| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Narrow class group |
Unit group torsion |
Unit group rank |
Regulator |
| 6.4.218491.1 |
$x^{6} - 3 x^{5} + 2 x^{4} + x^{3} - 3 x^{2} + 2 x + 1$ |
$6$ |
(4, 1) |
$-\,7^{5}\cdot 13$ |
$2$ |
$7.76078392578$ |
$18.248200448594663$ |
|
|
✓ |
$A_4\times C_2$ (as 6T6) |
trivial |
$[2]$ |
$2$ |
$4$ |
$2.26526479968$ |
| 6.4.689087.1 |
$x^{6} - 2 x^{5} - 3 x^{4} + 13 x^{3} - 12 x^{2} - 4 x + 8$ |
$6$ |
(4, 1) |
$-\,7^{5}\cdot 41$ |
$2$ |
$9.39822149451$ |
$32.407109386315106$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$[2]$ |
$2$ |
$4$ |
$4.78391581904$ |
| 6.2.722701.1 |
$x^{6} - 2 x^{5} + 4 x^{4} - 8 x^{3} + 2 x^{2} - 11 x + 1$ |
$6$ |
(2, 2) |
$7^{5}\cdot 43$ |
$2$ |
$9.47312153875$ |
$33.18811562467677$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$[2]$ |
$2$ |
$3$ |
$3.31543456345$ |
| 6.6.1075648.1 |
$x^{6} - 7 x^{4} + 14 x^{2} - 7$ |
$6$ |
(6, 0) |
$2^{6}\cdot 7^{5}$ |
$2$ |
$10.1222803696$ |
$10.122280369592772$ |
|
✓ |
✓ |
$C_6$ (as 6T1) |
trivial |
$[2]$ |
$2$ |
$5$ |
$7.70329572133$ |
| 6.2.1075648.1 |
$x^{6} - 7 x^{2} - 7$ |
$6$ |
(2, 2) |
$2^{6}\cdot 7^{5}$ |
$2$ |
$10.1222803696$ |
$17.023578553967216$ |
|
|
✓ |
$A_4\times C_2$ (as 6T6) |
trivial |
$[2]$ |
$2$ |
$3$ |
$4.36334588378$ |
| 6.2.1193297.1 |
$x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x - 13$ |
$6$ |
(2, 2) |
$7^{5}\cdot 71$ |
$2$ |
$10.298913838$ |
$42.64592522013582$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$[2]$ |
$2$ |
$3$ |
$5.19019197896$ |
| 6.4.1630279.1 |
$x^{6} - x^{5} - 6 x^{4} - x^{3} + 8 x^{2} + 20 x + 8$ |
$6$ |
(4, 1) |
$-\,7^{5}\cdot 97$ |
$2$ |
$10.848682246$ |
$49.84644999501567$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$[2]$ |
$2$ |
$4$ |
$7.82884389736$ |
| 6.0.2100875.1 |
$x^{6} - x^{5} + 8 x^{4} - 8 x^{3} + 22 x^{2} - 22 x + 29$ |
$6$ |
(0, 3) |
$-\,5^{3}\cdot 7^{5}$ |
$2$ |
$11.3170534969$ |
$11.317053496860568$ |
✓ |
✓ |
? |
$C_6$ (as 6T1) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$2.10181872849$ |
| 6.2.2134489.1 |
$x^{6} - 3 x^{5} + 9 x^{4} - 13 x^{3} + 11 x^{2} - 5 x - 13$ |
$6$ |
(2, 2) |
$7^{5}\cdot 127$ |
$2$ |
$11.3470330593$ |
$57.03615323819114$ |
|
|
✓ |
$A_4\times C_2$ (as 6T6) |
trivial |
$[2]$ |
$2$ |
$3$ |
$6.83966611552$ |
| 6.0.3042067.1 |
$x^{6} - x^{5} + 8 x^{4} - 8 x^{3} + 29 x^{2} - 15 x + 29$ |
$6$ |
(0, 3) |
$-\,7^{5}\cdot 181$ |
$2$ |
$12.0372735242$ |
$68.09067729578774$ |
✓ |
|
? |
$A_4\times C_2$ (as 6T6) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$2.10181872849$ |
