| 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 |
| 7.7.1817487424.1 |
$x^{7} - 8 x^{5} - 2 x^{4} + 16 x^{3} + 6 x^{2} - 6 x - 2$ |
$7$ |
[7,0] |
$2^{6}\cdot 73^{4}$ |
$2$ |
$21.0272089633$ |
$31.640326082417378$ |
|
|
✓ |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$346.793700867$ |
| 7.7.9597924961.1 |
$x^{7} - x^{6} - 15 x^{5} + 20 x^{4} + 33 x^{3} - 22 x^{2} - 32 x - 8$ |
$7$ |
[7,0] |
$313^{4}$ |
$1$ |
$26.6701424746$ |
$46.09950106351405$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$1193.62536712$ |
| 7.7.18078415936.1 |
$x^{7} - 14 x^{5} + 56 x^{3} - 56 x - 22$ |
$7$ |
[7,0] |
$2^{6}\cdot 7^{10}$ |
$2$ |
$29.1950097668$ |
$35.13938469045169$ |
|
|
✓ |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$1815.54779742$ |
| 7.7.100367308864.1 |
$x^{7} - 2 x^{6} - 14 x^{5} + 4 x^{4} + 30 x^{3} + 8 x^{2} - 6 x - 2$ |
$7$ |
[7,0] |
$2^{6}\cdot 199^{4}$ |
$2$ |
$37.2954661713$ |
$61.743952649783516$ |
|
|
✓ |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$3541.87067755$ |
| 7.7.272225149504.1 |
$x^{7} - 3 x^{6} - 15 x^{5} + 39 x^{4} + 43 x^{3} - 133 x^{2} + 63 x - 7$ |
$7$ |
[7,0] |
$2^{6}\cdot 7^{4}\cdot 11^{6}$ |
$3$ |
$43.0091815201$ |
$51.766250010785875$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$9516.2919469$ |
| 7.7.387790161984.1 |
$x^{7} - 18 x^{5} - 18 x^{4} + 60 x^{3} + 96 x^{2} + 44 x + 6$ |
$7$ |
[7,0] |
$2^{6}\cdot 3^{8}\cdot 31^{4}$ |
$3$ |
$45.2390864967$ |
$77.34433552870686$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$13908.2008402$ |
| 7.7.525346636864.1 |
$x^{7} - x^{6} - 25 x^{5} + 49 x^{4} + 131 x^{3} - 415 x^{2} + 281 x + 7$ |
$7$ |
[7,0] |
$2^{6}\cdot 7^{4}\cdot 43^{4}$ |
$3$ |
$47.244300406$ |
$81.35858268246776$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$9604.83873841$ |
| 7.7.591559418641.1 |
$x^{7} - 2 x^{6} - 20 x^{5} + 34 x^{4} + 107 x^{3} - 166 x^{2} - 119 x + 138$ |
$7$ |
[7,0] |
$877^{4}$ |
$1$ |
$48.0522860096$ |
$91.62199182116717$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$13548.3634132$ |
| 7.7.1624709678881.1 |
$x^{7} - x^{6} - 27 x^{5} - 14 x^{4} + 159 x^{3} + 164 x^{2} - 108 x - 40$ |
$7$ |
[7,0] |
$1129^{4}$ |
$1$ |
$55.5132352463$ |
$108.42496599557737$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$23932.3437186$ |
| 7.7.1688107729984.1 |
$x^{7} - x^{6} - 25 x^{5} + 15 x^{4} + 181 x^{3} - 37 x^{2} - 311 x - 121$ |
$7$ |
[7,0] |
$2^{6}\cdot 13^{4}\cdot 31^{4}$ |
$3$ |
$55.8176375434$ |
$98.83158066757649$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$16422.5599284$ |
| 7.7.2420662999104.1 |
$x^{7} - 42 x^{5} - 56 x^{4} + 126 x^{3} + 168 x^{2} - 98 x - 126$ |
$7$ |
[7,0] |
$2^{6}\cdot 3^{8}\cdot 7^{8}$ |
$3$ |
$58.7669939139$ |
$87.19653805851985$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$37308.8975207$ |
| 7.7.2528484794641.1 |
$x^{7} - 2 x^{6} - 20 x^{5} + 29 x^{4} + 119 x^{3} - 91 x^{2} - 234 x + 13$ |
$7$ |
[7,0] |
$13^{4}\cdot 97^{4}$ |
$2$ |
$59.1339911988$ |
$116.71949263039971$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$10253.067798$ |
| 7.7.5323914784321.1 |
$x^{7} - 28 x^{5} - 14 x^{4} + 196 x^{3} + 112 x^{2} - 364 x - 229$ |
$7$ |
[7,0] |
$7^{8}\cdot 31^{4}$ |
