| 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 |
| 21.1.238...101.1 |
$ x^{21} - 6 x^{18} - 6 x^{16} + 8 x^{15} - 8 x^{14} + 17 x^{13} - 3 x^{12} + \cdots - 1 $ |
$21$ |
[1,10] |
$23^{7}\cdot 41227^{3}$ |
$2$ |
$12.9783940136$ |
|
|
not computed |
$D_7\wr S_3$ (as 21T62) |
trivial |
$2$ |
$10$ |
$952.218112417$ |
| 21.3.321...607.1 |
$ x^{21} - 5 x^{14} - 8 x^{7} - 1 $ |
$21$ |
[3,9] |
$-\,7^{29}$ |
$1$ |
$14.6906208606$ |
|
|
not computed |
$C_3\times D_7$ (as 21T3) |
trivial |
$2$ |
$11$ |
$6020.25035863$ |
| 21.3.396...527.1 |
$ x^{21} - 5 x^{20} + 11 x^{19} - 20 x^{18} + 37 x^{17} - 68 x^{16} + \cdots + 27 $ |
$21$ |
[3,9] |
$-\,13^{2}\cdot 1801^{2}\cdot 193327^{3}$ |
$3$ |
$14.8362250548$ |
|
|
not computed |
$C_3^7.S_7$ (as 21T139) |
trivial |
$2$ |
$11$ |
$6158.71427835$ |
| 21.3.682...552.1 |
$ x^{21} - 2 x^{20} - x^{19} - 3 x^{18} + 10 x^{17} + 13 x^{16} + x^{15} + \cdots + 1 $ |
$21$ |
[3,9] |
$-\,2^{21}\cdot 71^{10}$ |
$2$ |
$15.2258515194$ |
|
|
not computed |
$S_3\times D_7$ (as 21T8) |
trivial |
$2$ |
$11$ |
$7666.61577427$ |
| 21.3.717...392.1 |
$ x^{21} - 7 x^{20} + 21 x^{19} - 42 x^{18} + 77 x^{17} - 126 x^{16} + \cdots - 1 $ |
$21$ |
[3,9] |
$-\,2^{18}\cdot 7^{23}$ |
$2$ |
$15.2619237063$ |
|
|
not computed |
$F_7$ (as 21T4) |
trivial |
$2$ |
$11$ |
$10096.3106241$ |
| 21.3.928...699.1 |
$ x^{21} - 5 x^{20} + 11 x^{19} - 13 x^{18} + 7 x^{17} + 4 x^{16} + \cdots - 1 $ |
$21$ |
[3,9] |
$-\,11^{9}\cdot 13^{14}$ |
$2$ |
$15.4504115563$ |
|
|
not computed |
$F_7$ (as 21T4) |
trivial |
$2$ |
$11$ |
$10371.33223$ |
| 21.3.109...167.1 |
$ x^{21} + x^{19} - 2 x^{18} - 2 x^{17} - 3 x^{16} - x^{15} + 4 x^{14} + 15 x^{13} + \cdots + 1 $ |
$21$ |
[3,9] |
$-\,31^{8}\cdot 67^{3}\cdot 349^{3}$ |
$3$ |
$15.5692033983$ |
|
|
not computed |
$S_3\times S_7$ (as 21T74) |
trivial |
$2$ |
$11$ |
$10492.3673171$ |
| 21.5.162...041.1 |
$ x^{21} - x^{20} - 6 x^{19} + 8 x^{18} + 15 x^{17} - 28 x^{16} - 39 x^{15} + \cdots - 1 $ |
$21$ |
[5,8] |
$13^{8}\cdot 109^{8}$ |
$2$ |
$15.8679874279$ |
|
|
not computed |
$\PSL(2,7)$ (as 21T14) |
trivial |
$2$ |
$12$ |
$17240.5464964$ |
| 21.1.214...721.1 |
