| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Narrow class group |
Unit group torsion |
Unit group rank |
Regulator |
Unit signature rank |
Max $p$ |
| 8.8.341...217.2 |
$x^{8} - x^{7} - 619 x^{6} + 516 x^{5} + 100995 x^{4} - 265618 x^{3} - 4617754 x^{2} + 18906996 x - 1404233$ |
$8$ |
(8, 0) |
$17^{7}\cdot 97^{6}$ |
$2$ |
$368.741150944$ |
$368.7411509442359$ |
|
✓ |
? |
$C_8$ (as 8T1) |
$[4]$ |
$[4]$ |
$2$ |
$7$ |
$12721087.5206$ |
$8$ |
$97$ |
| 8.0.162...449.2 |
$x^{8} - x^{7} + 495 x^{6} + 6713 x^{5} + 152728 x^{4} + 4973517 x^{3} + 53791169 x^{2} + 1407952788 x + 15398575715$ |
$8$ |
(0, 4) |
$41^{7}\cdot 97^{6}$ |
$2$ |
$796.644707638$ |
$796.6447076384409$ |
✓ |
✓ |
|
$C_8$ (as 8T1) |
$[3, 22668]$ |
$[3, 22668]$ |
$2$ |
$3$ |
$7407.38175249$ |
$0$ |
$97$ |
| 8.0.754...257.1 |
$x^{8} - x^{7} + 1653 x^{6} - 90525 x^{5} + 4041906 x^{4} - 129503291 x^{3} + 2884780885 x^{2} - 19822085248 x + 726328141651$ |
$8$ |
(0, 4) |
$97^{6}\cdot 137^{7}$ |
$2$ |
$2289.33473126$ |
$2289.334731264543$ |
✓ |
✓ |
|
$C_8$ (as 8T1) |
$[13, 64948]$ |
$[13, 64948]$ |
$2$ |
$3$ |
$64941.621143$ |
$0$ |
$137$ |
| 8.0.310...033.2 |
$x^{8} - x^{7} + 2811 x^{6} - 52254 x^{5} - 3686094 x^{4} - 24869438 x^{3} - 11423207327 x^{2} + 62346382835 x + 14647892617159$ |
$8$ |
(0, 4) |
$97^{6}\cdot 233^{7}$ |
$2$ |
$3643.47028241$ |
$3643.470282413289$ |
✓ |
✓ |
|
$C_8$ (as 8T1) |
$[378788]$ |
$[378788]$ |
$2$ |
$3$ |
$777847.419519$ |
$0$ |
$233$ |
| 8.8.616...697.1 |
$x^{8} - x^{7} - 9364 x^{6} + 325647 x^{5} + 9931086 x^{4} - 502649707 x^{3} + 566137340 x^{2} + 137355923229 x - 1039146593207$ |
$8$ |
(8, 0) |
$97^{6}\cdot 257^{7}$ |
$2$ |
$3969.81513919$ |
$3969.8151391881884$ |
|
✓ |
|
$C_8$ (as 8T1) |
$[12]$ |
$[12]$ |
$2$ |
$7$ |
$309134261617$ |
$8$ |
$257$ |
| 8.0.115...369.2 |
$x^{8} - x^{7} + 3390 x^{6} - 97090 x^{5} + 13332937 x^{4} + 218923695 x^{3} - 2804747704 x^{2} + 567143641620 x + 19966237674800$ |
$8$ |
(0, 4) |
$97^{6}\cdot 281^{7}$ |
$2$ |
$4292.36683486$ |
$4292.366834863436$ |
✓ |
✓ |
|
$C_8$ (as 8T1) |
$[9126116]$ |
$[9126116]$ |
$2$ |
$3$ |
$3100623.06925$ |
$0$ |
$281$ |
| 8.8.411...657.2 |
$x^{8} - x^{7} - 12279 x^{6} + 108298 x^{5} + 34593168 x^{4} - 416748568 x^{3} - 16953019328 x^{2} - 83100045472 x - 108573243968$ |
