| 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 |
| 29.29.383...121.1 |
$x^{29} - x^{28} - 28 x^{27} + 27 x^{26} + 351 x^{25} - 325 x^{24} - 2600 x^{23} + 2300 x^{22} + 12650 x^{21} - 10626 x^{20} - 42504 x^{19} + 33649 x^{18} + 100947 x^{17} - 74613 x^{16} - 170544 x^{15} + 116280 x^{14} + 203490 x^{13} - 125970 x^{12} - 167960 x^{11} + 92378 x^{10} + 92378 x^{9} - 43758 x^{8} - 31824 x^{7} + 12376 x^{6} + 6188 x^{5} - 1820 x^{4} - 560 x^{3} + 105 x^{2} + 15 x - 1$ |
$29$ |
[29,0] |
$59^{28}$ |
$1$ |
$51.2611268879$ |
$51.261126887866126$ |
|
✓ |
✓ |
$C_{29}$ (as 29T1) |
trivial |
$2$ |
$28$ |
$2275980944744796.5$ |
| 29.29.193...041.1 |
$x^{29} - x^{28} - 112 x^{27} + 91 x^{26} + 5198 x^{25} - 3644 x^{24} - 132219 x^{23} + 83238 x^{22} + 2053518 x^{21} - 1187959 x^{20} - 20553532 x^{19} + 11071128 x^{18} + 136460842 x^{17} - 69042962 x^{16} - 609473492 x^{15} + 292259011 x^{14} + 1836592125 x^{13} - 845018358 x^{12} - 3706016039 x^{11} + 1661552324 x^{10} + 4906886664 x^{9} - 2177019390 x^{8} - 4095369839 x^{7} + 1819962089 x^{6} + 1998032360 x^{5} - 895362174 x^{4} - 490947342 x^{3} + 221892059 x^{2} + 42927079 x - 19524467$ |
$29$ |
[29,0] |
$233^{28}$ |
$1$ |
$193.073628378$ |
$193.0736283776695$ |
|
✓ |
|
$C_{29}$ (as 29T1) |
trivial |
$2$ |
$28$ |
$900609177445488600000000$ |
| 29.29.158...201.1 |
$x^{29} - x^{28} - 168 x^{27} + 353 x^{26} + 11480 x^{25} - 34328 x^{24} - 410190 x^{23} + 1556443 x^{22} + 8267052 x^{21} - 38827232 x^{20} - 94788585 x^{19} + 575669857 x^{18} + 574148959 x^{17} - 5286405734 x^{16} - 1118675686 x^{15} + 30698615326 x^{14} - 6935797323 x^{13} - 112817035992 x^{12} + 51055206761 x^{11} + 256367413593 x^{10} - 136472035194 x^{9} - 340428884896 x^{8} + 170672875682 x^{7} + 236550118296 x^{6} - 94550319984 x^{5} - 69592403677 x^{4} + 18732474566 x^{3} + 3480965541 x^{2} - 875365500 x + 10242329$ |
$29$ |
[29,0] |
$349^{28}$ |
$1$ |
$285.194924016$ |
$285.19492401627184$ |
|
✓ |
|
$C_{29}$ (as 29T1) |
trivial |
$2$ |
$28$ |
$158942637080452900000000000$ |
| 29.29.131...481.1 |
$x^{29} - x^{28} - 252 x^{27} + 493 x^{26} + 26301 x^{25} - 70613 x^{24} - 1477005 x^{23} + 4757585 x^{22} + 49139083 x^{21} - 176708296 x^{20} - 1019533247 x^{19} + 3897692875 x^{18} + 13650905238 x^{17} - 52791707208 x^{16} - 121558760223 x^{15} + 441031541121 x^{14} + 744433170879 x^{13} - 2221117761731 x^{12} - 3198643328695 x^{11} + 6333895042002 x^{10} + 9161654939551 x^{9} - 8623697894872 x^{8} - 14867816867065 x^{7} + 2648025494151 x^{6} + 9891108006231 x^{5} + 1898151784214 x^{4} - 1956687026062 x^{3} - 891062263511 x^{2} - 130453149826 x - 6306528127$ |
$29$ |
[29,0] |
$523^{28}$ |
$1$ |
$421.463773603$ |
$421.4637736028196$ |
|
✓ |
|
$C_{29}$ (as 29T1) |
trivial |
$2$ |
$28$ |
$404654663243202000000000000000$ |
| 29.29.783...321.1 |
$x^{29} - 406 x^{27} - 261 x^{26} + 60784 x^{25} - 10237 x^{24} - 4881280 x^{23} + 6951010 x^{22} + 231791925 x^{21} - 664329796 x^{20} - 6378435885 x^{19} + 29829836682 x^{18} + 83025301615 x^{17} - 713976297106 x^{16} + 200377868604 x^{15} + 8552568793352 x^{14} - 19940770675013 x^{13} - 30466827556936 x^{12} + 199293371073354 x^{11} - 244879309451696 x^{10} - 341168817490702 x^{9} + 1410119390706929 x^{8} - 1755729397271788 x^{7} + 798559330062447 x^{6} + 263826444292294 x^{5} - 372309027818008 x^{4} + 45256457625802 x^{3} + 48917493171904 x^{2} - 7142036935967 x - 2480435158303$ |
$29$ |
[29,0] |
$29^{56}$ |
$1$ |
$666.716128821$ |
$666.7161288209335$ |
|
✓ |
|
$C_{29}$ (as 29T1) |
not computed |
$2$ |
$28$ |
|
| 29.29.127...161.1 |
$x^{29} - x^{28} - 448 x^{27} + 107 x^{26} + 76138 x^{25} - 43560 x^{24} - 6896718 x^{23} + 8492788 x^{22} + 374467531 x^{21} - 737137472 x^{20} - 12707566814 x^{19} + 34389111341 x^{18} + 270515586354 x^{17} - 939536322456 x^{16} - 3528471156331 x^{15} + 15628114907220 x^{14} + 26518327124887 x^{13} - 161458375653531 x^{12} - 93674380846644 x^{11} + 1045971567643780 x^{10} - 54383106047402 x^{9} - 4238937042324143 x^{8} + 1725076964802557 x^{7} + 10520005444822970 x^{6} - 6101874655993302 x^{5} - 15103434975606529 x^{4} + 9152562248392343 x^{3} + 10944332007104174 x^{2} - 5127494290967802 x - 2711408412652309$ |
$29$ |
[29,0] |
$929^{28}$ |
$1$ |
$733.956539804$ |
$733.956539804396$ |
|
✓ |
|
$C_{29}$ (as 29T1) |
not computed |
$2$ |
$28$ |
|
