Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
6.0.336091.1 |
x6 - x5 + x4 + 5x2 + 4x + 1 |
$6$ |
[0,3] |
$-\,7^{2}\cdot 19^{3}$ |
$2$ |
$8.33827371165$ |
|
|
? |
$S_3\times C_3$ (as 6T5) |
trivial |
$2$ |
$2$ |
$2.3409784627$ |
6.0.528143.1 |
x6 - x5 + 3x4 - x3 + 2x2 + 2x + 1 |
$6$ |
[0,3] |
$-\,7\cdot 11\cdot 19^{3}$ |
$3$ |
$8.99066718532$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$3.15256501689$ |
6.0.2668151.1 |
x6 - x5 + 2x4 - 4x3 + 5x2 - 6x + 4 |
$6$ |
[0,3] |
$-\,19^{3}\cdot 389$ |
$2$ |
$11.7770106385$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$7.22316357391$ |
6.0.3841040.1 |
x6 - 2x5 + 2x4 + 2x3 + 2x2 - 8x + 7 |
$6$ |
[0,3] |
$-\,2^{4}\cdot 5\cdot 7\cdot 19^{3}$ |
$4$ |
$12.5143454241$ |
|
|
|
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$13.2942421582$ |
6.0.4149695.1 |
x6 - 2x5 + 4x4 + x3 + 3x2 + 6x + 4 |
$6$ |
[0,3] |
$-\,5\cdot 11^{2}\cdot 19^{3}$ |
$3$ |
$12.6765973591$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$10.9226578915$ |
6.4.5027647.1 |
x6 - 3x5 - 3x4 + 8x3 + 7x2 - 3x - 2 |
$6$ |
[4,1] |
$-\,19^{3}\cdot 733$ |
$2$ |
$13.0886281523$ |
|
|
✓ |
$S_6$ (as 6T16) |
trivial |
$2$ |
$4$ |
$27.5366311582$ |
6.0.5377456.1 |
x6 - x5 - 5x3 + 10x2 - 5x + 1 |
$6$ |
[0,3] |
$-\,2^{4}\cdot 7^{2}\cdot 19^{3}$ |
$3$ |
$13.2361844615$ |
|
|
✓ |
$S_3\times C_3$ (as 6T5) |
$[3]$ |
$2$ |
$2$ |
$2.87637296087$ |
6.0.5377456.2 |
x6 - x5 - 2x4 + 11x3 + 18x2 + 7x + 1 |
$6$ |
[0,3] |
$-\,2^{4}\cdot 7^{2}\cdot 19^{3}$ |
$3$ |
$13.2361844615$ |
|
|
? |
$S_3\times C_3$ (as 6T5) |
$[3]$ |
$2$ |
$2$ |
$5.26788591245$ |
6.0.6035920.1 |
x6 - x5 + 2x4 - 7x3 + 16x2 - 11x + 5 |
$6$ |
[0,3] |
$-\,2^{4}\cdot 5\cdot 11\cdot 19^{3}$ |
$4$ |
$13.4934782235$ |
|
|
|
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$17.1303365085$ |
6.0.6591499.1 |
x6 - 9x4 - 14x3 + 25x2 + 25x + 125 |
$6$ |
[0,3] |
$-\,19^{3}\cdot 31^{2}$ |
$2$ |
$13.692960807$ |
|
|
? |
$D_{6}$ (as 6T3) |
trivial |
$2$ |
$2$ |
$7.32483413303$ |
6.0.6756115.1 |
x6 - 3x5 + 8x4 - 10x3 + 13x2 - 9x + 5 |
$6$ |
[0,3] |
$-\,5\cdot 19^{3}\cdot 197$ |
$3$ |
$13.7493712589$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$13.3230405322$ |
6.0.7414579.1 |
x6 - 4x4 - x3 + 4x2 + 2x + 5 |
$6$ |
[0,3] |
$-\,19^{3}\cdot 23\cdot 47$ |
$3$ |
$13.964147134$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$9.79724125963$ |
6.0.8347403.1 |
x6 + x4 - 2x3 + 5x2 - x + 1 |
$6$ |
[0,3] |
$-\,19^{3}\cdot 1217$ |
$2$ |