$8$ |
(8, 0) |
$97^{6}\cdot 337^{7}$ |
$2$ |
$5032.1660565$ |
$5032.1660565035445$ |
|
✓ |
|
$C_8$ (as 8T1) |
$[4]$ |
$[4]$ |
$2$ |
$7$ |
$1858615169430$ |
$8$ |
$337$ |
| 8.8.138...129.1 |
$x^{8} - x^{7} - 14611 x^{6} + 167762 x^{5} + 54504499 x^{4} - 1420847358 x^{3} - 30406309452 x^{2} + 1109176568242 x - 5770386205141$ |
$8$ |
(8, 0) |
$97^{6}\cdot 401^{7}$ |
$2$ |
$5859.08942792$ |
$5859.089427923591$ |
|
✓ |
|
$C_8$ (as 8T1) |
$[2260]$ |
$[2260]$ |
$2$ |
$7$ |
$1611497881.93$ |
$8$ |
$401$ |
| 8.0.159...401.2 |
$x^{8} - x^{7} + 4934 x^{6} - 141316 x^{5} + 32300105 x^{4} + 370673086 x^{3} - 8465842870 x^{2} + 2455741695187 x + 82395618774523$ |
$8$ |
(0, 4) |
$97^{6}\cdot 409^{7}$ |
$2$ |
$5961.24121195$ |
$5961.241211946956$ |
✓ |
✓ |
? |
$C_8$ (as 8T1) |
$[1406596]$ |
$[1406596]$ |
$2$ |
$3$ |
$190394.530957$ |
$0$ |
$409$ |
| 8.8.237...433.2 |
$x^{8} - x^{7} - 15777 x^{6} - 133858 x^{5} + 73449353 x^{4} + 615063164 x^{3} - 121038673002 x^{2} - 471273849700 x + 50244605116801$ |
$8$ |
(8, 0) |
$97^{6}\cdot 433^{7}$ |
$2$ |
$6266.22103309$ |
$6266.221033085626$ |
|
✓ |
|
$C_8$ (as 8T1) |
$[4]$ |
$[4]$ |
$2$ |
$7$ |
$717363337813$ |
$8$ |
$433$ |
| 8.0.346...097.1 |
$x^{8} - x^{7} + 5513 x^{6} + 806255 x^{5} + 51051896 x^{4} + 2060468911 x^{3} + 78159964013 x^{2} + 756166559158 x + 32330330838121$ |
$8$ |
(0, 4) |
$97^{6}\cdot 457^{7}$ |
$2$ |
$6569.09399004$ |
$6569.093990039318$ |
✓ |
✓ |
? |
$C_8$ (as 8T1) |
$[5, 469940]$ |
$[5, 469940]$ |
$2$ |
$3$ |
$156867.695289$ |
$0$ |
$457$ |
| 16.0.441...097.1 |
$x^{16} - 2 x^{15} - 72 x^{14} + 35 x^{13} + 1730 x^{12} + 1148 x^{11} - 13574 x^{10} - 13264 x^{9} + 62090 x^{8} + 91739 x^{7} + 59197 x^{6} + 222822 x^{5} + 337044 x^{4} - 93725 x^{3} + 157928 x^{2} + 79985 x + 87721$ |
$16$ |
(0, 8) |
$3^{8}\cdot 97^{13}$ |
$2$ |
$71.2545598053$ |
$94.8387660758292$ |
|
|
? |
$C_8\wr C_2$ (as 16T289) |
$[4]$ |
$[4]$ |
$6$ |
$7$ |
$56013234.4844$ |
$0$ |
$97$ |
| 16.0.144...737.2 |
$x^{16} - 5 x^{15} + 69 x^{14} + 34 x^{13} - 1281 x^{12} + 13607 x^{11} - 2308 x^{10} - 103011 x^{9} + 311153 x^{8} + 1254950 x^{7} + 6175739 x^{6} - 58786071 x^{5} + 127300119 x^{4} + 142003227 x^{3} - 46631222 x^{2} - 1734974481 x + 4308263105$ |
