| 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 |
| 20.0.957...125.1 |
$x^{20} - 10 x^{19} + 47 x^{18} - 134 x^{17} + 244 x^{16} - 252 x^{15} + 14 x^{14} + 403 x^{13} - 595 x^{12} + 136 x^{11} + 768 x^{10} - 1227 x^{9} + 749 x^{8} + 44 x^{7} - 325 x^{6} + 108 x^{5} + 101 x^{4} - 108 x^{3} + 46 x^{2} - 10 x + 1$ |
$20$ |
[0,10] |
$5^{15}\cdot 11^{12}$ |
$2$ |
$14.0949361983$ |
$22.76887911715532$ |
|
|
? |
$C_5\times F_5$ (as 20T29) |
trivial |
$10$ |
$9$ |
$7329.26903421$ |
| 20.0.291...125.2 |
$x^{20} - 2 x^{15} + 4 x^{10} - 3 x^{5} + 1$ |
$20$ |
[0,10] |
$5^{35}$ |
$1$ |
$16.7185076244$ |
$21.628814119831024$ |
|
|
✓ |
$C_5\times F_5$ (as 20T29) |
trivial |
$10$ |
$9$ |
$60106.390253$ |
| 20.0.181...125.4 |
$x^{20} - 10 x^{15} + 30 x^{10} - 15 x^{5} + 5$ |
$20$ |
[0,10] |
$5^{39}$ |
$1$ |
$23.067020864764707$ |
$31.82625288866059$ |
|
|
? |
$C_5\times F_5$ (as 20T29) |
trivial |
$10$ |
$9$ |
$1421757.9773811775$ |
| 20.0.627...000.1 |
$x^{20} - x^{19} - 14 x^{18} + 8 x^{17} + 84 x^{16} + 21 x^{15} - 284 x^{14} - 856 x^{13} + 2957 x^{12} - 2148 x^{11} - 454 x^{10} + 442 x^{9} + 1242 x^{8} - 2984 x^{7} + 2070 x^{6} + 2062 x^{5} - 2189 x^{4} - 693 x^{3} + 572 x^{2} + 154 x + 11$ |
$20$ |
[0,10] |
$2^{16}\cdot 5^{15}\cdot 11^{12}$ |
$3$ |
$24.540709294$ |
$39.642921082121845$ |
|
|
? |
$C_5\times F_5$ (as 20T29) |
$[5]$ |
$10$ |
$9$ |
$475214.0571061137$ |
| 20.0.913...125.1 |
$x^{20} - 118 x^{15} + 4169 x^{10} - 40172 x^{5} + 161051$ |
$20$ |
[0,10] |
$5^{35}\cdot 11^{12}$ |
$2$ |
$70.4746809913$ |
$147.28104481730549$ |
|
|
|
$C_5\times F_5$ (as 20T29) |
$[5]$ |
$10$ |
$9$ |
$25950246651.417282$ |
| 20.0.913...125.2 |
$x^{20} - 41 x^{15} + 1881 x^{10} - 54571 x^{5} + 1771561$ |
$20$ |
[0,10] |
$5^{35}\cdot 11^{12}$ |
$2$ |
$70.4746809913$ |
$129.48792039594974$ |
|
|
? |
$C_5\times F_5$ (as 20T29) |
$[55]$ |
$10$ |
$9$ |
$1114811725.378162$ |
| 20.0.254...125.1 |
$x^{20} - 8 x^{19} - 167 x^{18} + 374 x^{17} + 17039 x^{16} + 38288 x^{15} - 735310 x^{14} - 5128108 x^{13} + 7151967 x^{12} + 188733886 x^{11} + 569808055 x^{10} - 2282213678 x^{9} - 17208973972 x^{8} - 16433231696 x^{7} + 214119303238 x^{6} + 717838125680 x^{5} - 502397221205 x^{4} - 7823618530310 x^{3} - 8270841308686 x^{2} + 29747851180432 x + 86798990281751$ |
$20$ |
[0,10] |
$5^{15}\cdot 11^{12}\cdot 61^{12}$ |
$3$ |
$166.058463566$ |
$610.3873428357342$ |
|
|
|
$C_5\times F_5$ (as 20T29) |
$[5, 5, 5]$ |
$10$ |
$9$ |
$3970645939642.0083$ |
| 20.0.930...125.1 |
$x^{20} - 4 x^{19} - 180 x^{18} + 1861 x^{17} + 41285 x^{16} + 56486 x^{15} - 1770231 x^{14} + 13207675 x^{13} + 539202114 x^{12} + 6259348669 x^{11} + 44724494010 x^{10} + 229585020498 x^{9} + 900899023954 x^{8} + 2784140309493 x^{7} + 6871932187949 x^{6} + 13592479679308 x^{5} + 21415551177601 x^{4} + 26404835212626 x^{3} + 24419514025237 x^{2} + 15370942553698 x + 5232878702531$ |
$20$ |
[0,10] |
$3^{16}\cdot 5^{15}\cdot 11^{12}\cdot 41^{12}$ |
$4$ |
$315.086961494$ |
$1069.7092235816292$ |
|
|
? |
$C_5\times F_5$ (as 20T29) |
$[5, 5, 5, 1665305]$ |
$10$ |
$9$ |
$963337255.3397985$ |
| 20.0.206...125.1 |
$x^{20} - 25947 x^{15} - 76999681 x^{10} + 146151013550157 x^{5} + 3005011477995800801$ |
$20$ |
[0,10] |
$5^{35}\cdot 11^{12}\cdot 41^{12}$ |
$3$ |
$654.189294338$ |
$2873.25348267535$ |
|
|
? |
$C_5\times F_5$ (as 20T29) |
not computed |
$10$ |
$9$ |
|
| 20.0.158...000.1 |
