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 |
9.3.109880167.1 |
$x^{9} - 2 x^{8} + x^{7} + x^{6} - 3 x^{5} + x^{4} + 3 x^{3} - 2 x - 1$ |
$9$ |
[3,3] |
$-\,367\cdot 299401$ |
$2$ |
$7.82411957288$ |
$10482.374110858666$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$1.93836373256$ |
9.3.110852311.1 |
$x^{9} - x^{8} - 4 x^{7} + 2 x^{6} + 8 x^{5} - x^{4} - 8 x^{3} - 2 x^{2} + 3 x + 1$ |
$9$ |
[3,3] |
$-\,31^{3}\cdot 61^{2}$ |
$2$ |
$7.83178087654$ |
$86.27813264811779$ |
|
|
✓ |
$C_3 \wr S_3 $ (as 9T20) |
trivial |
$2$ |
$5$ |
$1.94853837145$ |
9.3.111543479.1 |
$x^{9} - x^{8} - x^{7} + 3 x^{6} - 2 x^{5} - x^{4} + 2 x^{3} - x^{2} - 1$ |
$9$ |
[3,3] |
$-\,111543479$ |
$1$ |
$7.83719161386$ |
$10561.414630625955$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$1.95734647671$ |
9.3.112700719.1 |
$x^{9} - x^{6} - x^{5} + 3 x^{4} + 2 x^{3} - 3 x^{2} - x + 1$ |
$9$ |
[3,3] |
$-\,7211\cdot 15629$ |
$2$ |
$7.84618458252$ |
$10616.059485515329$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$1.97058172746$ |
9.3.112978759.1 |
$x^{9} - 3 x^{8} + 2 x^{7} + 3 x^{6} - 5 x^{5} + x^{4} + 3 x^{3} - 3 x^{2} - x + 1$ |
$9$ |
[3,3] |
$-\,43\cdot 2627413$ |
$2$ |
$7.84833301095$ |
$10629.146673181249$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$1.9734591068$ |
9.3.112992391.1 |
$x^{9} - 2 x^{8} + x^{7} + 3 x^{6} - 6 x^{5} + 3 x^{4} + 2 x^{3} - 4 x^{2} + 2 x - 1$ |
$9$ |
[3,3] |
$-\,112992391$ |
$1$ |
$7.84843822516$ |
$10629.787909455203$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$1.97242112054$ |
9.3.113501567.1 |
$x^{9} - x^{8} - x^{7} + x^{6} - 3 x^{4} + x^{3} + 4 x^{2} - 1$ |
$9$ |
[3,3] |
$-\,53\cdot 797\cdot 2687$ |
$3$ |
$7.85236007762$ |
$10653.711419031399$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$1.97827200876$ |
9.3.113511599.1 |
$x^{9} - x^{8} - 2 x^{7} + 2 x^{6} + 3 x^{5} - 5 x^{4} - 3 x^{3} + 4 x^{2} + x - 1$ |
$9$ |
[3,3] |
$-\,193\cdot 727\cdot 809$ |
$3$ |
$7.85243719039$ |
$10654.182230467057$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$1.97953412598$ |
9.3.113931487.1 |
$x^{9} - 2 x^{6} - x^{5} - x^{4} + 2 x^{2} + x + 1$ |
$9$ |
[3,3] |
$-\,109\cdot 389\cdot 2687$ |
$3$ |
$7.85565931448$ |
$10673.86935464361$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$1.98338186845$ |
9.3.114479303.1 |
$x^{9} - 3 x^{8} + 4 x^{7} - x^{6} - 7 x^{5} + 11 x^{4} - 9 x^{3} + 3 x^{2} - x + 1$ |
$9$ |
[3,3] |
$-\,23^{3}\cdot 97^{2}$ |
$2$ |
$7.85984729638$ |
$101.2461243234224$ |
|
|
? |
$C_3 \wr S_3 $ (as 9T20) |
trivial |
$2$ |
$5$ |
$1.99189617114$ |
9.3.114807607.1 |
$x^{9} - x^{7} - 2 x^{6} + x^{5} + 4 x^{4} + 2 x^{3} - 2 x^{2} - 3 x - 1$ |
$9$ |
[3,3] |
$-\,29\cdot 3958883$ |
$2$ |
$7.86234860857$ |
$10714.83116992517$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$1.99317171241$ |
9.3.115041127.1 |
$x^{9} - x^{8} - 2 x^{7} + 3 x^{6} - 2 x^{4} - x^{3} + 2 x + 1$ |
$9$ |
[3,3] |
$-\,97\cdot 229\cdot 5179$ |
$3$ |
$7.86412390518$ |
$10725.722679614646$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$1.99470633921$ |
9.3.115270559.1 |
$x^{9} - 3 x^{8} + 3 x^{7} - 2 x^{6} + 2 x^{5} - 2 x^{4} - 2 x^{3} + 5 x^{2} - 4 x + 1$ |
$9$ |
