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 |
7.7.594823321.1 |
$x^{7} - x^{6} - 12 x^{5} + 7 x^{4} + 28 x^{3} - 14 x^{2} - 9 x - 1$ |
$7$ |
[7,0] |
$29^{6}$ |
$1$ |
$17.926025018$ |
$17.9260250179852$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$94.0778921898$ |
7.7.6321363049.1 |
$x^{7} - x^{6} - 18 x^{5} + 35 x^{4} + 38 x^{3} - 104 x^{2} + 7 x + 49$ |
$7$ |
[7,0] |
$43^{6}$ |
$1$ |
$25.125563989$ |
$25.125563989023604$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$562.369403915$ |
7.7.13841287201.1 |
$x^{7} - 21 x^{5} - 21 x^{4} + 91 x^{3} + 112 x^{2} - 84 x - 97$ |
$7$ |
[7,0] |
$7^{12}$ |
$1$ |
$28.1021467385$ |
$28.102146738487733$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$550.88577714$ |
7.7.128100283921.1 |
$x^{7} - x^{6} - 30 x^{5} - 3 x^{4} + 254 x^{3} + 246 x^{2} - 245 x - 137$ |
$7$ |
[7,0] |
$71^{6}$ |
$1$ |
$38.6182749562$ |
$38.6182749562038$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$4923.66713477$ |
7.7.2081951752609.1 |
$x^{7} - x^{6} - 48 x^{5} - 37 x^{4} + 312 x^{3} + 12 x^{2} - 49 x + 1$ |
$7$ |
[7,0] |
$113^{6}$ |
$1$ |
$57.5150528221$ |
$57.515052822114356$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$3480.45270075$ |
7.7.4195872914689.1 |
$x^{7} - x^{6} - 54 x^{5} + 31 x^{4} + 558 x^{3} + 32 x^{2} - 1713 x - 1121$ |
$7$ |
[7,0] |
$127^{6}$ |
$1$ |
$63.5711886985$ |
$63.57118869849136$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$8535.73766168$ |
7.7.58451728309129.1 |
$x^{7} - x^{6} - 84 x^{5} + 217 x^{4} + 1348 x^{3} - 3988 x^{2} - 1433 x + 1163$ |
$7$ |
[7,0] |
$197^{6}$ |
$1$ |
$92.6158542239$ |
$92.61585422390594$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$24266.4874851$ |
7.7.88245939632761.1 |
$x^{7} - x^{6} - 90 x^{5} - 69 x^{4} + 1306 x^{3} - 124 x^{2} - 5249 x + 4663$ |
$7$ |
[7,0] |
$211^{6}$ |
$1$ |
$98.2295386997$ |
$98.22953869965724$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$45986.5424474$ |
7.7.186374892382561.1 |
$x^{7} - x^{6} - 102 x^{5} + 195 x^{4} + 1850 x^{3} - 978 x^{2} - 8933 x - 5183$ |
$7$ |
[7,0] |
$239^{6}$ |
$1$ |
$109.301663642$ |
$109.30166364159797$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$47231.2823021$ |
7.7.492309163417681.1 |
$x^{7} - x^{6} - 120 x^{5} + 711 x^{4} - 784 x^{3} - 1956 x^{2} + 2863 x + 343$ |
$7$ |
[7,0] |
$281^{6}$ |
$1$ |
$125.57151424$ |
$125.57151423975624$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$190251.575488$ |
7.7.1464803622199009.1 |
$x^{7} - x^{6} - 144 x^{5} - 399 x^{4} + 2416 x^{3} + 10808 x^{2} + 10831 x + 1237$ |
$7$ |
[7,0] |
$337^{6}$ |
$1$ |
$146.737094349$ |
$146.73709434855056$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$85721.5666782$ |
7.7.2963706958323721.1 |
$x^{7} - x^{6} - 162 x^{5} + 201 x^{4} + 7822 x^{3} - 12322 x^{2} - 107717 x + 193369$ |
$7$ |
[7,0] |
$379^{6}$ |
$1$ |
$162.278946624$ |
$162.2789466236963$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$269113.064107$ |
7.7.5567914722008521.1 |
$x^{7} - x^{6} - 180 x^{5} + 103 x^{4} + 6180 x^{3} - 11596 x^{2} - 25209 x + 49213$ |
$7$ |
[7,0] |
$421^{6}$ |
$1$ |
$177.576157232$ |
$177.57615723232306$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$428479.510505$ |