$2$ |
$65.7707832238$ |
$109.78752339060705$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$25011.4574922$ |
| 7.7.5482378736704.1 |
$x^{7} - x^{6} - 27 x^{5} + 7 x^{4} + 219 x^{3} + 83 x^{2} - 495 x - 409$ |
$7$ |
[7,0] |
$2^{6}\cdot 541^{4}$ |
$2$ |
$66.0469427292$ |
$120.26997498474019$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$30666.8796637$ |
| 7.7.6029426229121.1 |
$x^{7} - 3 x^{6} - 32 x^{5} + 4 x^{4} + 179 x^{3} + 89 x^{2} - 231 x - 145$ |
$7$ |
[7,0] |
$1567^{4}$ |
$1$ |
$66.9504826583$ |
$134.91057635293424$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$47083.2701526$ |
| 7.7.10537502807104.1 |
$x^{7} - 28 x^{5} - 28 x^{4} + 182 x^{3} + 238 x^{2} - 266 x - 374$ |
$7$ |
[7,0] |
$2^{6}\cdot 7^{8}\cdot 13^{4}$ |
$3$ |
$72.5088639011$ |
$111.42085100550725$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$59419.6554275$ |
| 7.7.10804165206961.1 |
$x^{7} - 35 x^{5} - 70 x^{4} + 84 x^{3} + 196 x^{2} - 49 x - 134$ |
$7$ |
[7,0] |
$7^{8}\cdot 37^{4}$ |
$2$ |
$72.7681949782$ |
$123.53205755595745$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$51196.0969778$ |
| 7.7.11239665258721.1 |
$x^{7} - 2 x^{6} - 45 x^{5} + 23 x^{4} + 679 x^{3} + 384 x^{2} - 3372 x - 4399$ |
$7$ |
[7,0] |
$1831^{4}$ |
$1$ |
$73.180157458$ |
$149.66683090729433$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$20029.228234$ |
| 7.7.13603763435584.1 |
$x^{7} - 2 x^{6} - 36 x^{5} + 66 x^{4} + 166 x^{3} - 92 x^{2} - 116 x + 50$ |
$7$ |
[7,0] |
$2^{6}\cdot 7^{4}\cdot 97^{4}$ |
$3$ |
$75.203319368$ |
$139.93904101597664$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$56977.7595127$ |
| 7.7.15588038452561.1 |
$x^{7} - x^{6} - 47 x^{5} + 517 x^{3} + 506 x^{2} - 376 x - 168$ |
$7$ |
[7,0] |
$1987^{4}$ |
$1$ |
$76.6804222118$ |
$158.0514840500404$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$82013.4593856$ |
| 7.7.20161545805921.1 |
$x^{7} - 3 x^{6} - 38 x^{5} + 52 x^{4} + 351 x^{3} - 168 x^{2} - 321 x - 17$ |
$7$ |
[7,0] |
$13^{4}\cdot 163^{4}$ |
$2$ |
$79.5511131349$ |
$164.97594996882682$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$34216.2535877$ |
| 7.7.22747786847296.1 |
$x^{7} - x^{6} - 39 x^{5} + 75 x^{4} + 55 x^{3} - 123 x^{2} + 19 x + 9$ |
$7$ |
[7,0] |
$2^{6}\cdot 7^{4}\cdot 23^{6}$ |
$3$ |
$80.9345887524$ |
$97.41362211039652$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$93878.8391008$ |
| 7.7.24551549322304.1 |
$x^{7} - 2 x^{6} - 46 x^{5} + 184 x^{4} - 224 x^{3} + 68 x^{2} + 20 x - 2$ |
$7$ |
[7,0] |
$2^{6}\cdot 787^{4}$ |
$2$ |
$81.821684218$ |
$154.4100388152556$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$55577.6084602$ |
| 7.7.26226371926561.1 |
$x^{7} - x^{6} - 41 x^{5} + 39 x^{4} + 496 x^{3} - 434 x^{2} - 1643 x + 961$ |
$7$ |
[7,0] |
$31^{4}\cdot 73^{4}$ |
$2$ |
$82.596682129$ |
$172.36789156973535$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$88442.985189$ |
| 7.7.35271352782961.1 |
$x^{7} - 3 x^{6} - 54 x^{5} + 27 x^{4} + 809 x^{3} + 1563 x^{2} + 740 x - 171$ |
$7$ |
[7,0] |
$2437^{4}$ |
$1$ |
$86.1680007529$ |
$181.09384346420086$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$135074.477609$ |
| 7.7.35698940069881.1 |