[3,3] |
$-\,71\cdot 79\cdot 20551$ |
$3$ |
$7.86586500658$ |
$10736.412762184584$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$2.00001012155$ |
9.3.115691111.1 |
$x^{9} + 2 x^{7} - x^{6} + x^{4} - 5 x^{3} + 2 x^{2} + 2 x - 1$ |
$9$ |
[3,3] |
$-\,47\cdot 67\cdot 36739$ |
$3$ |
$7.86904848651$ |
$10755.980243566832$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$2.0022721667$ |
9.3.116188367.1 |
$x^{9} - 2 x^{7} - 3 x^{6} + x^{5} + 3 x^{4} + x^{3} - x^{2} + 1$ |
$9$ |
[3,3] |
$-\,116188367$ |
$1$ |
$7.87279935274$ |
$10779.070785554755$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$2.00837487251$ |
9.3.116817671.1 |
$x^{9} - x^{8} - 3 x^{7} + x^{6} + 5 x^{5} - 4 x^{3} + x + 1$ |
$9$ |
[3,3] |
$-\,53\cdot 2204107$ |
$2$ |
$7.8775258713974665$ |
$10808.222379281433$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$2.0168691883813112$ |
9.3.117283087.1 |
$x^{9} - 2 x^{8} - x^{7} + 5 x^{6} - 2 x^{5} - 2 x^{4} + x^{3} - x^{2} + x + 1$ |
$9$ |
[3,3] |
$-\,117283087$ |
$1$ |
$7.88100693794163$ |
$10829.73162179008$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$2.024209798952456$ |
9.3.118246927.1 |
$x^{9} - 4 x^{8} + 8 x^{7} - 12 x^{6} + 13 x^{5} - 10 x^{4} + 5 x^{3} - x^{2} + 1$ |
$9$ |
[3,3] |
$-\,31\cdot 3814417$ |
$2$ |
$7.88817708056$ |
$10874.140287857243$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$2.03050753091$ |
9.3.118347967.1 |
$x^{9} - x^{8} - 3 x^{7} + 2 x^{6} + 3 x^{5} - x^{4} + x^{2} - 2 x - 1$ |
$9$ |
[3,3] |
$-\,479\cdot 247073$ |
$2$ |
$7.888925720065851$ |
$10878.78518034068$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$2.034018940047565$ |
9.3.118357559.1 |
$x^{9} - 2 x^{8} + x^{6} + x^{4} - 3 x^{3} - 2 x^{2} + 2 x + 1$ |
$9$ |
[3,3] |
$-\,769\cdot 153911$ |
$2$ |
$7.888996760904876$ |
$10879.226029456324$ |
|
|
? |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$2.033105324327558$ |
9.3.118434167.1 |
$x^{9} - 4 x^{8} + 7 x^{7} - 9 x^{6} + 9 x^{5} - 7 x^{4} + 5 x^{3} - 2 x^{2} + 2 x - 1$ |
$9$ |
[3,3] |
$-\,31\cdot 3820457$ |
$2$ |
$7.889563956033352$ |
$10882.74629861415$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$2.0340630714495123$ |
9.3.118795951.1 |
$x^{9} - 2 x^{8} + x^{7} + 2 x^{6} - 4 x^{5} + x^{4} + 2 x^{3} - 3 x^{2} + 1$ |
$9$ |
[3,3] |
$-\,167\cdot 711353$ |
$2$ |
$7.89223815642$ |
$10899.355531406432$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$2.0358964195703666$ |
9.3.119070383.1 |
$x^{9} - x^{8} - 2 x^{7} + 3 x^{6} - 3 x^{4} + x^{3} + 2 x^{2} - x - 1$ |
$9$ |
[3,3] |
$-\,53\cdot 1327\cdot 1693$ |
$3$ |
$7.894261852578234$ |
$10911.93763728514$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$2.040657692881281$ |
9.3.119278283.1 |
$x^{9} - 3 x^{8} + 5 x^{7} - 8 x^{6} + 8 x^{5} - 5 x^{4} + 2 x^{3} + x^{2} - x + 1$ |
$9$ |
[3,3] |
$-\,119278283$ |
$1$ |
$7.895792175132679$ |
$10921.459746755467$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$2.046654077664487$ |
9.3.119747759.1 |
$x^{9} - 2 x^{8} + x^{7} + x^{6} - x^{5} - x^{4} + x^{3} - 2 x + 1$ |
$9$ |
[3,3] |
$-\,557\cdot 214987$ |
$2$ |
$7.899239218212771$ |
$10942.93191973705$ |
|
|
? |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$2.047212820083041$ |