$ x^{21} - x^{20} - x^{19} + 2 x^{18} + 2 x^{17} + x^{16} - 5 x^{15} - x^{14} + \cdots - 1 $ |
$21$ |
[1,10] |
$23^{7}\cdot 184607^{3}$ |
$2$ |
$16.0779415343$ |
|
|
not computed |
$S_3\times S_7$ (as 21T74) |
trivial |
$2$ |
$10$ |
$10455.3643856$ |
| 21.1.237...104.1 |
$ x^{21} + x^{19} - 5 x^{18} + 8 x^{17} - 5 x^{16} + 11 x^{15} - 40 x^{14} + \cdots + 1 $ |
$21$ |
[1,10] |
$2^{14}\cdot 11^{8}\cdot 41^{3}\cdot 461^{3}$ |
$4$ |
$16.1560089147$ |
|
|
not computed |
$S_3\times S_7$ (as 21T74) |
trivial |
$2$ |
$10$ |
$11721.4726991$ |
| 21.5.267...304.1 |
$ x^{21} - 5 x^{20} + 11 x^{19} - 16 x^{18} + 25 x^{17} - 38 x^{16} + \cdots - 1 $ |
$21$ |
[5,8] |
$2^{18}\cdot 317^{8}$ |
$2$ |
$16.2483846421$ |
|
|
not computed |
$\PSL(2,7)$ (as 21T14) |
trivial |
$2$ |
$12$ |
$25357.2549184$ |
| 21.3.657...567.1 |
$ x^{21} - 4 x^{20} + 12 x^{19} - 22 x^{18} + 41 x^{17} - 54 x^{16} + \cdots - 1 $ |
$21$ |
[3,9] |
$-\,3^{24}\cdot 7^{17}$ |
$2$ |
$16.959319372$ |
|
|
not computed |
$C_3\times F_7$ (as 21T9) |
trivial |
$2$ |
$11$ |
$31647.6272279$ |
| 21.1.759...229.1 |
$ x^{21} - x^{18} - 3 x^{15} + 2 x^{12} + 4 x^{9} - x^{6} - 2 x^{3} - 1 $ |
$21$ |
[1,10] |
$3^{21}\cdot 193607^{3}$ |
$2$ |
$17.0763753068$ |
|
|
✓ |
$C_3^6.(C_2\times S_7)$ (as 21T138) |
trivial |
$2$ |
$10$ |
$18363.369838$ |
| 21.5.855...849.1 |
$ x^{21} - 4 x^{19} + 23 x^{17} - 4 x^{16} - 54 x^{15} + 19 x^{14} + \cdots + 1 $ |
$21$ |
[5,8] |
$23^{8}\cdot 239^{3}\cdot 431^{3}$ |
$3$ |
$17.1742778909$ |
|
|
not computed |
$S_3\times S_7$ (as 21T74) |
trivial |
$2$ |
$12$ |
$45009.9851463$ |
| 21.3.108...223.1 |
$ x^{21} - 9 x^{14} - 12 x^{7} + 1 $ |
$21$ |
[3,9] |
$-\,3^{28}\cdot 7^{15}$ |
$2$ |
$17.3701324536$ |
|
|
not computed |
$C_3\times F_7$ (as 21T9) |
trivial |
$2$ |
$11$ |
$51151.7616302$ |
| 21.1.156...857.1 |
$ x^{21} - x^{20} - x^{19} + 2 x^{18} + 5 x^{17} + 2 x^{16} - 10 x^{15} + \cdots - 1 $ |
$21$ |
[1,10] |
$23^{7}\cdot 71^{9}$ |
$2$ |
$17.672814291$ |
|
|
not computed |
$S_3\times D_7$ (as 21T8) |
trivial |
$2$ |
$10$ |
$32527.0761402$ |
| 21.3.167...056.1 |
$ x^{21} - 7 x^{20} + 23 x^{19} - 46 x^{18} + 59 x^{17} - 38 x^{16} + \cdots + 1 $ |
$21$ |
[3,9] |
$-\,2^{18}\cdot 17^{6}\cdot 31^{9}$ |
$3$ |
$17.7311766635$ |
