| 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 |
| 28.0.305...909.1 |
$x^{28} - x^{27} + x^{26} - x^{25} + x^{24} - x^{23} + x^{22} - x^{21} + x^{20} - x^{19} + x^{18} - x^{17} + x^{16} - x^{15} + x^{14} - x^{13} + x^{12} - x^{11} + x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1$ |
$28$ |
[0,14] |
$29^{27}$ |
$1$ |
$25.7139916164$ |
$25.713991616408272$ |
✓ |
✓ |
✓ |
$C_{28}$ (as 28T1) |
$[2, 2, 2]$ |
$58$ |
$13$ |
$487075979.1876791$ |
| 28.0.327...933.1 |
$x^{28} - x + 1$ |
$28$ |
[0,14] |
$17787551\cdot 18\!\cdots\!83$ |
$2$ |
$27.9865347734$ |
$1.8083721028872995e+20$ |
|
|
✓ |
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$13$ |
$832511028.3094091$ |
| 28.2.335...539.1 |
$x^{28} - x - 1$ |
$28$ |
[2,13] |
$-\,349\cdot 14769635993383\cdot 6516302002526983353692617$ |
$3$ |
$28.0132926281$ |
$1.8327288288641178e+20$ |
|
|
✓ |
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$14$ |
$985266200.5138724$ |
| 28.0.194...021.1 |
$x^{28} + 28 x^{24} - 14 x^{23} - 35 x^{22} - 19 x^{21} + 1470 x^{20} - 4557 x^{19} + 9849 x^{18} - 9660 x^{17} + 2863 x^{16} + 12915 x^{15} - 18102 x^{14} + 12103 x^{13} - 2891 x^{12} - 21119 x^{11} + 2975 x^{10} - 4704 x^{9} + 70 x^{8} + 13698 x^{7} + 6909 x^{6} + 4900 x^{5} + 5047 x^{4} + 1015 x^{3} - 7 x^{2} - 7 x + 1$ |
$28$ |
[0,14] |
$3^{21}\cdot 7^{37}$ |
$2$ |
$29.824806642515952$ |
$31.97125685688869$ |
|
|
|
$D_{28}$ (as 28T10) |
trivial |
$6$ |
$13$ |
$13724323267.71925$ |
| 28.0.650...777.1 |
$x^{28} - 2 x^{27} + 4 x^{26} - 10 x^{25} + 5 x^{24} + 7 x^{23} - 18 x^{22} - 225 x^{21} - 120 x^{20} + 1331 x^{19} - 2152 x^{18} + 4025 x^{17} + 6967 x^{16} - 15748 x^{15} + 11604 x^{14} - 4171 x^{13} - 26180 x^{12} + 37520 x^{11} - 9040 x^{10} + 16909 x^{9} - 40976 x^{8} - 11561 x^{7} + 79270 x^{6} - 49005 x^{5} + 81626 x^{4} - 70530 x^{3} + 35205 x^{2} - 15236 x + 3229$ |
$28$ |
[0,14] |
$7^{21}\cdot 71^{13}$ |
$2$ |
$31.141271063244027$ |
$36.262079388792664$ |
|
|
? |
$D_{28}$ (as 28T10) |
trivial |
$2$ |
$13$ |
$3185481783.8925004$ |
| 28.4.653...056.1 |
$x^{28} - 4 x^{27} + 18 x^{26} - 60 x^{25} + 165 x^{24} - 420 x^{23} + 798 x^{22} - 1440 x^{21} + 2040 x^{20} - 2292 x^{19} + 2478 x^{18} - 756 x^{17} - 657 x^{16} + 1464 x^{15} - 4920 x^{14} + 3072 x^{13} - 1068 x^{12} + 3768 x^{11} + 1752 x^{10} - 4680 x^{9} - 1116 x^{8} + 672 x^{7} + 1800 x^{6} - 240 x^{5} - 216 x^{4} - 192 x^{3} + 24 x^{2} + 32 x + 4$ |