7.7.8193662024284801.1 |
$x^{7} - x^{6} - 192 x^{5} - 275 x^{4} + 3952 x^{3} - 4136 x^{2} - 81 x + 863$ |
$7$ |
[7,0] |
$449^{6}$ |
$1$ |
$187.652349591$ |
$187.6523495907157$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$263186.113809$ |
7.7.9851127637605409.1 |
$x^{7} - x^{6} - 198 x^{5} + 907 x^{4} + 4302 x^{3} - 20582 x^{2} - 18973 x + 56911$ |
$7$ |
[7,0] |
$463^{6}$ |
$1$ |
$192.656517928$ |
$192.65651792795916$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$191858.77331$ |
7.7.14011639427134441.1 |
$x^{7} - x^{6} - 210 x^{5} - 1423 x^{4} - 1410 x^{3} + 8538 x^{2} + 9203 x - 19427$ |
$7$ |
[7,0] |
$491^{6}$ |
$1$ |
$202.600857407$ |
$202.60085740689678$ |
|
✓ |
|
$C_7$ (as 7T1) |
$[2, 2, 2]$ |
$2$ |
$6$ |
$36153.2241228$ |
7.7.26786992617986329.1 |
$x^{7} - x^{6} - 234 x^{5} - 335 x^{4} + 13254 x^{3} + 42874 x^{2} - 55309 x - 71879$ |
$7$ |
[7,0] |
$547^{6}$ |
$1$ |
$222.252308039$ |
$222.25230803930208$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$1081131.34355$ |
7.7.55171016309022769.1 |
$x^{7} - x^{6} - 264 x^{5} + 151 x^{4} + 13288 x^{3} - 18556 x^{2} - 69425 x - 34621$ |
$7$ |
[7,0] |
$617^{6}$ |
$1$ |
$246.418323049$ |
$246.41832304919535$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$948249.056766$ |
7.7.63121332085847281.1 |
$x^{7} - x^{6} - 270 x^{5} - 116 x^{4} + 19848 x^{3} + 31904 x^{2} - 375552 x - 720896$ |
$7$ |
[7,0] |
$631^{6}$ |
$1$ |
$251.203198625$ |
$251.2031986249288$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$159039747.783$ |
7.7.81905390937410041.1 |
$x^{7} - x^{6} - 282 x^{5} - 1345 x^{4} + 5370 x^{3} + 30042 x^{2} - 14893 x - 115169$ |
$7$ |
[7,0] |
$659^{6}$ |
$1$ |
$260.727894919$ |
$260.7278949189025$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$1395957.12953$ |
7.7.92915974333361089.1 |
$x^{7} - x^{6} - 288 x^{5} - 316 x^{4} + 23504 x^{3} + 53056 x^{2} - 541952 x - 1722368$ |
$7$ |
[7,0] |
$673^{6}$ |
$1$ |
$265.468448834$ |
$265.4684488343775$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$113222151.583$ |
7.7.118661028367354201.1 |
$x^{7} - x^{6} - 300 x^{5} - 1631 x^{4} + 5140 x^{3} + 23794 x^{2} - 59049 x + 18773$ |
$7$ |
[7,0] |
$701^{6}$ |
$1$ |
$274.907679871$ |
$274.90767987111883$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$1357576.32866$ |
7.7.168241403464173649.1 |
$x^{7} - x^{6} - 318 x^{5} + 1031 x^{4} + 26070 x^{3} - 125148 x^{2} - 420841 x + 2302639$ |
$7$ |
[7,0] |
$743^{6}$ |
$1$ |
$288.966537864$ |
$288.9665378643925$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$995925.108939$ |
7.7.188180785490436649.1 |
$x^{7} - x^{6} - 324 x^{5} + 1483 x^{4} + 20876 x^{3} - 129744 x^{2} + 36999 x + 54027$ |
$7$ |
[7,0] |
$757^{6}$ |
$1$ |
$293.627324671$ |
$293.6273246706745$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$31817260.5598$ |
7.7.319913861015774089.1 |
$x^{7} - x^{6} - 354 x^{5} - 979 x^{4} + 30030 x^{3} + 111552 x^{2} - 715705 x - 2921075$ |
$7$ |
[7,0] |
$827^{6}$ |
$1$ |
$316.751739222$ |
$316.7517392217116$ |
|
✓ |
|
$C_7$ (as 7T1) |
$[2, 2, 2]$ |
$2$ |
$6$ |
$758444.158782$ |
7.7.473984589097059769.1 |
$x^{7} - x^{6} - 378 x^{5} + 973 x^{4} + 13106 x^{3} + 9624 x^{2} - 64665 x - 91125$ |