9.3.119783879.1 |
$x^{9} - 2 x^{8} + 2 x^{7} + x^{6} - 5 x^{5} + 6 x^{4} - x^{3} - 3 x^{2} + 3 x - 1$ |
$9$ |
[3,3] |
$-\,101\cdot 1185979$ |
$2$ |
$7.899503924885698$ |
$10944.582175670299$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$2.05024605008869$ |
9.3.120155887.1 |
$x^{9} - 2 x^{8} + 2 x^{7} - 6 x^{5} + 11 x^{4} - 13 x^{3} + 10 x^{2} - 5 x + 1$ |
$9$ |
[3,3] |
$-\,23\cdot 5224169$ |
$2$ |
$7.902226077812687$ |
$10961.564076353337$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$2.050524505530881$ |
9.3.120802519.1 |
$x^{9} - 4 x^{8} + 8 x^{7} - 11 x^{6} + 10 x^{5} - 7 x^{4} + 3 x^{3} + 1$ |
$9$ |
[3,3] |
$-\,120802519$ |
$1$ |
$7.906940001997267$ |
$10991.019925375442$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$2.0608425295141637$ |
9.3.121463543.1 |
$x^{9} - x^{8} - 2 x^{7} + 2 x^{5} + 3 x^{4} - x^{3} - x^{2} - x - 1$ |
$9$ |
[3,3] |
$-\,121463543$ |
$1$ |
$7.911735716556479$ |
$11021.049995349807$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$2.0657539325710625$ |
9.3.121510799.1 |
$x^{9} - 2 x^{7} - 3 x^{6} + x^{5} + 5 x^{4} + 4 x^{3} - x^{2} - 3 x - 1$ |
$9$ |
[3,3] |
$-\,2207\cdot 55057$ |
$2$ |
$7.91207766859$ |
$11023.193684227816$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$2.06801444028$ |
9.3.122317991.1 |
$x^{9} - 2 x^{8} + 3 x^{7} - 3 x^{6} + x^{4} - 3 x^{3} + 2 x^{2} - x + 1$ |
$9$ |
[3,3] |
$-\,19^{2}\cdot 79\cdot 4289$ |
$3$ |
$7.9179004600705065$ |
$2537.2798426661575$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$2.0775237955639283$ |
9.3.122854967.1 |
$x^{9} - 2 x^{8} + x^{6} - x^{5} + 3 x^{3} + 2 x^{2} - 2 x - 1$ |
$9$ |
[3,3] |
$-\,122854967$ |
$1$ |
$7.9217551213300315$ |
$11083.99598520317$ |
|
|
? |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$2.0836377950782463$ |
9.3.122933791.1 |
$x^{9} - x^{7} - 3 x^{6} + 3 x^{4} + 2 x^{3} - 2 x - 1$ |
$9$ |
[3,3] |
$-\,149\cdot 825059$ |
$2$ |
$7.922319695291742$ |
$11087.551172373456$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$2.081902760370103$ |
9.3.123301207.1 |
$x^{9} - 2 x^{8} + 2 x^{7} - 3 x^{5} + 4 x^{4} - 2 x^{3} + 2 x - 1$ |
$9$ |
[3,3] |
$-\,379\cdot 325333$ |
$2$ |
$7.924947060603365$ |
$11104.107663382953$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$2.0891551855684356$ |
9.3.123396607.1 |
$x^{9} - 3 x^{8} + 4 x^{7} - 7 x^{5} + 9 x^{4} - 2 x^{3} - 4 x^{2} + 4 x - 1$ |
$9$ |
[3,3] |
$-\,123396607$ |
$1$ |
$7.925628120976266$ |
$11108.402540419573$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$2.0903472187296215$ |
9.3.123595631.1 |
$x^{9} - 2 x^{8} + 2 x^{6} - x^{5} + 2 x^{4} - 2 x^{3} - 2 x^{2} + 2 x + 1$ |
$9$ |
[3,3] |
$-\,43\cdot 2874317$ |
$2$ |
$7.927047447439633$ |
$11117.357194945209$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$2.0898538788515912$ |
9.3.123636223.1 |
$x^{9} - 3 x^{7} + 5 x^{5} - x^{4} - 2 x^{3} + x^{2} - x - 1$ |
$9$ |
[3,3] |
$-\,17^{2}\cdot 43\cdot 9949$ |
$3$ |
$7.92733667714477$ |
$4324.373767232704$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$2.091420076266321$ |
9.3.123668767.1 |
$x^{9} - x^{8} - 2 x^{7} + 5 x^{6} - x^{5} - 5 x^{4} + 6 x^{3} - 3 x + 1$ |
$9$ |
