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 |
9.5.453771377.1 |
$x^{9} - x^{8} - 3 x^{7} + 3 x^{6} + 2 x^{5} - x^{4} - 3 x^{2} + 1$ |
$9$ |
[5,2] |
$453771377$ |
$1$ |
$9.15947936661$ |
$21301.910172564338$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$6$ |
$5.89844215304$ |
9.5.455809769.1 |
$x^{9} - x^{6} - 3 x^{5} + 4 x^{4} + x^{3} - 4 x^{2} + 1$ |
$9$ |
[5,2] |
$109\cdot 4181741$ |
$2$ |
$9.16404197719$ |
$21349.701848035256$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$6$ |
$5.9132753462$ |
9.5.460080721.1 |
$x^{9} - x^{8} - 2 x^{7} + 2 x^{5} + x^{4} - 5 x^{3} - x^{2} + 3 x + 1$ |
$9$ |
[5,2] |
$41\cdot 11221481$ |
$2$ |
$9.17354329592$ |
$21449.492324994546$ |
|
|
? |
$S_9$ (as 9T34) |
trivial |
$2$ |
$6$ |
$5.955048869306523$ |
9.5.467890073.1 |
$x^{9} - 2 x^{8} + x^{7} + 2 x^{6} - 5 x^{5} + 2 x^{4} + x^{3} - 3 x^{2} + x + 1$ |
$9$ |
[5,2] |
$7^{6}\cdot 41\cdot 97$ |
$3$ |
$9.19071532866$ |
$230.76847964399414$ |
|
|
✓ |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$6.00908707275$ |
9.5.507490937.1 |
$x^{9} - x^{8} - 5 x^{7} + 5 x^{6} + 7 x^{5} - 8 x^{4} - 2 x^{3} + 4 x^{2} - x - 1$ |
$9$ |
[5,2] |
$507490937$ |
$1$ |
$9.2740580522$ |
$22527.559499422037$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$6$ |
$6.32032258654$ |
9.5.672128737.1 |
$x^{9} - x^{8} - 4 x^{6} + 4 x^{5} + x^{4} - 5 x^{3} + 5 x^{2} + x - 1$ |
$9$ |
[5,2] |
$7^{6}\cdot 29\cdot 197$ |
$3$ |
$9.56815168396$ |
$276.5863896330595$ |
|
|
? |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$7.55238207911$ |
9.5.678717521.1 |
$x^{9} - x^{8} - 2 x^{7} + 7 x^{6} - 5 x^{5} - 5 x^{4} + 9 x^{3} - x^{2} - 3 x + 1$ |
$9$ |
[5,2] |
$678717521$ |
$1$ |
$9.57852825147$ |
$26052.20760319555$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$6$ |
$7.569374672378502$ |
9.5.689278977.1 |
$x^{9} - 3 x^{8} + 9 x^{6} - 9 x^{5} - 6 x^{4} + 11 x^{3} - 3 x + 1$ |
$9$ |
[5,2] |
$3^{12}\cdot 1297$ |
$2$ |
$9.59497599462$ |
$155.82303573761126$ |
|
|
✓ |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$7.6705025888$ |
9.5.710045729.1 |
$x^{9} - 3 x^{7} - 2 x^{6} + 3 x^{5} + 3 x^{4} - x^{3} + x^{2} - 1$ |
$9$ |
[5,2] |
$109\cdot 541\cdot 12041$ |
$3$ |
$9.62667383828$ |
$26646.683264526564$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$6$ |
$7.85677083129401$ |
9.5.741306349.1 |
$x^{9} - 4 x^{8} + 6 x^{7} - 8 x^{6} + 11 x^{5} - 7 x^{4} + 4 x^{3} - 3 x^{2} - 2 x + 1$ |
$9$ |
[5,2] |
$7^{6}\cdot 6301$ |
$2$ |
$9.67286891182$ |
$290.4714369409525$ |
|
|
✓ |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$8.21022401044$ |