|
|
not computed |
$S_3\times A_7$ (as 21T57) |
trivial |
$2$ |
$11$ |
$48967.484032$ |
| 21.3.188...059.1 |
$ x^{21} - 3 x^{20} + 2 x^{19} - 4 x^{18} + 10 x^{17} - 9 x^{16} + 70 x^{15} + \cdots + 1 $ |
$21$ |
[3,9] |
$-\,59^{8}\cdot 10859^{3}$ |
$2$ |
$17.8300144394$ |
|
|
not computed |
$S_3\times S_7$ (as 21T74) |
trivial |
$2$ |
$11$ |
$47990.3401891$ |
| 21.3.214...807.1 |
$ x^{21} - x^{20} - x^{19} + x^{18} - x^{17} + 6 x^{16} - 7 x^{15} + 2 x^{14} + \cdots + 1 $ |
$21$ |
[3,9] |
$-\,184607^{5}$ |
$1$ |
$17.9419073895$ |
|
|
not computed |
$S_7$ (as 21T38) |
trivial |
$2$ |
$11$ |
$59489.8190642$ |
| 21.3.270...407.1 |
$ x^{21} - 4 x^{18} - x^{17} + x^{16} + 7 x^{15} + x^{14} - 6 x^{13} - 11 x^{12} + \cdots - 1 $ |
$21$ |
[3,9] |
$-\,193327^{5}$ |
$1$ |
$18.1401583673$ |
|
|
not computed |
$S_7$ (as 21T38) |
trivial |
$2$ |
$11$ |
$75073.7253$ |
| 21.3.336...784.1 |
$ x^{21} - 5 x^{20} + 11 x^{19} - 5 x^{18} - 29 x^{17} + 64 x^{16} + \cdots - 1 $ |
$21$ |
[3,9] |
$-\,2^{14}\cdot 11^{13}\cdot 29^{6}$ |
$3$ |
$18.3310070912$ |
|
|
not computed |
$S_3\times A_7$ (as 21T57) |
trivial |
$2$ |
$11$ |
$73219.6797146$ |
| 21.3.930...607.1 |
$ x^{21} - 5 x^{20} + 36 x^{18} - 35 x^{17} - 108 x^{16} + 155 x^{15} + \cdots - 25 $ |
$21$ |
[3,9] |
$-\,151^{2}\cdot 2377^{2}\cdot 193327^{3}$ |
$3$ |
$19.2412307236$ |
|
|
not computed |
$C_3^7.S_7$ (as 21T139) |
trivial |
$2$ |
$11$ |
$99654.8309357$ |
| 21.1.126...441.1 |
$ x^{21} + 3 x^{19} - x^{18} + x^{17} + 8 x^{16} - 7 x^{15} + 24 x^{14} + \cdots + 1 $ |
$21$ |
[1,10] |
$31^{7}\cdot 71^{9}$ |
$2$ |
$19.5216714707$ |
|
|
not computed |
$S_3\times D_7$ (as 21T8) |
trivial |
$2$ |
$10$ |
$80948.9311635$ |
| 21.1.190...129.1 |
$ x^{21} - x^{14} + 1 $ |
$21$ |
[1,10] |
$7^{21}\cdot 23^{7}$ |
$2$ |
$19.907068859$ |
|
|
✓ |
$C_7^2:(C_6\times S_3)$ (as 21T29) |
trivial |
$2$ |
$10$ |
$141151.982984$ |
| 21.9.252...441.1 |
$ x^{21} - 9 x^{19} + 3 x^{17} + 66 x^{15} - 75 x^{14} - 90 x^{13} + \cdots + 3 $ |
$21$ |
[9,6] |
$3^{34}\cdot 73^{6}$ |
$2$ |
$20.1771578454$ |
|
|
not computed |
$C_3\times A_7$ (as 21T44) |
trivial |
$2$ |
$14$ |
$823613.327719$ |
| 21.9.332...609.1 |
