
$3011.61318621$ |
| 8.0.2837355127893.1 |
$x^{8} - 2 x^{7} - x^{6} + 28 x^{5} - 50 x^{4} - x^{3} + 557 x^{2} - 688 x + 247$ |
$8$ |
[0,4] |
$3^{6}\cdot 11^{6}\cdot 13^{3}$ |
$3$ |
$36.0258479759$ |
$49.642898539114476$ |
|
|
? |
$Z_8 : Z_8^\times$ (as 8T15) |
$[4]$ |
$6$ |
$3$ |
$637.290261154$ |
| 8.0.2837355127893.2 |
$x^{8} - 2 x^{7} - 14 x^{6} + 31 x^{5} + 127 x^{4} - 281 x^{3} - 797 x^{2} + 793 x + 2743$ |
$8$ |
[0,4] |
$3^{6}\cdot 11^{6}\cdot 13^{3}$ |
$3$ |
$36.0258479759$ |
$49.642898539114476$ |
|
|
? |
$Z_8 : Z_8^\times$ (as 8T15) |
$[4]$ |
$6$ |
$3$ |
$637.290261154$ |
| 8.0.2837355127893.3 |
$x^{8} - 35 x^{6} - 99 x^{5} + 315 x^{4} + 1914 x^{3} + 3382 x^{2} + 2442 x + 691$ |
$8$ |
[0,4] |
$3^{6}\cdot 11^{6}\cdot 13^{3}$ |
$3$ |
$36.0258479759$ |
$94.2633715237378$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
$[4]$ |
$6$ |
$3$ |
$643.51984901$ |
| 8.0.2837355127893.4 |
$x^{8} - x^{7} - 31 x^{6} + 74 x^{5} + 109 x^{4} - 434 x^{3} + 2615 x^{2} - 10607 x + 14371$ |
$8$ |
[0,4] |
$3^{6}\cdot 11^{6}\cdot 13^{3}$ |
$3$ |
$36.0258479759$ |
$94.2633715237378$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
$[4]$ |
$6$ |
$3$ |
$540.28701387$ |
| 8.0.4194149408768.1 |
$x^{8} - 2 x^{7} - 11 x^{6} + 54 x^{5} + 62 x^{4} - 144 x^{3} + 154 x^{2} - 68 x + 1156$ |
$8$ |
[0,4] |
$2^{13}\cdot 11^{6}\cdot 17^{2}$ |
$3$ |
$37.8294900693$ |
$167.53342325274502$ |
|
|
|
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2]$ |
$4$ |
$3$ |
$8428.99813202$ |
| 8.0.4194149408768.2 |
$x^{8} - 2 x^{7} + 11 x^{6} + 10 x^{5} - 59 x^{4} - 100 x^{3} + 352 x^{2} - 288 x + 100$ |
$8$ |
[0,4] |
$2^{13}\cdot 11^{6}\cdot 17^{2}$ |
$3$ |
$37.8294900693$ |
$167.53342325274502$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2]$ |
$4$ |
$3$ |
$3269.16319087$ |
| 8.4.4734801480992.1 |
$x^{8} - x^{7} - 13 x^{6} + 11 x^{5} + 9 x^{4} - 55 x^{3} + 37 x^{2} + 93 x - 18$ |
$8$ |
[4,2] |
$2^{5}\cdot 11^{6}\cdot 17^{4}$ |
$3$ |
$38.4072066237$ |
$99.61596946646334$ |
|
|
|
$S_4\wr C_2$ (as 8T47) |
trivial |
$2$ |
$5$ |
$33696.4956356$ |
| 8.4.5919913785357.1 |
$x^{8} - 3 x^{7} + 10 x^{6} - 63 x^{5} + 180 x^{4} - 236 x^{3} - 70 x^{2} + 207 x + 27$ |
$8$ |
[4,2] |
$3^{2}\cdot 11^{6}\cdot 13^{5}$ |
$3$ |
$39.4947548775$ |
$71.62467353357012$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
trivial |
$2$ |
$5$ |
$5314.08086922$ |
| 8.0.5919913785357.1 |
$x^{8} - x^{7} + 12 x^{6} + 6 x^{5} - x^{4} + 3 x^{3} - 217 x^{2} + 15 x + 471$ |
$8$ |
[0,4] |
$3^{2}\cdot 11^{6}\cdot 13^{5}$ |
$3$ |
$39.4947548775$ |
$71.62467353357012$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$[2]$ |
$2$ |
$3$ |
$1177.66564448$ |
| 8.2.9469602961984.1 |
$x^{8} + 11 x^{4} - 484$ |