| 6.2.3546277.1 |
$x^{6} - 2 x^{5} + 4 x^{4} - 8 x^{3} + 2 x^{2} + 17 x - 41$ |
$6$ |
(2, 2) |
$7^{5}\cdot 211$ |
$2$ |
$12.3489142775$ |
$73.51730771528517$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$[2]$ |
$2$ |
$3$ |
$5.99604335866$ |
| 6.6.4016873.1 |
$x^{6} - 2 x^{5} - 10 x^{4} + 13 x^{3} + 30 x^{2} - 11 x - 13$ |
$6$ |
(6, 0) |
$7^{5}\cdot 239$ |
$2$ |
$12.6080527405$ |
$78.24332848791921$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$[2]$ |
$2$ |
$5$ |
$17.7590530488$ |
| 6.0.4924451.1 |
$x^{6} - 2 x^{5} + 11 x^{4} - 8 x^{3} + 37 x^{2} - 11 x + 43$ |
$6$ |
(0, 3) |
$-\,7^{5}\cdot 293$ |
$2$ |
$13.0434647868$ |
$86.6327652291967$ |
✓ |
|
? |
$A_4\times C_2$ (as 6T6) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$2.10181872849$ |
| 6.4.5865643.1 |
$x^{6} - 2 x^{5} - 3 x^{4} - 8 x^{3} - 5 x^{2} + 31 x + 29$ |
$6$ |
(4, 1) |
$-\,7^{5}\cdot 349$ |
$2$ |
$13.4292761521$ |
$94.54990137269377$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$[2]$ |
$2$ |
$4$ |
$13.311322743$ |
| 6.2.5899257.1 |
$x^{6} - 3 x^{5} + 9 x^{4} - 13 x^{3} - 3 x^{2} + 9 x - 41$ |
$6$ |
(2, 2) |
$3^{3}\cdot 7^{5}\cdot 13$ |
$3$ |
$13.442072066$ |
$31.606810323667133$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
$[2]$ |
$[2, 2]$ |
$2$ |
$3$ |
$5.55815547952$ |
| 6.4.6336239.1 |
$x^{6} - x^{5} + x^{4} - 15 x^{3} - 13 x^{2} + 41 x + 29$ |
$6$ |
(4, 1) |
$-\,7^{5}\cdot 13\cdot 29$ |
$3$ |
$13.6031219578$ |
$98.26956684930803$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$[2, 2]$ |
$2$ |
$4$ |
$17.1208130292$ |
| 6.0.6336239.1 |
$x^{6} - 2 x^{5} + 11 x^{4} - 15 x^{3} + 44 x^{2} - 32 x + 64$ |
$6$ |
(0, 3) |
$-\,7^{5}\cdot 13\cdot 29$ |
$3$ |
$13.6031219578$ |
$98.26956684930803$ |
✓ |
|
? |
$A_4\times C_2$ (as 6T6) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$2$ |
$2.10181872849$ |
| 6.4.6336239.2 |
$x^{6} - 3 x^{5} - 5 x^{4} + 15 x^{3} - 3 x^{2} - 5 x + 43$ |
$6$ |
(4, 1) |
$-\,7^{5}\cdot 13\cdot 29$ |
$3$ |
$13.6031219578$ |
$98.26956684930803$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$[2, 2]$ |
$2$ |
$4$ |
$15.8146978255$ |
| 6.6.6369853.1 |
$x^{6} - 2 x^{5} - 10 x^{4} + 13 x^{3} + 30 x^{2} - 18 x - 27$ |
$6$ |
(6, 0) |
$7^{5}\cdot 379$ |
$2$ |
$13.6151229749$ |
$98.52988403875722$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$[2]$ |
$2$ |
$5$ |
$20.512067263$ |
| 6.4.7277431.1 |
$x^{6} - x^{5} + x^{4} - x^{3} - 41 x^{2} - x + 29$ |
$6$ |
(4, 1) |
$-\,7^{5}\cdot 433$ |
$2$ |
$13.9207622426$ |