9.5.823660649.1 |
$x^{9} - x^{8} + 4 x^{6} - 6 x^{5} - 3 x^{4} + 8 x^{3} + 2 x^{2} - 3 x - 1$ |
$9$ |
[5,2] |
$7^{6}\cdot 7001$ |
$2$ |
$9.78675467486$ |
$306.1813489978226$ |
|
|
✓ |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$8.5381469526$ |
9.5.830248993.1 |
$x^{9} - x^{8} - 2 x^{7} + 3 x^{6} + x^{5} - 6 x^{4} - x^{3} + 5 x^{2} - 1$ |
$9$ |
[5,2] |
$7^{6}\cdot 7057$ |
$2$ |
$9.79542200247$ |
$307.40346045185186$ |
|
|
✓ |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$8.57688308628$ |
9.5.840423481.1 |
$x^{9} - 2 x^{8} - x^{7} + 2 x^{6} - x^{5} + 6 x^{4} - 4 x^{3} - x - 1$ |
$9$ |
[5,2] |
$2293\cdot 366517$ |
$2$ |
$9.80868773281$ |
$28990.058313152804$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$6$ |
$8.723677925848085$ |
9.5.865377817.1 |
$x^{9} - 2 x^{8} + 3 x^{6} - 5 x^{5} + 5 x^{3} + x^{2} - x - 1$ |
$9$ |
[5,2] |
$865377817$ |
$1$ |
$9.8406290723$ |
$29417.304720181284$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$6$ |
$9.131853525653796$ |
9.5.960133489.1 |
$x^{9} - 3 x^{8} + 2 x^{7} - x^{5} + 4 x^{4} - 4 x^{3} - 2 x^{2} + 3 x + 1$ |
$9$ |
[5,2] |
$7^{6}\cdot 8161$ |
$2$ |
$9.95489873179$ |
$330.57528594593737$ |
|
|
? |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$9.71382080416$ |
9.5.1021310969.1 |
$x^{9} - x^{8} + 3 x^{7} - 6 x^{6} + 2 x^{5} - 4 x^{4} + x^{3} + 5 x^{2} - x - 1$ |
$9$ |
[5,2] |
$7^{6}\cdot 8681$ |
$2$ |
$10.023457543$ |
$340.94440776104506$ |
|
|
✓ |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$9.79641964427$ |
9.5.1058958649.1 |
$x^{9} + 2 x^{7} - 4 x^{6} - x^{5} - 3 x^{4} + 2 x^{3} + 6 x^{2} - 5 x + 1$ |
$9$ |
[5,2] |
$7^{6}\cdot 9001$ |
$2$ |
$10.0638541356$ |
$347.17150665476555$ |
|
|
✓ |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$10.4133226688$ |
9.5.1087194409.1 |
$x^{9} - x^{8} - 4 x^{7} - x^{6} + 8 x^{5} + 7 x^{4} - 3 x^{3} - 6 x^{2} - x + 1$ |
$9$ |
[5,2] |
$7^{6}\cdot 9241$ |
$2$ |
$10.09332214$ |
$351.76949756907226$ |
|
|
✓ |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$10.3008784678$ |
9.5.1091048373.1 |
$x^{9} - 3 x^{7} - x^{6} + 3 x^{5} - x^{3} + 3 x^{2} - 1$ |
$9$ |
[5,2] |
$3^{12}\cdot 2053$ |
$2$ |
$10.0972913933$ |
$196.04517030146403$ |
|
|
✓ |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$10.4179310363$ |
9.5.1149783677.1 |
$x^{9} - 2 x^{8} - 4 x^{7} + 8 x^{6} + 7 x^{5} - 9 x^{4} - 8 x^{3} + x^{2} + 4 x + 1$ |
$9$ |
[5,2] |
$7^{6}\cdot 29\cdot 337$ |
$3$ |
$10.1562907818$ |
$361.75341759911805$ |
|
|
✓ |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$10.6926461036$ |