$28$ |
[4,12] |
$2^{66}\cdot 3^{46}$ |
$2$ |
$31.146752035524152$ |
|
|
|
? |
$G(2,2)$ (as 28T393) |
trivial |
$2$ |
$15$ |
$31272111927.464275$ |
| 28.4.290...736.1 |
$x^{28} - 4 x^{27} + 18 x^{26} - 60 x^{25} + 171 x^{24} - 384 x^{23} + 780 x^{22} - 1296 x^{21} + 1893 x^{20} - 2436 x^{19} + 2766 x^{18} - 3036 x^{17} + 3807 x^{16} - 3504 x^{15} + 1176 x^{14} - 3408 x^{13} + 13503 x^{12} - 17676 x^{11} + 2646 x^{10} + 15564 x^{9} - 12315 x^{8} - 4656 x^{7} + 6252 x^{6} + 13440 x^{5} - 27621 x^{4} + 20340 x^{3} - 4998 x^{2} - 1364 x + 593$ |
$28$ |
[4,12] |
$2^{84}\cdot 3^{36}$ |
$2$ |
$32.84971455941284$ |
|
|
|
? |
$G(2,2)$ (as 28T393) |
trivial |
$2$ |
$15$ |
$139450119244.1394$ |
| 28.4.418...584.1 |
$x^{28} - 4 x^{27} - 6 x^{26} + 60 x^{25} - 87 x^{24} - 192 x^{23} + 876 x^{22} - 1176 x^{21} - 777 x^{20} + 8220 x^{19} - 19362 x^{18} + 3636 x^{17} + 78723 x^{16} - 142920 x^{15} - 20736 x^{14} + 354720 x^{13} - 380928 x^{12} - 100656 x^{11} + 533988 x^{10} - 391176 x^{9} - 25344 x^{8} + 134736 x^{7} + 42672 x^{6} - 127872 x^{5} + 61488 x^{4} - 14976 x^{3} + 13680 x^{2} - 5952 x - 564$ |
$28$ |
[4,12] |
$2^{72}\cdot 3^{46}$ |
$2$ |
$36.13426231985544$ |
|
|
|
? |
$G(2,2)$ (as 28T393) |
trivial |
$2$ |
$15$ |
$466642221703.6705$ |
| 28.2.462...167.1 |
$x^{28} - 3 x^{27} + 5 x^{26} - 37 x^{25} + 223 x^{24} - 471 x^{23} + 612 x^{22} - 2497 x^{21} + 8709 x^{20} - 13185 x^{19} + 9400 x^{18} - 14827 x^{17} + 46063 x^{16} - 65223 x^{15} + 33754 x^{14} - 24986 x^{13} + 51170 x^{12} - 43382 x^{11} - 84023 x^{10} + 134581 x^{9} - 102493 x^{8} + 27983 x^{7} - 169214 x^{6} + 162210 x^{5} - 64809 x^{4} - 131662 x^{3} + 54254 x^{2} - 97483 x - 91661$ |
$28$ |
[2,13] |
$-\,7^{21}\cdot 71^{14}$ |
$2$ |
$36.262079388792664$ |
$36.262079388792664$ |
|
|
? |
$D_{28}$ (as 28T10) |
trivial |
$2$ |
$14$ |
$46802852168.54651$ |
| 28.4.670...944.1 |
$x^{28} - 8 x^{27} + 36 x^{26} - 96 x^{25} + 156 x^{24} - 144 x^{23} + 342 x^{22} - 1656 x^{21} + 4914 x^{20} - 9396 x^{19} + 11448 x^{18} - 7092 x^{17} - 1560 x^{16} + 19680 x^{15} - 37440 x^{14} + 42264 x^{13} - 33021 x^{12} - 10152 x^{11} + 20760 x^{10} + 15684 x^{9} + 11376 x^{8} + 13152 x^{7} + 53130 x^{6} - 191412 x^{5} + 8874 x^{4} + 84924 x^{3} - 20700 x^{2} + 58756 x + 11038$ |