$105.31550506492208$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$[2]$ |
$2$ |
$4$ |
$18.7037870483$ |
| 6.4.7748027.1 |
$x^{6} - 3 x^{5} + 2 x^{4} + x^{3} - 31 x^{2} + 30 x + 43$ |
$6$ |
(4, 1) |
$-\,7^{5}\cdot 461$ |
$2$ |
$14.0669039124$ |
$108.66728820691225$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$[2]$ |
$2$ |
$4$ |
$15.2312707057$ |
| 6.2.7781641.1 |
$x^{6} - 2 x^{5} - 3 x^{4} + 6 x^{3} - 26 x^{2} + 24 x - 83$ |
$6$ |
(2, 2) |
$7^{5}\cdot 463$ |
$2$ |
$14.0770568719$ |
$108.9027538962374$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$[2]$ |
$2$ |
$3$ |
$11.84068216$ |
| 6.6.8252237.1 |
$x^{6} - x^{5} - 13 x^{4} + 6 x^{3} + 43 x^{2} - 8 x - 41$ |
$6$ |
(6, 0) |
$7^{5}\cdot 491$ |
$2$ |
$14.2154937487$ |
$112.14737502656472$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$[2]$ |
$2$ |
$5$ |
$24.7196621022$ |
| 6.2.8605184.1 |
$x^{6} - 28 x^{2} - 56$ |
$6$ |
(2, 2) |
$2^{9}\cdot 7^{5}$ |
$2$ |
$14.3150661808$ |
$24.0749756711442$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$[2]$ |
$2$ |
$3$ |
$11.1562627745$ |
| 6.6.8605184.1 |
$x^{6} - 14 x^{4} + 56 x^{2} - 56$ |
$6$ |
(6, 0) |
$2^{9}\cdot 7^{5}$ |
$2$ |
$14.3150661808$ |
$14.315066180821045$ |
|
✓ |
? |
$C_6$ (as 6T1) |
trivial |
$[2]$ |
$2$ |
$5$ |
$28.1866403529$ |
| 6.6.9193429.1 |
$x^{6} - x^{5} - 13 x^{4} + 6 x^{3} + 50 x^{2} - x - 41$ |
$6$ |
(6, 0) |
$7^{5}\cdot 547$ |
$2$ |
$14.4737007026$ |
$118.37010418039665$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$[2]$ |
$2$ |
$5$ |
$26.2569778265$ |
| 6.4.10101007.1 |
$x^{6} - x^{5} - 6 x^{4} + 13 x^{3} - 20 x^{2} - 64 x + 64$ |
$6$ |
(4, 1) |
$-\,7^{5}\cdot 601$ |
$2$ |
$14.7025989866$ |
$124.07537677583994$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$[2]$ |
$2$ |
$4$ |
$22.4369094772$ |
| 6.2.10605217.1 |
$x^{6} - x^{5} + x^{4} + 13 x^{3} - 41 x^{2} + 69 x - 83$ |
$6$ |
(2, 2) |
$7^{5}\cdot 631$ |
$2$ |
$14.822447697$ |
$127.13439078853315$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$[2]$ |
$2$ |
$3$ |
$14.3536795424$ |
| 6.2.11075813.1 |
$x^{6} - 3 x^{5} + 2 x^{4} + x^{3} - 45 x^{2} + 44 x - 83$ |
$6$ |
(2, 2) |
$7^{5}\cdot 659$ |
$2$ |
$14.930096076$ |
$129.92450592684958$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$[2]$ |
$2$ |
$3$ |
$8.30333792819$ |
| 6.2.12487601.1 |
$x^{6} - x^{5} + 8 x^{4} - x^{3} + 8 x^{2} - 22 x - 97$ |
$6$ |
(2, 2) |
$7^{5}\cdot 743$ |
$2$ |
$15.2316342376$ |
$137.95669247205615$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$[2]$ |
$2$ |
$3$ |
$14.4128223332$ |
| 6.4.12924583.1 |