9.5.1209078773.1 |
$x^{9} - 2 x^{8} + 3 x^{6} - 6 x^{5} + 4 x^{4} + 2 x^{3} - 4 x^{2} + 4 x - 1$ |
$9$ |
[5,2] |
$7^{6}\cdot 43\cdot 239$ |
$3$ |
$10.2131949505$ |
$370.96409038808986$ |
|
|
✓ |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$11.128579116$ |
9.5.1209078773.2 |
$x^{9} - 3 x^{8} + x^{7} + x^{6} + x^{5} + 4 x^{4} - 5 x^{3} - 3 x^{2} + 3 x + 1$ |
$9$ |
[5,2] |
$7^{6}\cdot 43\cdot 239$ |
$3$ |
$10.2131949505$ |
$370.96409038808986$ |
|
|
✓ |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$11.1353177196$ |
9.5.1215667117.1 |
$x^{9} - x^{8} - 4 x^{7} + 6 x^{6} + x^{5} - 7 x^{4} + 4 x^{3} + x^{2} - x + 1$ |
$9$ |
[5,2] |
$7^{6}\cdot 10333$ |
$2$ |
$10.2193636177$ |
$371.97342026159566$ |
|
|
✓ |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$11.1708382468$ |
9.5.1238726321.1 |
$x^{9} - 2 x^{8} - 2 x^{7} + 6 x^{6} - 5 x^{5} + 4 x^{3} + 2 x^{2} - 4 x + 1$ |
$9$ |
[5,2] |
$7^{6}\cdot 10529$ |
$2$ |
$10.2407224594$ |
$375.4847093609451$ |
|
|
? |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$10.9623890042$ |
9.5.1263235257.1 |
$x^{9} - 2 x^{6} - 4 x^{3} + 3 x + 1$ |
$9$ |
[5,2] |
$3^{12}\cdot 2377$ |
$2$ |
$10.2630401163$ |
$210.94841366208323$ |
|
|
✓ |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$11.0427461597$ |
9.5.1274962213.1 |
$x^{9} - 2 x^{8} - 2 x^{7} + 8 x^{6} - 3 x^{5} - 9 x^{4} + 8 x^{3} + 3 x^{2} - 4 x - 1$ |
$9$ |
[5,2] |
$7^{6}\cdot 10837$ |
$2$ |
$10.2735827583$ |
$380.937063822793$ |
|
|
✓ |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$11.479403783$ |
9.5.1299958592.1 |
$x^{9} - 2 x^{8} - 3 x^{7} + 9 x^{6} - x^{5} - 14 x^{4} + 10 x^{3} + 7 x^{2} - 7 x + 1$ |
$9$ |
[5,2] |
$2^{6}\cdot 37^{3}\cdot 401$ |
$3$ |
$10.2957700768$ |
$193.35691669702553$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$6$ |
$11.6514404114$ |
9.5.1330963137.1 |
$x^{9} - 2 x^{8} + 2 x^{7} + x^{6} - 8 x^{5} + 14 x^{4} - 13 x^{3} + 2 x^{2} + 3 x - 1$ |
$9$ |
[5,2] |
$3^{3}\cdot 7^{6}\cdot 419$ |
$3$ |
$10.3227693878$ |
$129.73774114425706$ |
|
|
? |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$11.4732826838$ |
9.5.1512142597.1 |
$x^{9} - 2 x^{8} + x^{7} - 2 x^{6} - 2 x^{5} + 5 x^{4} + 4 x^{3} - 3 x - 1$ |
$9$ |
[5,2] |
$7^{6}\cdot 12853$ |
$2$ |
$10.4701945071$ |
$414.85941166281214$ |
|
|
? |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$12.8545958634$ |
9.5.1610967757.1 |
$x^{9} - 4 x^{8} + 5 x^{7} + x^{6} - 7 x^{5} + 6 x^{4} - x^{3} - 5 x^{2} + 2 x + 1$ |
$9$ |
[5,2] |
$7^{6}\cdot 13693$ |
$2$ |
$10.544103246$ |
$428.20131573818907$ |
|
|