$x^{20} - 1814102 x^{15} + 4673959352304 x^{10} - 43581344807630608 x^{5} + 331470290341877498625616$ |
$20$ |
[0,10] |
$2^{16}\cdot 5^{35}\cdot 11^{12}\cdot 61^{12}$ |
$4$ |
$1445.62288997$ |
$6043.897920041531$ |
|
|
? |
$C_5\times F_5$ (as 20T29) |
not computed |
$10$ |
$9$ |
|
| 20.0.573...125.1 |
$x^{20} - 2 x^{19} - 3063 x^{18} + 56360 x^{17} + 3725721 x^{16} - 136176698 x^{15} - 775112280 x^{14} + 118143737840 x^{13} - 2064108884245 x^{12} - 10834777388248 x^{11} + 1034359675135247 x^{10} - 21566981447020668 x^{9} + 302277263506153992 x^{8} - 3933531629742272088 x^{7} + 52433632090043553846 x^{6} - 622457267869487652912 x^{5} + 5752830050933993979591 x^{4} - 38480091547554245555724 x^{3} + 177378875955066879158870 x^{2} - 508045130993392801755650 x + 725830423259092273389151$ |
$20$ |
[0,10] |
$5^{15}\cdot 11^{12}\cdot 41^{12}\cdot 61^{12}$ |
$4$ |
$1541.45669865$ |
$11907.829420678141$ |
|
|
|
$C_5\times F_5$ (as 20T29) |
not computed |
$10$ |
$9$ |
|
| 20.0.136...125.1 |
$x^{20} - 4 x^{19} - 11030 x^{18} - 349639 x^{17} + 43133865 x^{16} + 3165845986 x^{15} + 3297596774 x^{14} - 7831652014980 x^{13} - 366025154454816 x^{12} - 3519052998417431 x^{11} + 369783648942913960 x^{10} + 22397712541078584313 x^{9} + 716821696556315266424 x^{8} + 15845552032766343133183 x^{7} + 260355500215372228216244 x^{6} + 3260774067552606207924018 x^{5} + 31182656611119677641118731 x^{4} + 223683928418871140736442876 x^{3} + 1152215888689249604582827267 x^{2} + 3872795249613793564434947278 x + 6616039969022180498502070261$ |
$20$ |
[0,10] |
$5^{15}\cdot 11^{16}\cdot 31^{12}\cdot 181^{12}$ |
$4$ |
$4043.57788454$ |
$22728.661795152853$ |
|
|
? |
$C_5\times F_5$ (as 20T29) |
not computed |
$10$ |
$9$ |
|
| 20.0.551...000.1 |
$x^{20} - 2380244 x^{15} - 16449885784464 x^{10} - 54627959472340369984 x^{5} + 526728719890528781692016896$ |
$20$ |
[0,10] |
$2^{16}\cdot 5^{35}\cdot 11^{12}\cdot 461^{12}$ |
$4$ |
$4864.94203905$ |
$30479.93193938791$ |
|
|
? |
$C_5\times F_5$ (as 20T29) |
not computed |
$10$ |
$9$ |
|
| 20.0.254...125.1 |
$x^{20} - 10 x^{19} + 50 x^{18} - 165 x^{17} + 401 x^{16} + 29082274 x^{15} - 257595575 x^{14} + 1057621205 x^{13} - 2748329129 x^{12} + 5145784683 x^{11} + 771422587822781 x^{10} - 4170822961364545 x^{9} + 10946763251886561 x^{8} - 16613144662595113 x^{7} + 16782740267443763 x^{6} + 4211111527467189063284 x^{5} - 13145794848179964973699 x^{4} - 3097304809802488626839 x^{3} + 21237432158942543809016 x^{2} - 9205451745388989028944 x + 6578911714393603275321248551$ |
$20$ |
[0,10] |
$5^{15}\cdot 11^{12}\cdot 19^{16}\cdot 461^{12}$ |
$4$ |
$5892.32306458$ |
$32456.768093585557$ |
|
|
|
$C_5\times F_5$ (as 20T29) |
not computed |
$10$ |
$9$ |
|
| 20.0.122...125.1 |
$x^{20} - 78330153 x^{15} + 2737990582811559 x^{10} - 24499004414433966486927 x^{5} + 75302901891158409924316939431$ |
$20$ |
[0,10] |
$3^{16}\cdot 5^{35}\cdot 31^{12}\cdot 181^{12}$ |
$4$ |
$7150.20794974$ |
$45713.48451303589$ |
|
|
|
$C_5\times F_5$ (as 20T29) |
not computed |
$10$ |
$9$ |
|
| 20.0.154...000.1 |
$x^{20} - 851737518 x^{15} + 2128761163619493418224 x^{10} - 2467172500874840049039927482832 x^{5} + 67777855648151168856132999894099006781776$ |
$20$ |
[0,10] |
$2^{16}\cdot 3^{16}\cdot 5^{35}\cdot 11^{12}\cdot 41^{12}\cdot 61^{12}$ |
$6$ |
$32316.3523028$ |
$249645.42374627848$ |
|
|
? |
$C_5\times F_5$ (as 20T29) |
not computed |
$10$ |
$9$ |
|