$x^{7} - 3 x^{6} - 59 x^{5} + 83 x^{4} + 791 x^{3} - 507 x^{2} - 2555 x - 722$ |
$7$ |
[7,0] |
$11^{6}\cdot 67^{4}$ |
$2$ |
$86.3164593212$ |
$128.82658764505967$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$58979.9488235$ |
| 7.7.42748699986001.1 |
$x^{7} - 2 x^{6} - 47 x^{5} + 47 x^{4} + 430 x^{3} - 216 x^{2} - 200 x + 96$ |
$7$ |
[7,0] |
$2557^{4}$ |
$1$ |
$88.567564389$ |
$186.99090578896957$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$139632.45493$ |
| 7.7.48081576391744.1 |
$x^{7} - 70 x^{5} - 42 x^{4} + 1316 x^{3} + 1428 x^{2} - 2912 x - 1940$ |
$7$ |
[7,0] |
$2^{6}\cdot 7^{8}\cdot 19^{4}$ |
$3$ |
$90.0675574878$ |
$143.49605786761867$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$74888.0955702$ |
| 7.7.58280536320561.1 |
$x^{7} - 3 x^{6} - 36 x^{5} + 143 x^{4} + 204 x^{3} - 1476 x^{2} + 1800 x - 432$ |
$7$ |
[7,0] |
$3^{8}\cdot 307^{4}$ |
$2$ |
$92.5770553478$ |
$196.903720979923$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$211240.508114$ |
| 7.7.79818518042641.1 |
$x^{7} - 56 x^{5} - 42 x^{4} + 777 x^{3} + 1197 x^{2} + 455 x + 9$ |
$7$ |
[7,0] |
$7^{8}\cdot 61^{4}$ |
$2$ |
$96.8310873208$ |
$172.39781177387897$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$59355.338667$ |
| 7.7.90812685325761.1 |
$x^{7} - 42 x^{5} - 70 x^{4} + 168 x^{3} + 126 x^{2} - 84 x - 45$ |
$7$ |
[7,0] |
$3^{8}\cdot 7^{12}$ |
$2$ |
$98.6327021221$ |
$121.59092717489902$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$404679.433569$ |
| 7.7.91402930798144.1 |
$x^{7} - 2 x^{6} - 48 x^{5} - 60 x^{4} + 100 x^{3} + 132 x^{2} + 4 x - 12$ |
$7$ |
[7,0] |
$2^{6}\cdot 7^{4}\cdot 29^{6}$ |
$3$ |
$98.7240298101$ |
$118.82515845668567$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
$[7]$ |
$2$ |
$6$ |
$28128.2395665$ |
| 7.7.107103643129921.1 |
$x^{7} - 2 x^{6} - 43 x^{5} + 9 x^{4} + 527 x^{3} + 614 x^{2} - 488 x - 248$ |
$7$ |
[7,0] |
$3217^{4}$ |
$1$ |
$100.985204455$ |
$217.92181496115043$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$136530.255529$ |
| 7.7.156750600320064.1 |
$x^{7} - 30 x^{5} - 22 x^{4} + 252 x^{3} + 252 x^{2} - 636 x - 684$ |
$7$ |
[7,0] |
$2^{6}\cdot 3^{8}\cdot 139^{4}$ |
$3$ |
$106.631871206$ |
$210.3119339596481$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$348111.474798$ |
| 7.7.162614549665681.1 |
$x^{7} - x^{6} - 38 x^{5} + 87 x^{4} + 236 x^{3} - 772 x^{2} + 392 x + 96$ |
$7$ |
[7,0] |
$3571^{4}$ |
$1$ |
$107.192803292$ |
$233.6289014035564$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$306395.598289$ |
| 7.7.270595393646656.1 |
$x^{7} - x^{6} - 39 x^{5} - 17 x^{4} + 331 x^{3} + 291 x^{2} - 441 x - 83$ |
$7$ |
[7,0] |
$2^{6}\cdot 13^{4}\cdot 23^{6}$ |
$3$ |
$115.281616351$ |
$147.18037330360426$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$277525.070002$ |
| 7.7.316838611601521.1 |
$x^{7} - x^{6} - 45 x^{5} - 37 x^{4} + 267 x^{3} + 59 x^{2} - 287 x - 80$ |
$7$ |
[7,0] |
$4219^{4}$ |
$1$ |
$117.909364928$ |
$261.09968643070096$ |
|
|
|
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$961298.251359$ |
| 7.7.354452954340241.1 |
$x^{7} - 2 x^{6} - 64 x^{5} + 271 x^{4} + 326 x^{3} - 3242 x^{2} + 5176 x - 2281$ |
$7$ |
[7,0] |
$4339^{4}$ |
$1$ |
$119.814221847$ |