$ x^{21} - 6 x^{20} + 12 x^{19} - 2 x^{18} - 27 x^{17} + 36 x^{16} + \cdots - 9 $ |
$21$ |
[9,6] |
$3^{36}\cdot 53^{6}$ |
$2$ |
$20.4443072604$ |
|
|
not computed |
$C_3\times A_7$ (as 21T44) |
trivial |
$2$ |
$14$ |
$967276.035305$ |
| 21.3.426...007.1 |
$ x^{21} - x^{20} - 7 x^{19} + 6 x^{18} + 16 x^{17} - 27 x^{16} + 3 x^{15} + \cdots - 1 $ |
$21$ |
[3,9] |
$-\,7^{14}\cdot 184607^{3}$ |
$2$ |
$20.6880644133$ |
|
|
not computed |
$C_3\times S_7$ (as 21T56) |
trivial |
$2$ |
$11$ |
$201933.335135$ |
| 21.3.429...912.1 |
$ x^{21} - x^{20} + 9 x^{19} - 7 x^{18} + 35 x^{17} - 27 x^{16} + 83 x^{15} + \cdots + 4 $ |
$21$ |
[3,9] |
$-\,2^{38}\cdot 3^{18}\cdot 7^{9}$ |
$3$ |
$20.6950697419$ |
|
|
|
$\PGL(2,7)$ (as 21T20) |
trivial |
$2$ |
$11$ |
$1790438.21987$ |
| 21.3.490...767.1 |
$ x^{21} - x^{20} - 2 x^{19} + 9 x^{18} - 8 x^{17} - 16 x^{16} + 40 x^{15} + \cdots + 1 $ |
$21$ |
[3,9] |
$-\,7^{14}\cdot 193327^{3}$ |
$2$ |
$20.8249198157$ |
|
|
not computed |
$C_3\times S_7$ (as 21T56) |
trivial |
$2$ |
$11$ |
$299129.54193$ |
| 21.1.573...421.1 |
$ x^{21} - x - 1 $ |
$21$ |
[1,10] |
$1137694897331\cdot 5043293621028391$ |
$2$ |
$20.9818976857$ |
|
|
✓ |
$S_{21}$ (as 21T164) |
trivial |
$2$ |
$10$ |
$169158.997908$ |
| 21.1.594...421.1 |
$ x^{21} + x - 1 $ |
$21$ |
[1,10] |
$11\cdot 17\cdot 1033\cdot 1583\cdot 159503\cdot 121937899012999$ |
$6$ |
$21.0177955058$ |
|
|
✓ |
$S_{21}$ (as 21T164) |
trivial |
$2$ |
$10$ |
$312816.601488$ |
| 21.3.714...224.1 |
$ x^{21} - 3 x^{20} - 4 x^{19} + 16 x^{18} - 9 x^{17} - 33 x^{16} + \cdots + 1 $ |
$21$ |
[3,9] |
$-\,2^{64}\cdot 3^{18}$ |
$2$ |
$21.2024390858$ |
|
|
|
$\PGL(2,7)$ (as 21T20) |
trivial |
$2$ |
$11$ |
$3668230.07566$ |
| 21.1.739...928.1 |
$ x^{21} - 2 x^{20} - x^{19} + 7 x^{18} - 3 x^{17} - 13 x^{16} + 14 x^{15} + \cdots - 1 $ |
$21$ |
[1,10] |
$2^{3}\cdot 101\cdot 1951\cdot 7481\cdot 35629381\cdot 17609300881$ |
$6$ |
$21.237517341$ |
|
|
✓ |
$S_{21}$ (as 21T164) |
trivial |
$2$ |
$10$ |
$564425.480379$ |
| 21.3.897...231.1 |
$ x^{21} - x^{20} + 3 x^{19} + 4 x^{18} + 8 x^{17} - 12 x^{16} + \cdots - 1319 $ |
$21$ |
[3,9] |
$-\,7^{2}\cdot 13^{2}\cdot 71^{9}\cdot 4861^{2}$ |
$4$ |
$21.4332747759$ |
|
|
not computed |
