| 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 |
| 9.1.80190448927744.1 |
$x^{9} - 2 x^{8} + 12 x^{7} + 4 x^{6} + 14 x^{5} + 140 x^{4} - 48 x^{3} + 412 x^{2} - 51 x + 342$ |
$9$ |
[1,4] |
$2^{10}\cdot 23^{8}$ |
$2$ |
$35.0673151267$ |
$40.90704143524191$ |
|
|
|
$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T30) |
$[2]$ |
$2$ |
$4$ |
$7789.27566117$ |
| 9.3.200476122319360.1 |
$x^{9} - 3 x^{8} + 4 x^{7} + 2 x^{6} + 68 x^{5} - 176 x^{4} - 104 x^{3} + 488 x^{2} - 240 x - 32$ |
$9$ |
[3,3] |
$-\,2^{9}\cdot 5\cdot 23^{8}$ |
$3$ |
$38.8255907639$ |
$102.67264229377021$ |
|
|
? |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$5$ |
$16948.2217361$ |
| 9.1.320761795710976.1 |
$x^{9} - 4 x^{8} + 2 x^{7} - 14 x^{6} - 6 x^{5} + 18 x^{4} + 10 x^{3} - 118 x^{2} - 15 x - 18$ |
$9$ |
[1,4] |
$2^{12}\cdot 23^{8}$ |
$2$ |
$40.9070414352$ |
$64.93588060720973$ |
|
|
|
$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T30) |
$[2]$ |
$2$ |
$4$ |
$33495.2045165$ |
| 9.1.541285530262272.1 |
$x^{9} - x^{8} + 3 x^{7} - 11 x^{6} + 21 x^{5} - 79 x^{4} + 166 x^{3} - 216 x^{2} + 213 x - 81$ |
$9$ |
[1,4] |
$2^{8}\cdot 3^{3}\cdot 23^{8}$ |
$3$ |
$43.3558175214$ |
$70.85307415316427$ |
|
|
? |
$S_3\wr S_3$ (as 9T31) |
$[2]$ |
$2$ |
$4$ |
$14869.2766274$ |
| 9.1.1283047182843904.1 |
$x^{9} - 23 x^{6} + 23 x^{5} + 46 x^{4} + 138 x^{3} - 161 x^{2} - 276 x - 460$ |
$9$ |
[1,4] |
$2^{14}\cdot 23^{8}$ |
$2$ |
$47.7192517574$ |
$109.20869844789173$ |
|
|
|
$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T30) |
trivial |
$2$ |
$4$ |
$132501.665863$ |
| 9.1.1623856590786816.1 |
$x^{9} - 3 x^{8} + 4 x^{7} + 2 x^{6} - 24 x^{5} + 8 x^{4} + 126 x^{3} - 294 x^{2} + 243 x - 9$ |
$9$ |
[1,4] |
$2^{8}\cdot 3^{4}\cdot 23^{8}$ |
$3$ |
$48.9847451013$ |
$68.5248198611294$ |
|
|
? |
$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T30) |
$[2]$ |
$2$ |
$4$ |
$28455.2312338$ |
| 9.5.3132439411240000.1 |
$x^{9} - 3 x^{8} - 19 x^{7} + 71 x^{6} + 22 x^{5} - 360 x^{4} + 448 x^{3} + 120 x^{2} - 608 x + 336$ |
$9$ |
[5,2] |
$2^{6}\cdot 5^{4}\cdot 23^{8}$ |
$3$ |
$52.6944337722$ |
$86.16659076535258$ |
|
|
? |
$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T30) |
trivial |
$2$ |
$6$ |
$161543.54302$ |
| 9.1.3247713181573632.1 |
$x^{9} - x^{8} + 3 x^{7} + 35 x^{6} - 94 x^{5} + 358 x^{4} - 593 x^{3} + 911 x^{2} - 661 x + 425$ |
$9$ |
[1,4] |
$2^{9}\cdot 3^{4}\cdot 23^{8}$ |
$3$ |
$52.9064510038$ |
$104.66721719548653$ |
|
|
|
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$160929.86488$ |
| 9.1.3653677329270336.1 |
$x^{9} - 4 x^{8} + 25 x^{7} - 60 x^{6} + 155 x^{5} - 212 x^{4} + 171 x^{3} + 20 x^{2} - 176 x - 64$ |
$9$ |
[1,4] |
$2^{6}\cdot 3^{6}\cdot 23^{8}$ |
$3$ |
$53.603388402$ |
$95.7207822122898$ |
|
|
? |
$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T30) |
trivial |
$2$ |
$4$ |
$41313.3107106$ |
| 9.1.8019044892774400.1 |
$x^{9} - 4 x^{8} + 2 x^{7} + 78 x^{6} - 328 x^{5} + 340 x^{4} + 401 x^{3} - 348 x^{2} - 958 x + 856$ |
$9$ |
[1,4] |
$2^{12}\cdot 5^{2}\cdot 23^{8}$ |
$3$ |
$58.495807201$ |
$102.67264229377021$ |
|
|
|
$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T30) |