$8$ |
[2,3] |
$-\,2^{6}\cdot 11^{6}\cdot 17^{4}$ |
$3$ |
$41.8833558132$ |
$49.80798473323167$ |
|
|
|
$Z_8 : Z_8^\times$ (as 8T15) |
trivial |
$2$ |
$4$ |
$17615.6196768$ |
| 8.2.9469602961984.2 |
$x^{8} - x^{7} + 9 x^{6} - 11 x^{5} - 13 x^{4} - 77 x^{3} - 238 x^{2} + 412 x + 664$ |
$8$ |
[2,3] |
$-\,2^{6}\cdot 11^{6}\cdot 17^{4}$ |
$3$ |
$41.8833558132$ |
$49.80798473323167$ |
|
|
|
$Z_8 : Z_8^\times$ (as 8T15) |
trivial |
$2$ |
$4$ |
$17615.6196768$ |
| 8.2.9800105382144.1 |
$x^{8} - x^{7} - 2 x^{6} + 22 x^{5} - 112 x^{4} + 330 x^{3} - 546 x^{2} + 522 x - 216$ |
$8$ |
[2,3] |
$-\,2^{8}\cdot 3^{2}\cdot 7^{4}\cdot 11^{6}$ |
$4$ |
$42.0633485963$ |
$96.46664224648953$ |
|
|
|
$C_2 \wr S_4$ (as 8T44) |
trivial |
$2$ |
$4$ |
$28328.5018509$ |
| 8.2.9800105382144.2 |
$x^{8} - 22 x^{6} + 88 x^{4} + 726 x^{2} - 121$ |
$8$ |
[2,3] |
$-\,2^{8}\cdot 3^{2}\cdot 7^{4}\cdot 11^{6}$ |
$4$ |
$42.0633485963$ |
$96.46664224648953$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$2$ |
$4$ |
$9334.67879211$ |
| 8.4.10653303332232.1 |
$x^{8} - 2 x^{7} - x^{6} + 6 x^{5} - 50 x^{4} + 43 x^{3} + 51 x^{2} - 94 x + 38$ |
$8$ |
[4,2] |
$2^{3}\cdot 3^{2}\cdot 11^{6}\cdot 17^{4}$ |
$4$ |
$42.5045611566$ |
$122.0041477127521$ |
|
|
? |
$S_4\wr C_2$ (as 8T47) |
trivial |
$2$ |
$5$ |
$16566.9290265$ |
| 8.0.11791510016000.1 |
$x^{8} - 2 x^{7} + 2 x^{6} - 26 x^{5} + 38 x^{4} - 72 x^{3} + 494 x^{2} - 840 x + 410$ |
$8$ |
[0,4] |
$2^{12}\cdot 5^{3}\cdot 11^{6}\cdot 13$ |
$4$ |
$43.0473258778$ |
$145.9257784161254$ |
|
|
? |
$S_4\wr C_2$ (as 8T47) |
$[4]$ |
$4$ |
$3$ |
$2806.83870103$ |
| 8.2.12295205554203.1 |
$x^{8} - 3 x^{7} - 23 x^{6} + 91 x^{5} + 92 x^{4} - 621 x^{3} + 645 x^{2} - 112 x + 269$ |
$8$ |
[2,3] |
$-\,3^{5}\cdot 11^{6}\cdot 13^{4}$ |
$3$ |
$43.2729969628$ |
$78.46168920922729$ |
|
|
|
$S_4\wr C_2$ (as 8T47) |
$[2]$ |
$2$ |
$4$ |
$3110.02859522$ |
| 8.4.13088590290248.1 |
$x^{8} - 4 x^{7} - 33 x^{6} + 102 x^{5} + 409 x^{4} - 934 x^{3} - 2288 x^{2} + 4958 x - 437$ |
$8$ |
[4,2] |
$2^{3}\cdot 11^{6}\cdot 31^{4}$ |
$3$ |
$43.6125629346$ |
$95.11967424297421$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[2]$ |
$2$ |
$5$ |
$4262.55698919$ |
| 8.0.13088590290248.1 |
$x^{8} + 20 x^{6} - 44 x^{5} + 260 x^{4} - 781 x^{3} + 1743 x^{2} - 2838 x + 2990$ |
$8$ |
[0,4] |
$2^{3}\cdot 11^{6}\cdot 31^{4}$ |
$3$ |
$43.6125629346$ |
$95.11967424297421$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[2, 8]$ |
$2$ |
$3$ |
$281.975105268$ |
| 8.0.15447822362973.1 |
$x^{8} - x^{7} - 20 x^{6} + 85 x^{5} - 12 x^{4} - 742 x^{3} + 2164 x^{2} - 2621 x + 1237$ |
$8$ |
[0,4] |
$3^{4}\cdot 7^{2}\cdot 11^{6}\cdot 13^{3}$ |
$4$ |
$44.5254593253$ |
