| 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 |
| 23.1.831...703.1 |
$x^{23} - 2 x^{22} - 3 x^{21} + 13 x^{20} - 19 x^{19} + 21 x^{18} - 75 x^{16} + 202 x^{15} - 378 x^{14} + 596 x^{13} - 798 x^{12} + 955 x^{11} - 995 x^{10} + 849 x^{9} - 610 x^{8} + 384 x^{7} - 151 x^{6} + 2 x^{5} + 46 x^{4} - 37 x^{3} + 3 x^{2} + 20 x + 1$ |
$23$ |
[1,11] |
$-\,647^{11}$ |
$1$ |
$22.0976212489$ |
$25.436194683953808$ |
|
|
|
$D_{23}$ (as 23T2) |
trivial |
$2$ |
$11$ |
$1561186.27544$ |
| 23.1.152...439.1 |
$x^{23} + 4 x^{21} - 14 x^{20} + 25 x^{19} - 6 x^{18} - 14 x^{17} - 26 x^{16} + 31 x^{15} + 48 x^{14} - 62 x^{13} + 19 x^{12} + 19 x^{11} + 24 x^{10} - 17 x^{9} + 34 x^{8} + 40 x^{7} - 228 x^{6} + 76 x^{5} + 4 x^{4} + 28 x^{3} + 45 x^{2} + 49 x + 1$ |
$23$ |
[1,11] |
$-\,1039^{11}$ |
$1$ |
$27.7159120747$ |
$32.2335229225724$ |
|
|
|
$D_{23}$ (as 23T2) |
trivial |
$2$ |
$11$ |
$55921894.4803$ |
| 23.1.293...047.1 |
$x^{23} + 5 x^{21} - 17 x^{20} + 33 x^{19} - 14 x^{18} + 53 x^{17} - 34 x^{16} - 19 x^{15} + 140 x^{14} - 19 x^{13} + 257 x^{12} - 106 x^{11} - 16 x^{10} + 274 x^{9} + 165 x^{8} + 515 x^{7} - 28 x^{6} + 129 x^{5} + 89 x^{4} + 524 x^{3} + 244 x^{2} + 50 x - 1$ |
$23$ |
[1,11] |
$-\,1103^{11}$ |
$1$ |
$28.5196906393$ |
$33.21144381083123$ |
|
|
|
$D_{23}$ (as 23T2) |
trivial |
$2$ |
$11$ |
$42306743.1121$ |
| 23.1.149...079.1 |
$x^{23} - 7 x^{22} + 15 x^{21} - 6 x^{20} + x^{19} - 21 x^{18} + 17 x^{17} + 2 x^{16} + 46 x^{15} - 10 x^{14} + 108 x^{13} - 129 x^{12} - 98 x^{11} - 144 x^{10} - 85 x^{9} + 8 x^{8} + 187 x^{7} - 82 x^{6} + 363 x^{5} + 216 x^{4} - 128 x^{3} - 51 x^{2} + 77 x - 1$ |
$23$ |
[1,11] |
$-\,1279^{11}$ |
$1$ |
$30.612204664$ |
$35.76310948449533$ |
|
|
|
$D_{23}$ (as 23T2) |
trivial |
$2$ |
$11$ |
$195904703.063$ |
| 23.1.582...903.1 |
$x^{23} - 2 x^{22} + 16 x^{21} - 34 x^{20} + 68 x^{19} - 63 x^{18} + 17 x^{17} + 43 x^{16} - 139 x^{15} + 165 x^{14} + 25 x^{13} - 228 x^{12} + 265 x^{11} - 270 x^{10} + 75 x^{9} + 246 x^{8} - 130 x^{7} - 161 x^{6} + 240 x^{5} - 393 x^{4} + 569 x^{3} - 385 x^{2} + 99 x + 1$ |
$23$ |
[1,11] |
$-\,1447^{11}$ |
$1$ |
$32.4734497852$ |
$38.03945320322047$ |
|
|
|
$D_{23}$ (as 23T2) |
trivial |
$2$ |
$11$ |
$530761705.173$ |
| 23.1.697...671.1 |