trivial |
$2$ |
$4$ |
$199972.818026$ |
| 9.5.12529757644960000.1 |
$x^{9} - x^{8} - 20 x^{7} + 58 x^{6} - 94 x^{5} + 82 x^{4} - 18 x^{3} - 32 x^{2} + 75 x - 35$ |
$9$ |
[5,2] |
$2^{8}\cdot 5^{4}\cdot 23^{8}$ |
$3$ |
$61.4695872193$ |
$81.49133019274275$ |
|
|
? |
$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T30) |
trivial |
$2$ |
$6$ |
$375935.126178$ |
| 9.1.14614709317081344.1 |
$x^{9} - 3 x^{8} + 4 x^{7} + 2 x^{6} - 24 x^{5} + 238 x^{4} - 610 x^{3} - 18 x^{2} + 2773 x - 4793$ |
$9$ |
[1,4] |
$2^{8}\cdot 3^{6}\cdot 23^{8}$ |
$3$ |
$62.5299091906$ |
$111.66107214157705$ |
|
|
? |
$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T30) |
$[3]$ |
$2$ |
$4$ |
$41776.3216215$ |
| 9.5.28191954701160000.1 |
$x^{9} - 2 x^{8} - 11 x^{7} - 42 x^{6} + 129 x^{5} + 600 x^{4} - 485 x^{3} - 1658 x^{2} - 626 x - 210$ |
$9$ |
[5,2] |
$2^{6}\cdot 3^{2}\cdot 5^{4}\cdot 23^{8}$ |
$4$ |
$67.2653935793$ |
$99.80608871644023$ |
|
|
? |
$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T30) |
trivial |
$2$ |
$6$ |
$981604.808622$ |
| 9.1.117515422287300625.1 |
$x^{9} - 3 x^{8} + 27 x^{7} - 67 x^{6} + 390 x^{5} - 475 x^{4} + 2633 x^{3} - 1191 x^{2} + 1669 x + 13400$ |
$9$ |
[1,4] |
$5^{4}\cdot 7^{4}\cdot 23^{8}$ |
$3$ |
$78.8274009104$ |
$96.04146261452098$ |
|
|
|
$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T30) |
$[4]$ |
$2$ |
$4$ |
$419640.600702$ |
| 9.1.131532383853732096.1 |
$x^{9} - 2 x^{8} - 34 x^{7} + 50 x^{6} + 336 x^{5} - 504 x^{4} - 1060 x^{3} + 1424 x^{2} + 11656 x + 41512$ |
$9$ |
[1,4] |
$2^{8}\cdot 3^{8}\cdot 23^{8}$ |
$3$ |
$79.82055505843509$ |
$171.1783942507293$ |
|
|
? |
$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T30) |
trivial |
$2$ |
$4$ |
$509490.5851265325$ |
| 9.1.166470673314879684.1 |
$x^{9} - 69 x^{6} + 1587 x^{3} + 2116$ |
$9$ |
[1,4] |
$2^{2}\cdot 3^{12}\cdot 23^{8}$ |
$3$ |
$81.9373606959$ |
$118.51677254412442$ |
|
|
? |
$(C_3^3:C_3):C_2$ (as 9T21) |
trivial |
$2$ |
$4$ |
$229115.26089$ |
| 9.1.199...449.1 |
$x^{9} - 16767 x^{4} - 217971 x^{3} - 1810836 x^{2} - 7243344 x - 10814715$ |
$9$ |
[1,4] |
$3^{26}\cdot 23^{8}$ |
$2$ |
$387.9493553459356$ |
$465.902717571641$ |
|
|
? |
$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T30) |
$[8]$ |
$2$ |
$4$ |
$30800203.2192838$ |
| 10.2.332...000.1 |
$x^{10} - 690 x^{7} + 158700 x^{4} - 12167000 x + 22667121$ |
$10$ |
[2,4] |
$2^{11}\cdot 3^{12}\cdot 5^{8}\cdot 23^{8}$ |
$4$ |
$356.645520142$ |
$2601.081123171644$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$4199739778.22$ |
| 10.2.849...000.1 |
$x^{10} - 33534 x^{5} - 4471200 x^{3} - 74520000 x + 281132289$ |
$10$ |
[2,4] |
$2^{15}\cdot 3^{25}\cdot 5^{8}\cdot 23^{8}$ |
$4$ |
$1962.93718682$ |
$17653.93490151343$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$26062528660400$ |
| 10.0.133...000.1 |
$x^{10} - 26082 x^{5} + 579600 x^{3} - 1610000 x + 170067681$ |
$10$ |
[0,5] |
$-\,2^{10}\cdot 3^{10}\cdot 5^{11}\cdot 7^{8}\cdot 23^{8}$ |
$5$ |
$2053.42552398$ |
$30335.783313274234$ |
|
|
? |
$S_{10}$ (as 10T45) |
$[3]$ |
$2$ |
$4$ |
$9836152021940$ |
| 10.2.924...000.1 |