$7$ |
[7,0] |
$883^{6}$ |
$1$ |
$335.049654549$ |
$335.04965454876634$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$129015047.061$ |
7.7.571623746239596961.1 |
$x^{7} - x^{6} - 390 x^{5} + 223 x^{4} + 18058 x^{3} - 30856 x^{2} - 116657 x + 225929$ |
$7$ |
[7,0] |
$911^{6}$ |
$1$ |
$344.135945282$ |
$344.1359452820763$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$7877583.34144$ |
7.7.749130369924173329.1 |
$x^{7} - x^{6} - 408 x^{5} - 992 x^{4} + 48064 x^{3} + 204560 x^{2} - 1603520 x - 8290816$ |
$7$ |
[7,0] |
$953^{6}$ |
$1$ |
$357.691154601$ |
$357.6911546007666$ |
|
✓ |
|
$C_7$ (as 7T1) |
$[71]$ |
$2$ |
$6$ |
$4478301.42813$ |
7.7.817633815294109969.1 |
$x^{7} - x^{6} - 414 x^{5} + 4381 x^{4} - 10434 x^{3} - 32702 x^{2} + 167651 x - 182573$ |
$7$ |
[7,0] |
$967^{6}$ |
$1$ |
$362.190435696$ |
$362.19043569583914$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$3027322.57187$ |
7.7.1055229678769825441.1 |
$x^{7} - x^{6} - 432 x^{5} + 247 x^{4} + 59784 x^{3} - 15272 x^{2} - 2647129 x - 374699$ |
$7$ |
[7,0] |
$1009^{6}$ |
$1$ |
$375.633102055$ |
$375.6331020554405$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$8038322.35166$ |
7.7.1347771585762793801.1 |
$x^{7} - x^{6} - 450 x^{5} - 4247 x^{4} - 6450 x^{3} + 22774 x^{2} + 25691 x + 5653$ |
$7$ |
[7,0] |
$1051^{6}$ |
$1$ |
$388.996044442$ |
$388.99604444207904$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$2327124.38908$ |
7.7.1704986606307341449.1 |
$x^{7} - x^{6} - 468 x^{5} - 2543 x^{4} + 23004 x^{3} + 169598 x^{2} + 130839 x - 450131$ |
$7$ |
[7,0] |
$1093^{6}$ |
$1$ |
$402.282895508$ |
$402.2828955083758$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$9655295.79813$ |
7.7.2474447753486836009.1 |
$x^{7} - x^{6} - 498 x^{5} + 1780 x^{4} + 72184 x^{3} - 361600 x^{2} - 2988416 x + 16876544$ |
$7$ |
[7,0] |
$1163^{6}$ |
$1$ |
$424.267490752$ |
$424.26749075235574$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$458862243.387$ |
7.7.4586881327254923761.1 |
$x^{7} - x^{6} - 552 x^{5} - 5577 x^{4} - 5280 x^{3} + 59010 x^{2} - 42769 x - 7019$ |
$7$ |
[7,0] |
$1289^{6}$ |
$1$ |
$463.373370733$ |
$463.3733707325986$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$178245209.06$ |
7.7.4894028501935246129.1 |
$x^{7} - x^{6} - 558 x^{5} - 4893 x^{4} + 17638 x^{3} + 254174 x^{2} + 353419 x - 218405$ |
$7$ |
[7,0] |
$1303^{6}$ |
$1$ |
$467.683831865$ |
$467.6838318654922$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$102202414.924$ |
7.7.6699204317182001689.1 |
$x^{7} - x^{6} - 588 x^{5} + 1513 x^{4} + 65884 x^{3} + 33346 x^{2} - 962361 x - 55903$ |
$7$ |
[7,0] |
$1373^{6}$ |
$1$ |
$489.138546916$ |
$489.1385469162994$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$5167793.74822$ |
7.7.8233120419813614521.1 |
$x^{7} - 609 x^{5} - 2030 x^{4} + 70847 x^{3} + 133980 x^{2} - 1467487 x - 2403694$ |
$7$ |
[7,0] |
$7^{12}\cdot 29^{6}$ |
$2$ |
$503.759785493$ |
$503.75978549322235$ |
|
✓ |
|
$C_7$ (as 7T1) |
$[7]$ |
$2$ |
$6$ |
$140334638.823$ |
7.7.8233120419813614521.2 |
$x^{7} - 609 x^{5} - 2233 x^{4} + 36743 x^{3} + 62118 x^{2} - 576520 x + 3625$ |
$7$ |
[7,0] |
$7^{12}\cdot 29^{6}$ |
$2$ |