✓ |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$13.3770802693$ |
9.5.1619909081.1 |
$x^{9} - x^{8} + 2 x^{7} - 7 x^{6} + 7 x^{3} + 3 x^{2} - 3 x - 1$ |
$9$ |
[5,2] |
$7^{8}\cdot 281$ |
$2$ |
$10.5505897878$ |
$94.52602987072896$ |
|
|
? |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$13.3970481809$ |
9.5.1626740901.1 |
$x^{9} - 3 x^{7} - 4 x^{6} + 3 x^{5} + 9 x^{4} - 6 x^{2} + 1$ |
$9$ |
[5,2] |
$3^{12}\cdot 3061$ |
$2$ |
$10.5555245628$ |
$239.38301786312434$ |
|
|
✓ |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$13.2920242823$ |
9.5.1630732789.1 |
$x^{9} + x^{7} - x^{6} - 2 x^{5} - 3 x^{4} - 3 x^{3} + 3 x^{2} + 4 x + 1$ |
$9$ |
[5,2] |
$7^{6}\cdot 83\cdot 167$ |
$3$ |
$10.5583994718$ |
$430.8201177647773$ |
|
|
✓ |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$13.4684200729$ |
9.5.1653791993.1 |
$x^{9} - 2 x^{7} - 3 x^{6} - x^{5} + 4 x^{4} + 4 x^{3} + x^{2} - 2 x - 1$ |
$9$ |
[5,2] |
$7^{6}\cdot 14057$ |
$2$ |
$10.5748850166$ |
$433.85540846417985$ |
|
|
✓ |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$12.9974380833$ |
9.5.1669812553.1 |
$x^{9} - 4 x^{5} + 3 x - 1$ |
$9$ |
[5,2] |
$37\cdot 757\cdot 59617$ |
$3$ |
$10.586218606$ |
$40863.339963835555$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$6$ |
$12.99379870020899$ |
9.5.1684851329.1 |
$x^{9} - 3 x^{8} + 3 x^{7} - 2 x^{6} - 5 x^{5} + 13 x^{4} - 2 x^{3} - 5 x^{2} + 1$ |
$9$ |
[5,2] |
$7^{6}\cdot 14321$ |
$2$ |
$10.59677003$ |
$437.9105071580079$ |
|
|
✓ |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$13.7141696567$ |
9.5.1699910401.1 |
$x^{9} - 4 x^{8} + 4 x^{7} + x^{6} - 5 x^{5} + 4 x^{4} - x^{3} + 5 x^{2} - 5 x + 1$ |
$9$ |
[5,2] |
$7^{6}\cdot 14449$ |
$2$ |
$10.6072521392$ |
$439.8631589700912$ |
|
|
? |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$13.3763049081$ |
9.5.1730969737.1 |
$x^{9} - x^{8} - 3 x^{7} + 5 x^{6} - 2 x^{5} - 3 x^{4} + 7 x^{3} - 4 x - 1$ |
$9$ |
[5,2] |
$7^{6}\cdot 14713$ |
$2$ |
$10.6286133465$ |
$443.86337475050937$ |
|
|
? |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$13.7667614034$ |
9.5.1742734637.1 |
$x^{9} - x^{8} - x^{7} + 6 x^{6} - x^{5} - 4 x^{4} + 3 x^{3} - 3 x - 1$ |
$9$ |
[5,2] |
$7^{6}\cdot 14813$ |
$2$ |
$10.6366158263$ |
$445.3692257810948$ |
|
|
✓ |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$13.7796253945$ |
9.5.1783676489.1 |
$x^{9} - 2 x^{8} + 2 x^{7} - 2 x^{6} - 4 x^{5} + 9 x^{4} - 7 x^{3} + 5 x - 1$ |
$9$ |
[5,2] |
$7^{6}\cdot 15161$ |
$2$ |
$10.6640951097$ |
$450.5703581396421$ |
|
|
? |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$14.3680714141$ |
9.5.1790264833.1 |