$16$ |
(0, 8) |
$11^{8}\cdot 97^{13}$ |
$2$ |
$136.442094218$ |
$181.60241101432212$ |
|
|
|
$C_8\wr C_2$ (as 16T289) |
$[4]$ |
$[4]$ |
$2$ |
$7$ |
$24789625089.4$ |
$0$ |
$97$ |
| 16.0.574...857.1 |
$x^{16} - 120 x^{14} - 65 x^{13} + 7240 x^{12} + 4104 x^{11} - 222291 x^{10} - 107963 x^{9} + 3658272 x^{8} - 417737 x^{7} - 5867102 x^{6} + 57052889 x^{5} + 65035479 x^{4} - 62698039 x^{3} + 522253735 x^{2} + 39537623 x + 61970299$ |
$16$ |
(0, 8) |
$31^{8}\cdot 97^{13}$ |
$2$ |
$229.051363297$ |
$304.8639795462677$ |
|
|
? |
$C_8\wr C_2$ (as 16T289) |
$[12]$ |
$[12]$ |
$2$ |
$7$ |
$120221303327$ |
$0$ |
$97$ |
| 16.0.623...269.1 |
$x^{16} - 2 x^{15} + 399 x^{14} - 2711 x^{13} + 103419 x^{12} + 279510 x^{11} + 1693093 x^{10} + 41451267 x^{9} + 185117827 x^{8} - 139494109 x^{7} + 3373927822 x^{6} + 26975210449 x^{5} + 52686411171 x^{4} + 66288478809 x^{3} + 859291849829 x^{2} + 2588516506113 x + 13518186693977$ |
$16$ |
(0, 8) |
$53^{11}\cdot 97^{13}$ |
$2$ |
$630.509586949$ |
$1075.5538759909816$ |
|
|
|
$C_8^2:C_4$ (as 16T664) |
$[20]$ |
$[20]$ |
$2$ |
$7$ |
$1148945996290000$ |
$0$ |
$97$ |
| 16.4.330...257.1 |
$x^{16} - 6 x^{15} - 175 x^{14} - 1817 x^{13} + 21444 x^{12} + 112467 x^{11} + 3449660 x^{10} + 52134733 x^{9} - 1317451956 x^{8} + 2708069139 x^{7} + 5210403611 x^{6} - 459523014803 x^{5} + 9654583612006 x^{4} - 35886040757802 x^{3} - 68604664792184 x^{2} + 404169111556833 x - 1396976825268463$ |
$16$ |
(4, 6) |
$53^{12}\cdot 97^{13}$ |
$2$ |
$808.088518563$ |
$1075.5538759909816$ |
|
|
|
$C_8^2:C_4$ (as 16T664) |
$[4]$ |
$[4, 2]$ |
$2$ |
$9$ |
$69605075091400000$ |
$3$ |
$97$ |
| 16.4.928...913.1 |
$x^{16} - 6 x^{15} + 83 x^{14} - 5839 x^{13} - 88558 x^{12} + 4991811 x^{11} - 68227378 x^{10} + 565496352 x^{9} - 5457176579 x^{8} + 46740060492 x^{7} - 90039477368 x^{6} - 2130562816119 x^{5} + 16926569569710 x^{4} - 16101025136047 x^{3} - 325769428937561 x^{2} + 1527829574366336 x - 2168030084595671$ |
$16$ |
(4, 6) |
$53^{14}\cdot 97^{13}$ |
$2$ |
$1327.37434649$ |
$1766.715638773827$ |
|
|
? |
$C_8^2:C_4$ (as 16T694) |
$[4]$ |
$[2, 2, 4]$ |
$2$ |
$9$ |
$2094930558310000000$ |
$2$ |
$97$ |