$x^{10} - 160 x^{8} - 1600 x^{7} + 29040 x^{6} + 111040 x^{5} - 1933280 x^{4} - 4310400 x^{3} + 66307880 x^{2} + 65270400 x - 917798472$ |
$10$ |
[2,4] |
$2^{19}\cdot 3^{10}\cdot 5^{18}\cdot 23^{8}$ |
$4$ |
$2492.33561264$ |
$26367.317845528076$ |
|
|
|
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$136616577799000$ |
| 10.2.711...000.1 |
$x^{10} - 3450 x^{7} + 3967500 x^{4} - 1520875000 x + 5100102225$ |
$10$ |
[2,4] |
$2^{11}\cdot 3^{19}\cdot 5^{18}\cdot 23^{8}$ |
$4$ |
$3847.61541325$ |
$29073.309426575124$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$533778400213000$ |
| 10.0.431...000.1 |
$x^{10} + 900 x^{8} - 19800 x^{7} + 317250 x^{6} - 2485080 x^{5} + 13271400 x^{4} - 32329800 x^{3} + 49679325 x^{2} + 33742200 x + 165200580$ |
$10$ |
[0,5] |
$-\,2^{10}\cdot 3^{24}\cdot 5^{19}\cdot 23^{8}$ |
$4$ |
$7303.75647012$ |
$40833.874212151415$ |
|
|
? |
$S_{10}$ (as 10T45) |
$[2, 2]$ |
$2$ |
$4$ |
$1406320448360000$ |
| 10.0.758...000.1 |
$x^{10} + 1152 x^{8} - 360 x^{7} + 517050 x^{6} - 37800 x^{5} + 115470000 x^{4} - 675000 x^{3} + 12969703125 x^{2} - 1875000 x + 583571250000$ |
$10$ |
[0,5] |
$-\,2^{11}\cdot 3^{24}\cdot 5^{7}\cdot 11^{8}\cdot 23^{8}$ |
$5$ |
$7726.79564806$ |
$119435.79829978883$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$4$ |
$10007039169600000$ |
| 10.0.414...000.1 |
$x^{10} - 838350 x^{5} + 558900000 x^{3} - 46575000000 x + 175707680625$ |
$10$ |
[0,5] |
$-\,2^{15}\cdot 3^{25}\cdot 5^{19}\cdot 23^{8}$ |
$4$ |
$11528.5160187$ |
$78442.91514510846$ |
|
|
? |
$S_{10}$ (as 10T45) |
$[2, 2]$ |
$2$ |
$4$ |
$23449906840200000$ |
| 10.0.221...000.1 |
$x^{10} + 450 x^{8} - 14400 x^{7} + 599400 x^{6} - 8536320 x^{5} + 96325200 x^{4} - 568684800 x^{3} + 3016731600 x^{2} - 6999859200 x + 23436876960$ |
$10$ |
[0,5] |
$-\,2^{19}\cdot 3^{24}\cdot 5^{19}\cdot 23^{8}$ |
$4$ |
$13629.2914976$ |
$76198.70362440265$ |
|
|
? |
$S_{10}$ (as 10T45) |
$[2]$ |
$2$ |
$4$ |
$68649670193200000$ |
| 10.0.802...000.1 |
$x^{10} - 1639440 x^{5} + 1457280000 x^{3} - 161920000000 x + 671940878400$ |
$10$ |
[0,5] |
$-\,2^{19}\cdot 3^{14}\cdot 5^{19}\cdot 11^{8}\cdot 23^{8}$ |
$5$ |
$30936.1434976$ |
$146446.58955424774$ |
|
|
? |
$S_{10}$ (as 10T45) |
$[2]$ |
$2$ |
$4$ |
$7146134103780000000$ |
| 10.0.442...000.1 |
$x^{10} - 70421400 x^{5} + 281685600000 x^{3} - 140842800000000 x + 1239793394490000$ |
$10$ |
[0,5] |
$-\,2^{14}\cdot 3^{22}\cdot 5^{19}\cdot 7^{8}\cdot 23^{8}$ |
$5$ |
$36695.4707443$ |
$144594.38809596232$ |
|
|
? |
$S_{10}$ (as 10T45) |
$[2, 2]$ |
$2$ |
$4$ |
$6809849089430000000$ |
| 12.2.233...112.1 |
$x^{12} - 64 x^{9} + 368 x^{3} + 2944$ |
$12$ |
[2,5] |
$-\,2^{8}\cdot 3^{19}\cdot 23^{8}$ |
$3$ |
$73.1050212624$ |
$171.1783942507293$ |
|
|
? |
$C_3^3:S_4$ (as 12T177) |
trivial |
$2$ |
$6$ |
$15403399.8971$ |
| 12.2.597...347.1 |
$x^{12} - x^{11} + 13 x^{10} + 54 x^{9} + 348 x^{8} + 1416 x^{7} + 2856 x^{6} + 6720 x^{5} + 6816 x^{4} + 4528 x^{3} + 215 x^{2} - 338 x - 57$ |
$12$ |
[2,5] |
$-\,3^{27}\cdot 23^{8}$ |
$2$ |
$95.7946776735$ |
$465.902717571641$ |
|
|
? |
$C_3^3:S_4$ (as 12T177) |
trivial |
$2$ |
$6$ |
$63508116.7925$ |