$x^{6} - 3 x^{5} + 9 x^{4} - 13 x^{3} - 45 x^{2} + 51 x + 71$ |
$6$ |
(4, 1) |
$-\,7^{5}\cdot 769$ |
$2$ |
$15.3192001354$ |
$140.34971548618705$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$[2]$ |
$2$ |
$4$ |
$23.4424922291$ |
| 6.4.13395179.1 |
$x^{6} - x^{5} - 6 x^{4} - 8 x^{3} - 6 x^{2} + 76 x + 71$ |
$6$ |
(4, 1) |
$-\,7^{5}\cdot 797$ |
$2$ |
$15.4107847179$ |
$142.88200221237858$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$[2]$ |
$2$ |
$4$ |
$17.7810661216$ |
| 6.2.13899389.1 |
$x^{6} - x^{5} + 8 x^{4} + 6 x^{3} - 20 x^{2} + 90 x - 97$ |
$6$ |
(2, 2) |
$7^{5}\cdot 827$ |
$2$ |
$15.5059823374$ |
$145.54628389389742$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$[2]$ |
$2$ |
$3$ |
$12.1776413165$ |
| 6.0.13983424.1 |
$x^{6} + 14 x^{4} + 63 x^{2} + 91$ |
$6$ |
(0, 3) |
$-\,2^{6}\cdot 7^{5}\cdot 13$ |
$3$ |
$15.5215678516$ |
$51.61370512661073$ |
✓ |
|
✓ |
$A_4\times C_2$ (as 6T6) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$2$ |
$2.10181872849$ |
| 6.4.13983424.1 |
$x^{6} - 49 x^{2} + 91$ |
$6$ |
(4, 1) |
$-\,2^{6}\cdot 7^{5}\cdot 13$ |
$3$ |
$15.5215678516$ |
$51.61370512661073$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$[2, 2]$ |
$2$ |
$4$ |
$21.0089305385$ |
| 6.4.13983424.2 |
$x^{6} - 7 x^{4} - 14 x^{2} + 91$ |
$6$ |
(4, 1) |
$-\,2^{6}\cdot 7^{5}\cdot 13$ |
$3$ |
$15.5215678516$ |
$51.61370512661073$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$[2, 2]$ |
$2$ |
$4$ |
$25.8623810323$ |
| 6.4.14336371.1 |
$x^{6} - 2 x^{5} - 3 x^{4} - x^{3} - 40 x^{2} + 3 x + 71$ |
$6$ |
(4, 1) |
$-\,7^{5}\cdot 853$ |
$2$ |
$15.5861866181$ |
$147.81648891293273$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$[2]$ |
$2$ |
$4$ |
$20.0826798057$ |
| 6.0.14806967.1 |
$x^{6} - x^{5} + 15 x^{4} - x^{3} + 71 x^{2} + 27 x + 127$ |
$6$ |
(0, 3) |
$-\,7^{5}\cdot 881$ |
$2$ |
$15.6703134893$ |
$150.2229620055192$ |
✓ |
|
? |
$A_4\times C_2$ (as 6T6) |
$[6]$ |
$[6]$ |
$2$ |
$2$ |
$2.10181872849$ |
| 6.2.14840581.1 |
$x^{6} - x^{5} + x^{4} - 8 x^{3} - 27 x^{2} + 48 x - 139$ |
$6$ |
(2, 2) |
$7^{5}\cdot 883$ |
$2$ |
$15.6762368762$ |
$150.39337948743616$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$[2]$ |
$2$ |
$3$ |
$10.461520269$ |
| 6.2.15311177.1 |
$x^{6} - 3 x^{5} + 9 x^{4} - 13 x^{3} - 10 x^{2} + 16 x - 104$ |
$6$ |
(2, 2) |
$7^{5}\cdot 911$ |
$2$ |
$15.7580120958$ |
$152.75926326353007$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$[2]$ |
$2$ |
$3$ |
$19.3595488567$ |
| 6.0.15748159.1 |
$x^{6} - x^{5} + 15 x^{4} - 15 x^{3} + 85 x^{2} - 43 x + 127$ |
$6$ |