$x^{9} - 2 x^{8} + 2 x^{7} + 2 x^{6} - 7 x^{5} + 4 x^{4} - 2 x^{3} - 6 x^{2} + 6 x + 1$ |
$9$ |
[5,2] |
$7^{6}\cdot 15217$ |
$2$ |
$10.6684645901$ |
$451.40172425205924$ |
|
|
? |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$14.1931912755$ |
9.5.1837191537.1 |
$x^{9} - 3 x^{8} + 7 x^{6} - 6 x^{5} + 5 x^{3} - 6 x^{2} + 1$ |
$9$ |
[5,2] |
$3^{12}\cdot 3457$ |
$2$ |
$10.6991799724$ |
$254.39663517156413$ |
|
|
✓ |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$13.6940072971$ |
9.5.1861324829.1 |
$x^{9} - x^{8} + 4 x^{7} - x^{6} + 2 x^{5} + 5 x^{4} - 12 x^{3} - x^{2} + 5 x - 1$ |
$9$ |
[5,2] |
$7^{6}\cdot 13\cdot 1217$ |
$3$ |
$10.7147055611$ |
$460.2731685624242$ |
|
|
? |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$14.5686204324$ |
9.5.1890972377.1 |
$x^{9} - 2 x^{8} + x^{7} + x^{6} + x^{5} + x^{4} - 8 x^{3} - x^{2} + 4 x + 1$ |
$9$ |
[5,2] |
$7^{6}\cdot 16073$ |
$2$ |
$10.7335355321$ |
$463.9243476095044$ |
|
|
? |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$14.4555866466$ |
9.5.1928620057.1 |
$x^{9} - 4 x^{8} + 6 x^{7} - 4 x^{6} - 2 x^{5} + 5 x^{4} - 4 x^{3} - x^{2} + 3 x + 1$ |
$9$ |
[5,2] |
$7^{6}\cdot 13^{2}\cdot 97$ |
$3$ |
$10.7570719989$ |
$199.2569425075224$ |
|
|
✓ |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$15.0276828703$ |
9.5.2096622829.1 |
$x^{9} - x^{8} + x^{7} - 2 x^{6} - 3 x^{5} - 5 x^{3} + 2 x^{2} + 5 x + 1$ |
$9$ |
[5,2] |
$7^{6}\cdot 71\cdot 251$ |
$3$ |
$10.8573660213$ |
$488.5001804066271$ |
|
|
? |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$16.2490777372$ |
9.5.2116387861.1 |
$x^{9} - 4 x^{8} + 5 x^{7} + 3 x^{6} - 17 x^{5} + 20 x^{4} - 7 x^{3} - 5 x^{2} + 4 x + 1$ |
$9$ |
[5,2] |
$7^{6}\cdot 17989$ |
$2$ |
$10.8686912379$ |
$490.7973444592458$ |
|
|
✓ |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$16.1524193705$ |
9.5.2143301553.1 |
$x^{9} - 3 x^{7} + 3 x^{5} - 4 x^{3} + 3 x - 1$ |
$9$ |
[5,2] |
$3^{12}\cdot 37\cdot 109$ |
$3$ |
$10.8839623542$ |
$274.77409362113264$ |
|
|
✓ |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$14.9148673744$ |
9.5.2159425756.1 |
$x^{9} - x^{8} + 2 x^{6} - 4 x^{5} + 4 x^{4} - 7 x^{2} + 2 x + 2$ |
$9$ |
[5,2] |
$2^{2}\cdot 539856439$ |
$2$ |
$10.8930299433$ |
$46469.621862029395$ |
|
|
? |
$S_9$ (as 9T34) |
trivial |
$2$ |
$6$ |
$24.603917125$ |
9.5.2165800441.1 |
$x^{9} - x^{8} - 2 x^{6} - 2 x^{5} - 4 x^{3} - 2 x^{2} + 2 x + 1$ |
$9$ |
[5,2] |
$7^{6}\cdot 41\cdot 449$ |
$3$ |
$10.8965982118$ |
$496.4937572674992$ |
|
|
✓ |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$16.1061671291$ |