$28$ |
[4,12] |
$2^{60}\cdot 3^{54}$ |
$2$ |
$36.74740672698717$ |
|
|
|
? |
$G(2,2)$ (as 28T393) |
trivial |
$2$ |
$15$ |
$633689078785.1482$ |
| 28.4.848...976.1 |
$x^{28} - 8 x^{27} + 18 x^{26} + 12 x^{25} - 114 x^{24} + 252 x^{23} - 414 x^{22} + 216 x^{21} + 936 x^{20} - 2592 x^{19} + 4950 x^{18} - 7236 x^{17} + 6228 x^{16} - 3924 x^{15} - 3402 x^{14} + 21024 x^{13} - 46377 x^{12} + 96192 x^{11} - 166428 x^{10} + 245340 x^{9} - 336312 x^{8} + 394416 x^{7} - 416520 x^{6} + 396720 x^{5} - 316008 x^{4} + 228528 x^{3} - 129168 x^{2} + 56640 x - 18096$ |
$28$ |
[4,12] |
$2^{54}\cdot 3^{58}$ |
$2$ |
$37.057869520204406$ |
|
|
|
? |
$G(2,2)$ (as 28T393) |
$[2]$ |
$2$ |
$15$ |
$274493762880.8474$ |
| 28.0.849...381.1 |
$x^{28} - 8 x^{27} + 39 x^{26} - 147 x^{25} + 484 x^{24} - 1461 x^{23} + 4001 x^{22} - 10052 x^{21} + 23841 x^{20} - 52926 x^{19} + 109173 x^{18} - 208723 x^{17} + 369896 x^{16} - 608215 x^{15} + 913744 x^{14} - 1246890 x^{13} + 1584122 x^{12} - 1829692 x^{11} + 1878311 x^{10} - 1777347 x^{9} + 1518093 x^{8} - 1036936 x^{7} + 598732 x^{6} - 344364 x^{5} + 177291 x^{4} - 79332 x^{3} + 46992 x^{2} - 15367 x + 6413$ |
$28$ |
[0,14] |
$11^{14}\cdot 181^{13}$ |
$2$ |
$37.05990078737718$ |
$44.62062303464621$ |
|
|
|
$D_{28}$ (as 28T10) |
trivial |
$2$ |
$13$ |
$81264745077.87146$ |
| 28.4.941...064.1 |
$x^{28} - 4 x^{27} + 12 x^{26} - 12 x^{25} - 15 x^{24} + 228 x^{22} - 648 x^{21} + 15 x^{20} + 1308 x^{19} - 2868 x^{18} - 5316 x^{17} + 3567 x^{16} - 4800 x^{15} - 24120 x^{14} - 7152 x^{13} + 6543 x^{12} - 30252 x^{11} - 41388 x^{10} + 3180 x^{9} + 23871 x^{8} - 576 x^{7} - 7596 x^{6} + 504 x^{5} + 2433 x^{4} - 1260 x^{3} + 276 x^{2} - 28 x + 1$ |
$28$ |
[4,12] |
$2^{70}\cdot 3^{48}$ |
$2$ |
$37.19607717383448$ |
|
|
|
|
$G(2,2)$ (as 28T393) |
trivial |
$2$ |
$15$ |
$511133804481.5497$ |
| 28.4.376...256.1 |
$x^{28} + 6 x^{26} - 12 x^{25} + 15 x^{24} - 60 x^{23} + 180 x^{22} + 420 x^{21} + 1473 x^{20} + 4188 x^{19} + 6318 x^{18} + 10128 x^{17} + 10377 x^{16} - 2976 x^{15} - 22656 x^{14} - 48960 x^{13} - 80637 x^{12} - 73104 x^{11} - 8190 x^{10} + 47772 x^{9} + 42297 x^{8} + 7644 x^{7} - 9012 x^{6} - 5892 x^{5} - 837 x^{4} + 276 x^{3} + 42 x^{2} - 32 x - 9$ |
$28$ |
[4,12] |
$2^{72}\cdot 3^{48}$ |
$2$ |
$39.08402502226406$ |
|
|
|
? |