[3,3] |
$-\,123668767$ |
$1$ |
$7.927568501571172$ |
$11120.645979438425$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$2.092367943187346$ |
9.3.123972119.1 |
$x^{9} - x^{8} - 3 x^{7} + 3 x^{6} + 2 x^{5} - 3 x^{4} + x^{3} + 1$ |
$9$ |
[3,3] |
$-\,123972119$ |
$1$ |
$7.929726799194135$ |
$11134.276761424606$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$2.0938044391871804$ |
9.3.124007591.1 |
$x^{9} - x^{7} - 3 x^{6} - x^{5} + 3 x^{4} + 4 x^{3} + x^{2} - 2 x - 1$ |
$9$ |
[3,3] |
$-\,124007591$ |
$1$ |
$7.929978869764873$ |
$11135.86956640567$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$2.096434050847929$ |
9.3.124683371.1 |
$x^{9} - 2 x^{8} - x^{7} + 4 x^{6} - 4 x^{4} + 2 x^{3} + 2 x^{2} - 2 x - 1$ |
$9$ |
[3,3] |
$-\,124683371$ |
$1$ |
$7.934768886711151$ |
$11166.170829787623$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$2.1042228787639967$ |
9.3.124885927.1 |
$x^{9} - x^{8} + x^{6} - 2 x^{5} + 2 x^{4} - x^{3} - x^{2} + x - 1$ |
$9$ |
[3,3] |
$-\,17\cdot 7346231$ |
$2$ |
$7.936200135009763$ |
$11175.237223432889$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$2.1045734000862644$ |
9.3.125535947.1 |
$x^{9} - 2 x^{8} - x^{7} + 5 x^{6} - x^{5} - 5 x^{4} + x^{3} + 3 x^{2} - x - 1$ |
$9$ |
[3,3] |
$-\,125535947$ |
$1$ |
$7.940779242019193$ |
$11204.28252946167$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$2.112811739659526$ |
9.3.125785223.1 |
$x^{9} - 2 x^{7} - x^{6} + 2 x^{5} - x^{4} - 3 x^{3} + 3 x^{2} + x - 1$ |
$9$ |
[3,3] |
$-\,1013\cdot 124171$ |
$2$ |
$7.942529693222725$ |
$11215.401151987387$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$2.111808822163256$ |
9.3.126100423.1 |
$x^{9} - 3 x^{8} + x^{7} + 5 x^{6} - 5 x^{5} + 2 x^{3} - 2 x^{2} + x + 1$ |
$9$ |
[3,3] |
$-\,126100423$ |
$1$ |
$7.944738662802956$ |
$11229.444465333092$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$2.1188208372797885$ |
9.3.126180871.1 |
$x^{9} - x^{8} - x^{7} - x^{6} + x^{5} + 2 x^{4} + x^{3} - 2 x - 1$ |
$9$ |
[3,3] |
$-\,103\cdot 569\cdot 2153$ |
$3$ |
$7.945301668392246$ |
$11233.025905783357$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$2.1178231815653623$ |
9.3.126591211.1 |
$x^{9} - 3 x^{7} - x^{6} + x^{5} + 4 x^{4} + 3 x^{3} - 4 x^{2} - x + 1$ |
$9$ |
[3,3] |
$-\,126591211$ |
$1$ |
$7.948168428450958$ |
$11251.275972084233$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$2.1232828660446263$ |
9.3.128374559.1 |
$x^{9} - 2 x^{8} + x^{6} - x^{5} + 3 x^{4} - x^{3} - x^{2} - 1$ |
$9$ |
[3,3] |
$-\,128374559$ |
$1$ |
$7.960532269609266$ |
$11330.249732463975$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$2.1427495887847146$ |
9.3.128467639.1 |
$x^{9} - 3 x^{8} + 3 x^{7} + 2 x^{6} - 7 x^{5} + 5 x^{4} - 3 x^{2} + 2 x - 1$ |
$9$ |
[3,3] |
$-\,131\cdot 389\cdot 2521$ |
$3$ |
$7.961173386320041$ |
$11334.356576356684$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$2.145720386631395$ |
9.3.128607823.1 |
$x^{9} - x^{8} - 4 x^{7} + 4 x^{6} + 6 x^{5} - 3 x^{4} - 6 x^{3} + 3 x + 1$ |
$9$ |
[3,3] |
$-\,73\cdot 1761751$ |
$2$ |
$7.962138167334574$ |
$11340.538920174826$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$2.1428959225465967$ |