$14.2426859044$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$11.5959545008$ |
6.0.8896123.1 |
x6 - x5 - x4 + 2x3 + 3x + 5 |
$6$ |
[0,3] |
$-\,19^{3}\cdot 1297$ |
$2$ |
$14.3946175238$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$12.6350401061$ |
6.0.9911255.1 |
x6 - x5 + 6x3 + 14x2 + 15x + 9 |
$6$ |
[0,3] |
$-\,5\cdot 17^{2}\cdot 19^{3}$ |
$3$ |
$14.6562019866$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$16.8867242745$ |
6.0.10459975.1 |
x6 - 2x5 + 6x4 - 11x3 + 17x2 - 15x + 9 |
$6$ |
[0,3] |
$-\,5^{2}\cdot 19^{3}\cdot 61$ |
$3$ |
$14.7884199361$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$18.533334861$ |
6.4.10590296.1 |
x6 - x5 - 5x4 + 7x3 + 5x2 - 10x + 1 |
$6$ |
[4,1] |
$-\,2^{3}\cdot 19^{3}\cdot 193$ |
$3$ |
$14.8189699195$ |
|
|
✓ |
$S_6$ (as 6T16) |
trivial |
$2$ |
$4$ |
$44.5947147682$ |
6.0.12682291.1 |
x6 - 3x5 + 6x4 + 7x3 + 11x2 + 2x + 4 |
$6$ |
[0,3] |
$-\,19^{3}\cdot 43^{2}$ |
$2$ |
$15.2709581042$ |
|
|
|
$S_3\times C_3$ (as 6T5) |
trivial |
$2$ |
$2$ |
$22.7661138895$ |
6.0.13368191.1 |
x6 - 4x4 - x3 + 23x2 - 17x + 5 |
$6$ |
[0,3] |
$-\,19^{3}\cdot 1949$ |
$2$ |
$15.4056055432$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$21.4266793797$ |
6.0.13862039.1 |
x6 - x5 - 3x4 - 3x3 + 10x2 + 28x + 17 |
$6$ |
[0,3] |
$-\,19^{3}\cdot 43\cdot 47$ |
$3$ |
$15.499030018$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$18.8126717374$ |
6.0.15124095.1 |
x6 - 2x5 + 3x3 + 3x2 - x + 1 |
$6$ |
[0,3] |
$-\,3^{2}\cdot 5\cdot 7^{2}\cdot 19^{3}$ |
$4$ |
$15.7257572028$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
$[3]$ |
$2$ |
$2$ |
$8.86918469048$ |
6.0.15974611.1 |
x6 + 3x4 - 2x3 + 7x2 - 3x + 1 |
$6$ |
[0,3] |
$-\,17\cdot 19^{3}\cdot 137$ |
$3$ |
$15.8698095615$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$13.8301860891$ |
6.0.16468459.1 |
x6 - x5 + 10x4 - 7x3 + 75x2 - 16x + 239 |
$6$ |
[0,3] |
$-\,7^{4}\cdot 19^{3}$ |
$2$ |
$15.9505437935$ |
✓ |
✓ |
? |
$C_6$ (as 6T1) |
$[3]$ |
$2$ |
$2$ |
$2.10181872849$ |
6.0.17373847.1 |
x6 - 2x5 - 4x4 + 6x3 + 10x2 - 12x + 5 |
$6$ |
[0,3] |
$-\,17\cdot 19^{3}\cdot 149$ |
$3$ |
$16.0934565608$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$26.9248377723$ |
6.0.19205200.1 |
x6 - x5 - 2x4 - 3x3 + 6x2 - x + 7 |
$6$ |
[0,3] |
$-\,2^{4}\cdot 5^{2}\cdot 7\cdot 19^{3}$ |
$4$ |
$16.3645150193$ |
|
|
|
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$27.8462557594$ |
6.2.20741616.1 |
x6 - x5 - 6x4 + 14x2 + 16x + 4 |