$G(2,2)$ (as 28T393) |
$[2]$ |
$2$ |
$15$ |
$763171552960.3567$ |
| 28.4.376...256.2 |
$x^{28} - 9 x^{27} + 30 x^{26} - 45 x^{25} + 12 x^{24} + 132 x^{23} - 348 x^{22} - 96 x^{21} + 2547 x^{20} - 7095 x^{19} + 8130 x^{18} + 9057 x^{17} - 52884 x^{16} + 103116 x^{15} - 112728 x^{14} + 17268 x^{13} + 221331 x^{12} - 520155 x^{11} + 640578 x^{10} - 363759 x^{9} - 238344 x^{8} + 825552 x^{7} - 1079628 x^{6} + 933324 x^{5} - 569583 x^{4} + 237027 x^{3} - 63090 x^{2} + 14627 x - 3984$ |
$28$ |
[4,12] |
$2^{72}\cdot 3^{48}$ |
$2$ |
$39.08402502226406$ |
|
|
|
? |
$G(2,2)$ (as 28T393) |
trivial |
$2$ |
$15$ |
$742728597672.5787$ |
| 28.4.376...256.3 |
$x^{28} - 9 x^{27} + 30 x^{26} - 45 x^{25} + 12 x^{24} + 132 x^{23} - 348 x^{22} - 96 x^{21} + 2547 x^{20} - 7095 x^{19} + 8130 x^{18} + 9057 x^{17} - 52884 x^{16} + 103116 x^{15} - 112728 x^{14} + 17268 x^{13} + 221331 x^{12} - 520155 x^{11} + 640578 x^{10} - 363759 x^{9} - 238344 x^{8} + 825552 x^{7} - 1079628 x^{6} + 933324 x^{5} - 569583 x^{4} + 237027 x^{3} - 63090 x^{2} + 14627 x - 3984$ |
$28$ |
[4,12] |
$2^{72}\cdot 3^{48}$ |
$2$ |
$39.08402502226406$ |
|
|
|
? |
$G(2,2)$ (as 28T393) |
trivial |
$2$ |
$15$ |
$742728597672.5787$ |
| 28.0.503...649.1 |
$x^{28} - x^{27} + 14 x^{26} - 11 x^{25} + 115 x^{24} - 79 x^{23} + 617 x^{22} - 353 x^{21} + 2421 x^{20} - 1188 x^{19} + 7015 x^{18} - 2803 x^{17} + 15415 x^{16} - 5107 x^{15} + 25195 x^{14} - 6334 x^{13} + 30532 x^{12} - 6088 x^{11} + 26057 x^{10} - 3239 x^{9} + 15207 x^{8} - 1590 x^{7} + 5362 x^{6} - 70 x^{5} + 1050 x^{4} - 84 x^{3} + 77 x^{2} + 7 x + 1$ |
$28$ |
[0,14] |
$3^{14}\cdot 29^{26}$ |
$2$ |
$39.4913177365$ |
$39.49131773649383$ |
✓ |
✓ |
? |
$C_2\times C_{14}$ (as 28T2) |
$[4, 4, 12]$ |
$6$ |
$13$ |
$487075979.1876791$ |
| 28.4.669...344.1 |
$x^{28} - 4 x^{27} + 12 x^{25} + 12 x^{24} - 264 x^{22} + 336 x^{21} + 387 x^{20} + 396 x^{19} - 2016 x^{18} - 3780 x^{17} + 3330 x^{16} + 13104 x^{15} - 1728 x^{14} - 6192 x^{13} - 28233 x^{12} + 3780 x^{11} + 27216 x^{10} + 3348 x^{9} - 17496 x^{8} + 68688 x^{7} - 71064 x^{6} + 95904 x^{5} - 36315 x^{4} - 118476 x^{3} + 123120 x^{2} - 14364 x - 41526$ |
$28$ |
[4,12] |
$2^{76}\cdot 3^{46}$ |
$2$ |
$39.89546011169115$ |
|
|
|
? |
$G(2,2)$ (as 28T393) |
trivial |
$2$ |
$15$ |
$1653920951549.6929$ |
| 28.2.725...875.1 |