$C_3^7:D_7$ (as 21T76) |
trivial |
$2$ |
$11$ |
$277898.768894$ |
| 21.1.990...104.1 |
$ x^{21} - 3 x^{20} - 2 x^{19} + 25 x^{18} - 40 x^{17} - 24 x^{16} + \cdots - 38 $ |
$21$ |
[1,10] |
$2^{14}\cdot 11^{10}\cdot 13^{12}$ |
$3$ |
$21.5341136548$ |
|
|
not computed |
$C_{21}:C_6$ (as 21T10) |
trivial |
$2$ |
$10$ |
$637026.16318$ |
| 21.3.103...503.1 |
$ x^{21} - 6 x^{20} - x^{19} + 72 x^{18} - 100 x^{17} - 299 x^{16} + \cdots + 1 $ |
$21$ |
[3,9] |
$-\,11^{4}\cdot 103^{4}\cdot 184607^{3}$ |
$3$ |
$21.5813816248$ |
|
|
✓ |
$C_3^6.S_7$ (as 21T130) |
trivial |
$2$ |
$11$ |
$361691.21971$ |
| 21.5.123...001.1 |
$ x^{21} - 2 x^{19} - x^{18} - 8 x^{17} + 16 x^{15} + 16 x^{14} + 21 x^{13} + \cdots - 1 $ |
$21$ |
[5,8] |
$7^{9}\cdot 12503^{5}$ |
$2$ |
$21.7602786875$ |
|
|
not computed |
$S_7$ (as 21T38) |
trivial |
$2$ |
$12$ |
$564369.598704$ |
| 21.1.153...777.1 |
$ x^{21} + x^{7} - 1 $ |
$21$ |
[1,10] |
$7^{21}\cdot 31^{7}$ |
$2$ |
$21.9896645667$ |
|
|
✓ |
$C_7^2:(C_6\times S_3)$ (as 21T29) |
trivial |
$2$ |
$10$ |
$472261.200133$ |
| 21.9.184...873.1 |
$ x^{21} - 2 x^{20} - 2 x^{19} + 12 x^{18} - 25 x^{17} + x^{16} + 48 x^{15} + \cdots - 23 $ |
$21$ |
[9,6] |
$71^{3}\cdot 8623^{3}\cdot 283573^{2}$ |
$3$ |
$22.1821586762$ |
|
|
not computed |
$C_3^7.S_7$ (as 21T139) |
trivial |
$2$ |
$14$ |
$1614740.57391$ |
| 21.3.190...271.1 |
$ x^{21} - 9 x^{20} + 23 x^{19} + 24 x^{18} - 196 x^{17} + 152 x^{16} + \cdots + 1 $ |
$21$ |
[3,9] |
$-\,67^{2}\cdot 71^{9}\cdot 9613^{2}$ |
$3$ |
$22.214074314$ |
|
|
not computed |
$C_3^7:D_7$ (as 21T76) |
trivial |
$2$ |
$11$ |
$520928.798224$ |
| 21.3.207...824.1 |
$ x^{21} - 4 x^{20} + 8 x^{19} - 12 x^{18} + 12 x^{17} - 16 x^{16} + \cdots + 4 $ |
$21$ |
[3,9] |
$-\,2^{20}\cdot 11^{7}\cdot 317^{6}$ |
$3$ |
$22.3056297787$ |
|
|
not computed |
$S_3\times \GL(3,2)$ (as 21T27) |
trivial |
$2$ |
$11$ |
$999740.077738$ |
| 21.3.207...824.2 |
$ x^{21} - 2 x^{20} + 2 x^{19} - 4 x^{16} - 6 x^{15} + 8 x^{14} - 16 x^{13} + \cdots + 2 $ |
$21$ |
[3,9] |
$-\,2^{20}\cdot 11^{7}\cdot 317^{6}$ |
$3$ |
$22.3056297787$ |
|
|
not computed |
$S_3\times \GL(3,2)$ (as 21T27) |
trivial |
$2$ |
$11$ |
$999740.077738$ |