$99.79891905946309$ |
|
|
? |
$Z_8 : Z_8^\times$ (as 8T15) |
$[4]$ |
$6$ |
$3$ |
$1693.46113145$ |
| 8.0.15447822362973.2 |
$x^{8} - 2 x^{7} - 12 x^{6} + 39 x^{5} + 93 x^{4} - 881 x^{3} + 2438 x^{2} - 3086 x + 1501$ |
$8$ |
[0,4] |
$3^{4}\cdot 7^{2}\cdot 11^{6}\cdot 13^{3}$ |
$4$ |
$44.5254593253$ |
$99.79891905946309$ |
|
|
? |
$Z_8 : Z_8^\times$ (as 8T15) |
$[4]$ |
$6$ |
$3$ |
$1047.04274549$ |
| 8.0.15447822362973.3 |
$x^{8} - 4 x^{7} - 15 x^{6} + 59 x^{5} + 201 x^{4} - 505 x^{3} - 2566 x^{2} + 2829 x + 14029$ |
$8$ |
[0,4] |
$3^{4}\cdot 7^{2}\cdot 11^{6}\cdot 13^{3}$ |
$4$ |
$44.5254593253$ |
$99.79891905946309$ |
|
|
? |
$Z_8 : Z_8^\times$ (as 8T15) |
$[4]$ |
$6$ |
$3$ |
$1047.04274549$ |
| 8.0.15447822362973.4 |
$x^{8} - 2 x^{7} - 25 x^{6} + 31 x^{5} + 402 x^{4} - 204 x^{3} - 3624 x^{2} + 1189 x + 15349$ |
$8$ |
[0,4] |
$3^{4}\cdot 7^{2}\cdot 11^{6}\cdot 13^{3}$ |
$4$ |
$44.5254593253$ |
$99.79891905946309$ |
|
|
? |
$Z_8 : Z_8^\times$ (as 8T15) |
$[4]$ |
$6$ |
$3$ |
$1693.46113145$ |
| 8.0.16776597635072.1 |
$x^{8} - 22 x^{6} + 77 x^{4} + 484 x^{2} + 968$ |
$8$ |
[0,4] |
$2^{15}\cdot 11^{6}\cdot 17^{2}$ |
$3$ |
$44.9870987474$ |
$182.69649353699992$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2]$ |
$4$ |
$3$ |
$5979.55463826$ |
| 8.0.16776597635072.2 |
$x^{8} - 22 x^{6} + 154 x^{4} + 1936 x^{2} + 3872$ |
$8$ |
[0,4] |
$2^{15}\cdot 11^{6}\cdot 17^{2}$ |
$3$ |
$44.9870987474$ |
$182.69649353699992$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2]$ |
$4$ |
$3$ |
$5046.06004563$ |
| 8.0.19372019535000.1 |
$x^{8} - x^{7} - 11 x^{6} + 26 x^{5} + 52 x^{4} - 175 x^{3} - 176 x^{2} + 380 x + 400$ |
$8$ |
[0,4] |
$2^{3}\cdot 3^{7}\cdot 5^{4}\cdot 11^{6}$ |
$4$ |
$45.8033098561$ |
$141.8957348747347$ |
|
|
|
$S_4\wr C_2$ (as 8T47) |
$[2, 4]$ |
$2$ |
$3$ |
$7075.35546847$ |
| 8.2.22050237109824.1 |
$x^{8} - 2 x^{7} - 18 x^{6} + 48 x^{5} + 160 x^{4} - 432 x^{3} - 336 x^{2} + 1568 x - 1568$ |
$8$ |
[2,3] |
$-\,2^{6}\cdot 3^{4}\cdot 7^{4}\cdot 11^{6}$ |
$4$ |
$46.5507473736$ |
$96.46664224648953$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[2]$ |
$2$ |
$4$ |
$6947.81449575$ |
| 8.2.22050237109824.2 |
$x^{8} - 2 x^{7} - 3 x^{6} - 24 x^{5} + 127 x^{4} + 324 x^{3} - 1083 x^{2} + 782 x + 1126$ |
$8$ |
[2,3] |
$-\,2^{6}\cdot 3^{4}\cdot 7^{4}\cdot 11^{6}$ |
$4$ |
$46.5507473736$ |
$96.46664224648953$ |
|
|
|
$C_2 \wr S_4$ (as 8T44) |
$[2]$ |
$2$ |
$4$ |
$27394.8441834$ |
| 8.2.22755800252416.1 |
$x^{8} + 16 x^{6} - 44 x^{5} - 25 x^{4} + 44 x^{3} - 404 x^{2} + 528 x + 1422$ |
$8$ |
[2,3] |
$-\,2^{18}\cdot 7^{2}\cdot 11^{6}$ |
$3$ |
$46.7343830781$ |
$148.68792313236614$ |
|
|
? |
$S_4\wr C_2$ (as 8T47) |
trivial |
$2$ |
$4$ |