$x^{28} - 5 x^{27} - 3 x^{26} + 57 x^{25} - 13 x^{24} - 420 x^{23} + 259 x^{22} + 2099 x^{21} - 1147 x^{20} - 7975 x^{19} + 7844 x^{18} + 15881 x^{17} - 34395 x^{16} - 17074 x^{15} + 107194 x^{14} - 103829 x^{13} + 94772 x^{12} - 84342 x^{11} - 113950 x^{10} + 177636 x^{9} - 26899 x^{8} + 2410 x^{7} + 74025 x^{6} - 120275 x^{5} - 49775 x^{4} + 101875 x^{3} - 41875 x^{2} + 31250 x - 15625$ |
$28$ |
[2,13] |
$-\,5^{14}\cdot 499^{13}$ |
$2$ |
$40.01055182531362$ |
$49.949974974968704$ |
|
|
|
$D_{28}$ (as 28T10) |
trivial |
$2$ |
$14$ |
$2346058429844.763$ |
| 28.0.941...672.1 |
$x^{28} - 3 x^{14} + 3$ |
$28$ |
[0,14] |
$2^{28}\cdot 3^{27}\cdot 7^{28}$ |
$3$ |
$40.3839918504$ |
$71.99977726879091$ |
|
|
✓ |
$D_4\times F_7$ (as 28T41) |
trivial |
$6$ |
$13$ |
$647468634170.5619$ |
| 28.4.135...616.1 |
$x^{28} - 4 x^{27} + 36 x^{25} - 81 x^{24} - 108 x^{23} + 360 x^{22} - 504 x^{21} - 1971 x^{20} - 312 x^{19} - 2442 x^{18} - 12744 x^{17} - 21879 x^{16} - 36504 x^{15} - 61020 x^{14} - 77040 x^{13} - 88110 x^{12} - 110808 x^{11} - 134790 x^{10} - 148188 x^{9} - 149472 x^{8} - 130860 x^{7} - 93852 x^{6} - 55404 x^{5} - 27342 x^{4} - 10656 x^{3} - 2808 x^{2} - 368 x - 4$ |
$28$ |
[4,12] |
$2^{58}\cdot 3^{58}$ |
$2$ |
$40.915205136350075$ |
|
|
|
|
$G(2,2)$ (as 28T393) |
trivial |
$2$ |
$15$ |
$5246116940069.939$ |
| 28.4.135...616.2 |
$x^{28} - 4 x^{27} + 36 x^{25} - 81 x^{24} - 108 x^{23} + 360 x^{22} - 504 x^{21} - 1971 x^{20} - 312 x^{19} - 2442 x^{18} - 12744 x^{17} - 21879 x^{16} - 36504 x^{15} - 61020 x^{14} - 77040 x^{13} - 88110 x^{12} - 110808 x^{11} - 134790 x^{10} - 148188 x^{9} - 149472 x^{8} - 130860 x^{7} - 93852 x^{6} - 55404 x^{5} - 27342 x^{4} - 10656 x^{3} - 2808 x^{2} - 368 x - 4$ |
$28$ |
[4,12] |
$2^{58}\cdot 3^{58}$ |
$2$ |
$40.915205136350075$ |
|
|
|
|
$G(2,2)$ (as 28T393) |
trivial |
$2$ |
$15$ |
$5246116940069.939$ |
| 28.0.192...877.1 |
$x^{28} - 12 x^{27} + 74 x^{26} - 288 x^{25} + 773 x^{24} - 1407 x^{23} + 1601 x^{22} - 676 x^{21} - 794 x^{20} + 2173 x^{19} - 6644 x^{18} + 23336 x^{17} - 53512 x^{16} + 82551 x^{15} - 80880 x^{14} + 23133 x^{13} + 117766 x^{12} - 327568 x^{11} + 536090 x^{10} - 646700 x^{9} + 621936 x^{8} - 488735 x^{7} + 317878 x^{6} - 166984 x^{5} + 68952 x^{4} - 21502 x^{3} + 5711 x^{2} - 1133 x + 193$ |
$28$ |
[0,14] |
$43^{14}\cdot 53^{13}$ |