$266.0274388940905$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
$[4]$ |
$2$ |
$6$ |
$29721.3812455$ |
| 7.7.394259782912576.1 |
$x^{7} - x^{6} - 63 x^{5} + 89 x^{4} + 1203 x^{3} - 1951 x^{2} - 7145 x + 12679$ |
$7$ |
[7,0] |
$2^{6}\cdot 7^{4}\cdot 37^{6}$ |
$3$ |
$121.649907387$ |
$146.41895746445294$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$479900.742126$ |
| 7.7.500422134593689.1 |
$x^{7} - 77 x^{5} + 1694 x^{3} - 9317 x - 8228$ |
$7$ |
[7,0] |
$7^{10}\cdot 11^{6}$ |
$2$ |
$125.865068316$ |
$151.49236427646426$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$416880.805487$ |
| 7.7.523361201113921.1 |
$x^{7} - 47 x^{5} - 9 x^{4} + 529 x^{3} + 392 x^{2} - 1115 x - 1079$ |
$7$ |
[7,0] |
$4783^{4}$ |
$1$ |
$126.67354714$ |
$283.879209526855$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$199659.43561$ |
| 7.7.971365931561536.1 |
$x^{7} - 3 x^{6} - 33 x^{5} + 85 x^{4} + 25 x^{3} - 117 x^{2} + 29 x + 7$ |
$7$ |
[7,0] |
$2^{6}\cdot 7^{4}\cdot 43^{6}$ |
$3$ |
$138.374063729$ |
$166.54830724122723$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
$[7]$ |
$2$ |
$6$ |
$84469.7144991$ |
| 7.7.3405864388526656.1 |
$x^{7} - x^{6} - 45 x^{5} - 65 x^{4} + 85 x^{3} + 129 x^{2} + 9 x - 11$ |
$7$ |
[7,0] |
$2^{6}\cdot 7^{4}\cdot 53^{6}$ |
$3$ |
$165.534919388$ |
$199.23936517004583$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
$[2]$ |
$2$ |
$6$ |
$577698.230197$ |
| 7.7.3429038075724121.1 |
$x^{7} - 203 x^{5} - 406 x^{4} + 9338 x^{3} + 49126 x^{2} + 70035 x + 4408$ |
$7$ |
[7,0] |
$7^{8}\cdot 29^{6}$ |
$2$ |
$165.695353395$ |
$199.4324650301191$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
$[7]$ |
$2$ |
$6$ |
$165602.32598$ |
| 7.7.25300544239856704.1 |
$x^{7} - 84 x^{5} - 28 x^{4} + 1456 x^{3} + 1806 x^{2} - 3906 x - 5238$ |
$7$ |
[7,0] |
$2^{6}\cdot 7^{12}\cdot 13^{4}$ |
$3$ |
$220.447037148$ |
$281.44537045926666$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$2562207.56344$ |
| 7.7.32027016613996096.1 |
$x^{7} - 154 x^{5} + 6776 x^{3} - 74536 x - 39930$ |
$7$ |
[7,0] |
$2^{6}\cdot 7^{10}\cdot 11^{6}$ |
$3$ |
$227.997941756$ |
$274.42043856096353$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$4482293.71248$ |
| 7.7.32027016613996096.2 |
$x^{7} - 154 x^{5} + 6776 x^{3} - 74536 x - 77198$ |
$7$ |
[7,0] |
$2^{6}\cdot 7^{10}\cdot 11^{6}$ |
$3$ |
$227.997941756$ |
$274.42043856096353$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$3741007.61656$ |
| 7.7.32027016613996096.3 |
$x^{7} - 154 x^{5} + 6776 x^{3} - 74536 x - 95832$ |
$7$ |
[7,0] |
$2^{6}\cdot 7^{10}\cdot 11^{6}$ |
$3$ |
$227.997941756$ |
$274.42043856096353$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$2883046.48624$ |
| 7.7.32027016613996096.4 |
$x^{7} - 154 x^{5} + 6776 x^{3} - 74536 x - 96360$ |
$7$ |
[7,0] |
$2^{6}\cdot 7^{10}\cdot 11^{6}$ |
$3$ |
$227.997941756$ |
$274.42043856096353$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$2396810.65353$ |
| 7.7.32027016613996096.5 |
$x^{7} - 154 x^{5} + 6776 x^{3} - 74536 x - 99220$ |
$7$ |
[7,0] |
$2^{6}\cdot 7^{10}\cdot 11^{6}$ |
$3$ |
$227.997941756$ |
$274.42043856096353$ |
|
|
? |
$C_7:C_3$ (as 7T3) |
trivial |
$2$ |
$6$ |
$3240000.23501$ |