$6$ |
[2,2] |
$2^{4}\cdot 3^{3}\cdot 7\cdot 19^{3}$ |
$4$ |
$16.5757720217$ |
|
|
|
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$3$ |
$121.936345332$ |
6.2.21036553.1 |
x6 - x5 - 3x4 + 15x3 - 18x2 + 13x - 3 |
$6$ |
[2,2] |
$19^{3}\cdot 3067$ |
$2$ |
$16.6148246871$ |
|
|
? |
$S_6$ (as 6T16) |
trivial |
$2$ |
$3$ |
$53.083313125$ |
6.0.21269759.1 |
x6 - x5 + 14x3 + 10x2 - 5x + 1 |
$6$ |
[0,3] |
$-\,7\cdot 19^{3}\cdot 443$ |
$3$ |
$16.6453818142$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$28.8628556961$ |
6.0.21352067.1 |
x6 + 7x4 - 2x3 + 17x2 - 7x + 1 |
$6$ |
[0,3] |
$-\,11\cdot 19^{3}\cdot 283$ |
$3$ |
$16.6561000382$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$28.8920193812$ |
6.0.23766435.1 |
x6 - 3x5 + 7x4 - 6x3 + 9x2 + 9 |
$6$ |
[0,3] |
$-\,3^{2}\cdot 5\cdot 7\cdot 11\cdot 19^{3}$ |
$5$ |
$16.9561535321$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$27.6126273408$ |
6.0.23793871.1 |
x6 - x5 - 3x4 + 7x3 + 5x2 - 12x + 7 |
$6$ |
[0,3] |
$-\,19^{3}\cdot 3469$ |
$2$ |
$16.9594143312$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$17.6989096879$ |
6.0.23876179.1 |
x6 - x5 + 12x4 - 11x3 + 73x2 + 26x + 172 |
$6$ |
[0,3] |
$-\,19^{3}\cdot 59^{2}$ |
$2$ |
$16.9691779644$ |
|
|
|
$D_{6}$ (as 6T3) |
trivial |
$2$ |
$2$ |
$26.5504287195$ |
6.0.24692400.1 |
x6 - x5 + 8x4 - 17x3 + 10x2 - 9x + 9 |
$6$ |
[0,3] |
$-\,2^{4}\cdot 3^{2}\cdot 5^{2}\cdot 19^{3}$ |
$4$ |
$17.0645124252$ |
|
|
? |
$S_3^2$ (as 6T9) |
$[3]$ |
$2$ |
$2$ |
$11.6203549343$ |
6.0.25001055.1 |
x6 + 6x4 - x3 + 9x2 - 3x + 5 |
$6$ |
[0,3] |
$-\,3^{6}\cdot 5\cdot 19^{3}$ |
$3$ |
$17.099879733$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$35.4382566042$ |
6.0.25138235.1 |
x6 - 3x5 + 11x4 - 14x3 + 35x2 - 16x + 35 |
$6$ |
[0,3] |
$-\,5\cdot 19^{3}\cdot 733$ |
$3$ |
$17.1154818509$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$39.381790529$ |
6.0.25522339.1 |
x6 - x5 + 12x4 - 10x3 + 44x2 - 18x + 45 |
$6$ |
[0,3] |
$-\,19^{3}\cdot 61^{2}$ |
$2$ |
$17.1587934127$ |
|
|
? |
$S_3\times C_3$ (as 6T5) |
trivial |
$2$ |
$2$ |
$32.2408021923$ |
6.0.25570352.1 |
x6 - 3x5 + 8x4 - 9x3 + 2x2 + x + 1 |
$6$ |
[0,3] |
$-\,2^{4}\cdot 19^{3}\cdot 233$ |
$3$ |
$17.1641690964$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
$[6]$ |
$2$ |
$2$ |
$3.80423987172$ |
6.0.25961315.1 |
x6 - x5 - 2x4 + 11x3 - x2 - 12x + 20 |
$6$ |
[0,3] |
$-\,5\cdot 19^{3}\cdot 757$ |
$3$ |
$17.2076321875$ |
|
|
|