$x^{23} - 5 x^{22} + 3 x^{21} + 3 x^{20} + 43 x^{19} - 6 x^{18} - 31 x^{17} - 56 x^{16} - 68 x^{15} - 89 x^{14} + 147 x^{13} + 180 x^{12} + 274 x^{11} + 240 x^{10} - 211 x^{9} - 521 x^{8} - 383 x^{7} - 275 x^{6} + 291 x^{5} + 249 x^{4} + 358 x^{3} - 9 x^{2} + 107 x + 1$ |
$23$ |
[1,11] |
$-\,1471^{11}$ |
$1$ |
$32.7299386538$ |
$38.353617821530214$ |
|
|
|
$D_{23}$ (as 23T2) |
trivial |
$2$ |
$11$ |
$492297100.302$ |
| 23.1.687...411.1 |
$x^{23} - 3 x^{22} + 7 x^{21} - 8 x^{20} - 11 x^{19} + 19 x^{18} + 160 x^{17} + 291 x^{16} + 464 x^{15} - 35 x^{14} - 648 x^{13} - 1313 x^{12} - 1101 x^{11} - 240 x^{10} + 1477 x^{9} + 1043 x^{8} + 863 x^{7} - 10 x^{6} - 264 x^{5} - 712 x^{4} - 80 x^{3} - 2304 x^{2} - 2048 x - 1024$ |
$23$ |
[1,11] |
$-\,1811^{11}$ |
$1$ |
$36.1522149922$ |
$42.555845661906424$ |
|
|
|
$D_{23}$ (as 23T2) |
trivial |
$2$ |
$11$ |
$9293967260.34$ |
| 23.1.182...779.1 |
$x^{23} - 11 x^{22} + 47 x^{21} - 78 x^{20} - 51 x^{19} + 367 x^{18} - 359 x^{17} - 364 x^{16} + 1182 x^{15} - 712 x^{14} - 1586 x^{13} + 3310 x^{12} - 393 x^{11} - 5271 x^{10} + 5059 x^{9} + 3246 x^{8} - 8091 x^{7} - 125 x^{6} + 10047 x^{5} - 6818 x^{4} - 2608 x^{3} + 2872 x^{2} + 1488 x - 2176$ |
$23$ |
[1,11] |
$-\,1979^{11}$ |
$1$ |
$37.7190748431$ |
$44.48595283907045$ |
|
|
|
$D_{23}$ (as 23T2) |
trivial |
$2$ |
$11$ |
$15406380217.0$ |
| 23.1.865...983.1 |
$x^{23} - 23 x^{20} + 184 x^{19} - 1334 x^{18} + 3680 x^{17} - 7567 x^{16} + 3381 x^{15} + 48346 x^{14} - 105455 x^{13} + 165048 x^{12} - 1033942 x^{11} + 3237457 x^{10} - 6694426 x^{9} + 24074675 x^{8} - 57748676 x^{7} + 58090042 x^{6} - 24771506 x^{5} + 67771087 x^{4} - 75769360 x^{3} + 19385596 x^{2} - 386078 x + 1437601$ |
$23$ |
[1,11] |
$-\,23^{33}$ |
$1$ |
$89.9049112995$ |
$96.24677714683362$ |
|
|
|
$D_{23}$ (as 23T2) |
trivial |
$2$ |
$11$ |
$35038470243900$ |
| 23.23.126...657.1 |
$x^{23} - 11 x^{22} - 49 x^{21} + 847 x^{20} + 333 x^{19} - 27195 x^{18} + 26294 x^{17} + 472463 x^{16} - 807088 x^{15} - 4813093 x^{14} + 11025393 x^{13} + 28842666 x^{12} - 85904881 x^{11} - 92539623 x^{10} + 401542378 x^{9} + 86961683 x^{8} - 1107595373 x^{7} + 357772746 x^{6} + 1662322180 x^{5} - 1168158873 x^{4} - 1079773672 x^{3} + 1139070319 x^{2} + 85927891 x - 235248461$ |
$23$ |
[23,0] |
$23593^{11}$ |
$1$ |
$123.40452372$ |
$153.60013020827813$ |
|
|
|
$D_{23}$ (as 23T2) |
trivial |
$2$ |
$22$ |
$122630019967000000$ |