$503.759785493$ |
$503.75978549322235$ |
|
✓ |
|
$C_7$ (as 7T1) |
$[7]$ |
$2$ |
$6$ |
$5753883.56452$ |
7.7.8233120419813614521.3 |
$x^{7} - 609 x^{5} - 2233 x^{4} + 48111 x^{3} - 40194 x^{2} - 87696 x + 77517$ |
$7$ |
[7,0] |
$7^{12}\cdot 29^{6}$ |
$2$ |
$503.759785493$ |
$503.75978549322235$ |
|
✓ |
|
$C_7$ (as 7T1) |
$[7]$ |
$2$ |
$6$ |
$64309241.25$ |
7.7.8233120419813614521.4 |
$x^{7} - 609 x^{5} - 609 x^{4} + 104951 x^{3} + 119770 x^{2} - 5123720 x - 9825577$ |
$7$ |
[7,0] |
$7^{12}\cdot 29^{6}$ |
$2$ |
$503.759785493$ |
$503.75978549322235$ |
|
✓ |
|
$C_7$ (as 7T1) |
$[7]$ |
$2$ |
$6$ |
$1232531.80142$ |
7.7.8233120419813614521.5 |
$x^{7} - 609 x^{5} - 609 x^{4} + 36743 x^{3} + 162400 x^{2} + 179452 x - 12151$ |
$7$ |
[7,0] |
$7^{12}\cdot 29^{6}$ |
$2$ |
$503.759785493$ |
$503.75978549322235$ |
|
✓ |
|
$C_7$ (as 7T1) |
$[7]$ |
$2$ |
$6$ |
$1458812.01451$ |
7.7.8233120419813614521.6 |
$x^{7} - 609 x^{5} - 6293 x^{4} + 2639 x^{3} + 125454 x^{2} - 133168 x + 30479$ |
$7$ |
[7,0] |
$7^{12}\cdot 29^{6}$ |
$2$ |
$503.759785493$ |
$503.75978549322235$ |
|
✓ |
|
$C_7$ (as 7T1) |
$[7]$ |
$2$ |
$6$ |
$934548.225652$ |
7.7.8515170979269874921.1 |
$x^{7} - x^{6} - 612 x^{5} + 1983 x^{4} + 118732 x^{3} - 607744 x^{2} - 6889121 x + 43521943$ |
$7$ |
[7,0] |
$1429^{6}$ |
$1$ |
$506.189740934$ |
$506.1897409342453$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$9587300.65259$ |
7.7.101...321.1 |
$x^{7} - x^{6} - 630 x^{5} - 1321 x^{4} + 105050 x^{3} + 532744 x^{2} - 1423169 x - 1017227$ |
$7$ |
[7,0] |
$1471^{6}$ |
$1$ |
$518.91542038$ |
$518.9154203798864$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$10351757.8241$ |
7.7.113...001.1 |
$x^{7} - x^{6} - 642 x^{5} + 367 x^{4} + 114514 x^{3} - 287002 x^{2} - 6382709 x + 28440251$ |
$7$ |
[7,0] |
$1499^{6}$ |
$1$ |
$527.370321112$ |
$527.3703211123925$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$22758620.4726$ |
7.7.157...369.1 |
$x^{7} - x^{6} - 678 x^{5} - 517 x^{4} + 79450 x^{3} - 44802 x^{2} - 1841157 x + 1084293$ |
$7$ |
[7,0] |
$1583^{6}$ |
$1$ |
$552.601695053$ |
$552.6016950526441$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$819365058.399$ |
7.7.165...929.1 |
$x^{7} - x^{6} - 684 x^{5} + 391 x^{4} + 101924 x^{3} + 148956 x^{2} - 2012697 x - 4567671$ |
$7$ |
[7,0] |
$1597^{6}$ |
$1$ |
$556.788078733$ |
$556.7880787332699$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$162869375.771$ |
7.7.214...369.1 |
$x^{7} - x^{6} - 714 x^{5} + 1837 x^{4} + 97138 x^{3} + 129892 x^{2} - 1667073 x - 2477977$ |
$7$ |
[7,0] |
$1667^{6}$ |
$1$ |
$577.642429039$ |
$577.6424290387587$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$9685504.78334$ |
7.7.249...241.1 |
$x^{7} - x^{6} - 732 x^{5} + 3104 x^{4} + 155808 x^{3} - 1028208 x^{2} - 6517504 x + 42320896$ |
$7$ |
[7,0] |
$1709^{6}$ |
$1$ |
$590.094773444$ |
$590.0947734443631$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$1611972567.68$ |
7.7.261...489.1 |
$x^{7} - x^{6} - 738 x^{5} + 9283 x^{4} - 11418 x^{3} - 331708 x^{2} + 1727391 x - 2487539$ |
$7$ |
[7,0] |
$1723^{6}$ |
$1$ |
$594.235795514$ |
$594.2357955136594$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$13885411.1162$ |