(0, 3) |
$-\,7^{5}\cdot 937$ |
$2$ |
$15.8320917671$ |
$154.9238075701752$ |
✓ |
|
? |
$A_4\times C_2$ (as 6T6) |
$[6]$ |
$[6]$ |
$2$ |
$2$ |
$2.10181872849$ |
| 6.2.16252369.1 |
$x^{6} - x^{5} + 8 x^{4} + 13 x^{3} - 20 x^{2} + 76 x - 104$ |
$6$ |
(2, 2) |
$7^{5}\cdot 967$ |
$2$ |
$15.9154691714$ |
$157.3843713687782$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$[2]$ |
$2$ |
$3$ |
$17.3597615828$ |
| 6.4.17159947.1 |
$x^{6} - 2 x^{5} - 10 x^{4} + 6 x^{3} + 2 x^{2} + 101 x + 71$ |
$6$ |
(4, 1) |
$-\,7^{5}\cdot 1021$ |
$2$ |
$16.0602631515$ |
$161.71907095186447$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$[2]$ |
$2$ |
$4$ |
$28.1196240028$ |
| 6.4.17630543.1 |
$x^{6} - 3 x^{5} - 5 x^{4} + 15 x^{3} - 17 x^{2} + 9 x + 113$ |
$6$ |
(4, 1) |
$-\,7^{5}\cdot 1049$ |
$2$ |
$16.1328445097$ |
$163.92157218834464$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$[2]$ |
$2$ |
$4$ |
$31.3900144971$ |
| 6.6.17664157.1 |
$x^{6} - 3 x^{5} - 12 x^{4} + 29 x^{3} + 53 x^{2} - 68 x - 97$ |
$6$ |
(6, 0) |
$7^{5}\cdot 1051$ |
$2$ |
$16.1379668623$ |
$164.07776238308165$ |
|
|
✓ |
$A_4\times C_2$ (as 6T6) |
trivial |
$[2]$ |
$2$ |
$5$ |
$39.9375480644$ |
| 6.2.18134753.1 |
$x^{6} - x^{5} + 8 x^{4} - 15 x^{3} - 20 x^{2} - 92 x - 104$ |
$6$ |
(2, 2) |
$7^{5}\cdot 13\cdot 83$ |
$3$ |
$16.2088402053$ |
$166.24901812583286$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
$[2]$ |
$[2, 2]$ |
$2$ |
$3$ |
$9.20256984928$ |
| 6.6.18134753.1 |
$x^{6} - 2 x^{5} - 17 x^{4} + 20 x^{3} + 86 x^{2} - 18 x - 83$ |
$6$ |
(6, 0) |
$7^{5}\cdot 13\cdot 83$ |
$3$ |
$16.2088402053$ |
$166.24901812583286$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$[2, 2]$ |
$2$ |
$5$ |
$41.89999413$ |
| 6.2.18134753.2 |
$x^{6} - 2 x^{5} + 4 x^{4} - 22 x^{3} - 19 x^{2} - 46 x - 97$ |
$6$ |
(2, 2) |
$7^{5}\cdot 13\cdot 83$ |
$3$ |
$16.2088402053$ |
$166.24901812583286$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
$[2]$ |
$[2, 2]$ |
$2$ |
$3$ |
$10.1117028565$ |
| 6.2.18605349.1 |
$x^{6} - 2 x^{5} + 11 x^{4} - 36 x^{3} + 9 x^{2} - 67 x - 83$ |
$6$ |
(2, 2) |
$3^{3}\cdot 7^{5}\cdot 41$ |
$3$ |
$16.2781971293$ |
$56.13075998354003$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
$[2]$ |
$[2, 2]$ |
$2$ |
$3$ |
$7.47304999062$ |
| 6.4.19512927.1 |
$x^{6} - 2 x^{5} - 10 x^{4} + 27 x^{3} - 12 x^{2} - 109 x + 169$ |
$6$ |
(4, 1) |
$-\,3^{3}\cdot 7^{5}\cdot 43$ |
$3$ |
$16.4079278114$ |
$57.48350246941067$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
$[2]$ |
$[2, 2]$ |
$2$ |
$4$ |
$15.8454290193$ |