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$45.1282741559$ |
6.0.30179600.1 |
x6 - 3x5 + 2x4 - x3 + 7x + 5 |
$6$ |
[0,3] |
$-\,2^{4}\cdot 5^{2}\cdot 11\cdot 19^{3}$ |
$4$ |
$17.6448882917$ |
|
|
|
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$41.6851730474$ |
6.2.31112424.1 |
x6 - x5 - 2x4 - 3x3 + 6x2 + 18x - 12 |
$6$ |
[2,2] |
$2^{3}\cdot 3^{4}\cdot 7\cdot 19^{3}$ |
$4$ |
$17.7346371857$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$3$ |
$153.855276722$ |
6.0.31613131.1 |
x6 - x5 - 2x4 - 7x3 - 11x2 + 32x + 43 |
$6$ |
[0,3] |
$-\,11\cdot 19^{3}\cdot 419$ |
$3$ |
$17.7818899654$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$31.2730653286$ |
6.0.31695439.1 |
x6 - 2x5 + 4x4 - 7x3 + 11x2 - 6x + 4 |
$6$ |
[0,3] |
$-\,19^{3}\cdot 4621$ |
$2$ |
$17.7895977676$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$32.4795564412$ |
6.2.31853196.1 |
x6 + 2x4 - 9x3 + x2 - 9x + 6 |
$6$ |
[2,2] |
$2^{2}\cdot 3^{3}\cdot 19^{3}\cdot 43$ |
$4$ |
$17.8043245503$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$3$ |
$122.469323824$ |
6.0.33176983.1 |
x6 - 2x5 + 8x4 - 5x3 + 15x2 - 12x + 20 |
$6$ |
[0,3] |
$-\,7\cdot 19^{3}\cdot 691$ |
$3$ |
$17.9255634257$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$49.9214110431$ |
6.0.33917755.1 |
x6 - 2x5 - x4 + 5x3 - 2x2 - 3x + 45 |
$6$ |
[0,3] |
$-\,5\cdot 19^{3}\cdot 23\cdot 43$ |
$4$ |
$17.9916578362$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$35.1193746553$ |
6.0.34349872.1 |
x6 - 8x4 - 2x3 + 16x2 + 8x + 20 |
$6$ |
[0,3] |
$-\,2^{4}\cdot 19^{3}\cdot 313$ |
$3$ |
$18.0296593173$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
$[3]$ |
$2$ |
$2$ |
$13.7796618545$ |
6.0.35097503.1 |
x6 - x5 + 5x4 - 3x3 + 11x2 + 7 |
$6$ |
[0,3] |
$-\,7\cdot 17\cdot 19^{3}\cdot 43$ |
$4$ |
$18.0944770748$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$27.7287311135$ |
6.0.35975455.1 |
x6 - 2x5 + 5x4 - 11x3 + 11x2 - 14x + 17 |
$6$ |
[0,3] |
$-\,5\cdot 19^{3}\cdot 1049$ |
$3$ |
$18.16914047$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$39.6124345562$ |
6.2.36297828.1 |
x6 - x5 - 8x3 + 21x2 - 7x - 14 |
$6$ |
[2,2] |
$2^{2}\cdot 3^{3}\cdot 7^{2}\cdot 19^{3}$ |
$4$ |
$18.19617506$ |
|
|
? |
$S_3^2$ (as 6T9) |
trivial |
$2$ |
$3$ |
$137.309649925$ |
6.2.36297828.2 |
x6 - x5 - 4x4 - 2x3 - 5x2 + 15x - 12 |
$6$ |
[2,2] |
$2^{2}\cdot 3^{3}\cdot 7^{2}\cdot 19^{3}$ |
$4$ |
$18.19617506$ |
|
|
? |
$S_3^2$ (as 6T9) |
trivial |
$2$ |
$3$ |
$139.723097096$ |