$19138.5736958$ |
| 8.2.25652959736547.1 |
$x^{8} - 2 x^{7} + 26 x^{6} - 73 x^{5} + 248 x^{4} - 751 x^{3} + 676 x^{2} - 2909 x - 3273$ |
$8$ |
[2,3] |
$-\,3\cdot 11^{6}\cdot 13^{6}$ |
$3$ |
$47.4397274148$ |
$71.62467353357012$ |
|
|
|
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
trivial |
$2$ |
$4$ |
$19063.1203376$ |
| 8.6.25652959736547.1 |
$x^{8} - 2 x^{7} - 18 x^{6} - 7 x^{5} + 61 x^{4} + 195 x^{3} + 247 x^{2} + 39 x - 39$ |
$8$ |
[6,1] |
$-\,3\cdot 11^{6}\cdot 13^{6}$ |
$3$ |
$47.4397274148$ |
$71.62467353357012$ |
|
|
|
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
trivial |
$2$ |
$6$ |
$43010.0697803$ |
| 8.0.26574536398113.1 |
$x^{8} - x^{7} - 20 x^{6} + 107 x^{5} - 56 x^{4} - 973 x^{3} + 3715 x^{2} - 7120 x + 5824$ |
$8$ |
[0,4] |
$3^{7}\cdot 11^{6}\cdot 19^{3}$ |
$3$ |
$47.6494851098$ |
$68.84975706953298$ |
|
|
|
$Z_8 : Z_8^\times$ (as 8T15) |
$[4]$ |
$6$ |
$3$ |
$9711.7638788$ |
| 8.0.26574536398113.2 |
$x^{8} - 4 x^{7} + 40 x^{6} - 106 x^{5} + 586 x^{4} - 1000 x^{3} + 3781 x^{2} - 3298 x + 12676$ |
$8$ |
[0,4] |
$3^{7}\cdot 11^{6}\cdot 19^{3}$ |
$3$ |
$47.6494851098$ |
$68.84975706953298$ |
|
|
|
$Z_8 : Z_8^\times$ (as 8T15) |
$[4]$ |
$6$ |
$3$ |
$9711.7638788$ |
| 8.0.33223013502525.1 |
$x^{8} - 2 x^{7} + 10 x^{6} + 6 x^{5} + 93 x^{4} + 615 x^{3} - 48 x^{2} - 2745 x + 2271$ |
$8$ |
[0,4] |
$3^{7}\cdot 5^{2}\cdot 7^{3}\cdot 11^{6}$ |
$4$ |
$48.9981719949$ |
$132.73130613644196$ |
|
|
? |
$S_4\wr C_2$ (as 8T47) |
$[4]$ |
$6$ |
$3$ |
$3401.41014166$ |
| 8.4.35650269974528.1 |
$x^{8} - 2 x^{7} - 23 x^{6} + 28 x^{5} + 258 x^{4} - 166 x^{3} - 1654 x^{2} - 1700 x - 391$ |
$8$ |
[4,2] |
$2^{12}\cdot 11^{6}\cdot 17^{3}$ |
$3$ |
$49.4319625158$ |
$70.43912752420829$ |
|
|
? |
$Z_8 : Z_8^\times$ (as 8T15) |
trivial |
$2$ |
$5$ |
$6159.21800968$ |
| 8.0.35650269974528.2 |
$x^{8} - 4 x^{7} + 8 x^{6} - 10 x^{5} + 3 x^{4} - 38 x^{3} + 68 x^{2} - 28 x + 130$ |
$8$ |
[0,4] |
$2^{12}\cdot 11^{6}\cdot 17^{3}$ |
$3$ |
$49.4319625158$ |
$143.02969034239467$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
$[4]$ |
$4$ |
$3$ |
$12905.7328265$ |
| 8.4.35650269974528.2 |
$x^{8} - 4 x^{7} - 4 x^{6} + 26 x^{5} - 140 x^{4} + 232 x^{3} + 811 x^{2} - 922 x + 631$ |
$8$ |
[4,2] |
$2^{12}\cdot 11^{6}\cdot 17^{3}$ |
$3$ |
$49.4319625158$ |
$70.43912752420829$ |
|
|
? |
$Z_8 : Z_8^\times$ (as 8T15) |
trivial |
$2$ |
$5$ |
$6159.21800968$ |
| 8.0.35650269974528.4 |
$x^{8} - 4 x^{7} + 8 x^{6} - 10 x^{5} + 267 x^{4} + 50 x^{3} - 856 x^{2} + 544 x + 37090$ |
$8$ |
[0,4] |
$2^{12}\cdot 11^{6}\cdot 17^{3}$ |
$3$ |
$49.4319625158$ |
$143.02969034239467$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
$[4]$ |
$4$ |
$3$ |
$5151.8470253$ |