| 21.5.279...288.1 |
$ x^{21} - 2 x^{19} - 7 x^{18} - 5 x^{17} + 11 x^{16} + 17 x^{15} + \cdots - 5 $ |
$21$ |
[5,8] |
$2^{27}\cdot 181^{9}$ |
$2$ |
$22.6263811101$ |
|
|
|
$\PGL(2,7)$ (as 21T20) |
trivial |
$2$ |
$12$ |
$2296254.50823$ |
| 21.3.310...319.1 |
$ x^{21} - x^{20} - 7 x^{19} + 6 x^{18} + 3 x^{17} - 30 x^{16} + 72 x^{15} + \cdots - 1 $ |
$21$ |
[3,9] |
$-\,7^{14}\cdot 71^{9}$ |
$2$ |
$22.7402444296$ |
|
|
not computed |
$C_3\times D_7$ (as 21T3) |
trivial |
$2$ |
$11$ |
$725840.889095$ |
| 21.1.341...000.1 |
$ x^{21} - 10 x^{18} + 36 x^{15} - 76 x^{12} - 224 x^{9} - 144 x^{6} + \cdots - 16 $ |
$21$ |
[1,10] |
$2^{20}\cdot 3^{34}\cdot 5^{9}$ |
$3$ |
$22.8420900179$ |
|
|
not computed |
$S_3\times F_7$ (as 21T15) |
trivial |
$2$ |
$10$ |
$2085380.41806$ |
| 21.5.348...177.1 |
$ x^{21} - 2 x^{20} - 5 x^{18} + 12 x^{17} - 5 x^{16} + 4 x^{15} - 27 x^{14} + \cdots - 1 $ |
$21$ |
[5,8] |
$3^{8}\cdot 37^{5}\cdot 2381^{5}$ |
$3$ |
$22.8629450794$ |
|
|
not computed |
$S_7$ (as 21T38) |
trivial |
$2$ |
$12$ |
$1358971.01083$ |
| 21.5.417...153.1 |
$ x^{21} - 3 x^{19} - 2 x^{18} + 15 x^{17} + 6 x^{16} - 23 x^{15} + \cdots - 1 $ |
$21$ |
[5,8] |
$23^{7}\cdot 107^{3}\cdot 21557^{3}$ |
$3$ |
$23.062442084$ |
|
|
not computed |
$S_3\times S_7$ (as 21T74) |
trivial |
$2$ |
$12$ |
$895675.424859$ |
| 21.1.753...068.1 |
$ x^{21} - 2 x^{20} - x^{19} + 7 x^{18} - 3 x^{17} - 13 x^{16} + 14 x^{15} + \cdots - 1 $ |
$21$ |
[1,10] |
$2^{2}\cdot 11\cdot 29\cdot 1447\cdot 2579\cdot 4423\cdot 3578836676945557$ |
$7$ |
$23.7195344256$ |
|
|
✓ |
$S_{21}$ (as 21T164) |
trivial |
$2$ |
$10$ |
$2395762.98687$ |
| 21.9.778...553.1 |
$ x^{21} - 8 x^{20} + 15 x^{19} + 42 x^{18} - 181 x^{17} + 43 x^{16} + \cdots + 1 $ |
$21$ |
[9,6] |
$71^{3}\cdot 157^{2}\cdot 3709^{2}\cdot 8623^{3}$ |
$4$ |
$23.7555403331$ |
|
|
not computed |
$C_3^7.S_7$ (as 21T139) |
trivial |
$2$ |
$14$ |
$3400600.48543$ |
| 21.7.105...767.1 |
$ x^{21} - x^{20} - 6 x^{19} + 11 x^{18} + 47 x^{17} - 45 x^{16} - 170 x^{15} + \cdots - 1 $ |
$21$ |
[7,7] |
$-\,17^{3}\cdot 23^{8}\cdot 64879^{3}$ |
$3$ |
$24.0976852901$ |
|
|
not computed |
$S_3\times S_7$ (as 21T74) |
trivial |
$2$ |
$13$ |
$2726200.25314$ |