$2$ |
$41.42770561891819$ |
$47.738873049120045$ |
|
|
? |
$D_{28}$ (as 28T10) |
$[3]$ |
$2$ |
$13$ |
$71584737217.10019$ |
| 28.4.211...544.1 |
$x^{28} - 4 x^{27} + 6 x^{26} + 12 x^{25} + 117 x^{24} - 192 x^{23} - 408 x^{22} - 1176 x^{21} + 2703 x^{20} + 4044 x^{19} + 606 x^{18} - 14532 x^{17} - 13677 x^{16} + 27552 x^{15} + 37308 x^{14} - 46728 x^{13} - 32919 x^{12} + 39348 x^{11} + 20994 x^{10} - 29004 x^{9} + 1233 x^{8} + 5808 x^{7} + 1140 x^{6} - 3600 x^{5} + 1713 x^{4} - 276 x^{3} + 6 x^{2} - 4 x + 1$ |
$28$ |
[4,12] |
$2^{84}\cdot 3^{42}$ |
$2$ |
$41.569219381653056$ |
|
|
|
? |
$G(2,2)$ (as 28T393) |
trivial |
$2$ |
$15$ |
$3258752842616.154$ |
| 28.4.211...544.2 |
$x^{28} - 4 x^{27} + 30 x^{26} - 108 x^{25} + 462 x^{24} - 1560 x^{23} + 5136 x^{22} - 14280 x^{21} + 35046 x^{20} - 73584 x^{19} + 133980 x^{18} - 213792 x^{17} + 296802 x^{16} - 356640 x^{15} + 342528 x^{14} - 222384 x^{13} - 3012 x^{12} + 271296 x^{11} - 496488 x^{10} + 629424 x^{9} - 610656 x^{8} + 453888 x^{7} - 187584 x^{6} - 38784 x^{5} + 100104 x^{4} - 81888 x^{3} + 50544 x^{2} - 18880 x + 2968$ |
$28$ |
[4,12] |
$2^{84}\cdot 3^{42}$ |
$2$ |
$41.569219381653056$ |
|
|
|
? |
$G(2,2)$ (as 28T393) |
$[2]$ |
$2$ |
$15$ |
$2522687043294.189$ |
| 28.4.211...544.3 |
$x^{28} - 12 x^{25} + 48 x^{24} - 48 x^{23} + 72 x^{22} - 168 x^{21} + 105 x^{20} + 768 x^{19} - 1188 x^{18} + 972 x^{17} - 1914 x^{16} + 6648 x^{15} - 5064 x^{14} - 3096 x^{13} + 4335 x^{12} - 312 x^{11} + 11280 x^{10} - 50508 x^{9} + 17676 x^{8} + 39912 x^{7} - 38904 x^{6} - 56496 x^{5} + 8235 x^{4} + 35832 x^{3} - 6420 x^{2} - 35108 x - 14634$ |
$28$ |
[4,12] |
$2^{84}\cdot 3^{42}$ |
$2$ |
$41.569219381653056$ |
|
|
|
? |
$\PSU(3,3)$ (as 28T323) |
$[2]$ |
$2$ |
$15$ |
$1829195696216.8582$ |
| 28.2.265...875.1 |
$x^{28} - 9 x^{27} + 53 x^{26} - 226 x^{25} + 695 x^{24} - 1455 x^{23} + 1352 x^{22} + 4587 x^{21} - 26437 x^{20} + 75511 x^{19} - 148243 x^{18} + 166438 x^{17} - 8850 x^{16} - 553583 x^{15} + 1599191 x^{14} - 2514414 x^{13} + 2904360 x^{12} - 819447 x^{11} - 1193138 x^{10} + 5517125 x^{9} - 17624126 x^{8} + 7384001 x^{7} - 17552991 x^{6} + 11860646 x^{5} - 8713168 x^{4} - 7406098 x^{3} - 9688274 x^{2} - 1853761 x - 465059$ |
$28$ |
[2,13] |
$-\,3^{14}\cdot 5^{21}\cdot 71^{13}$ |
$3$ |
$41.90838600179758$ |
$48.79971717169349$ |
|
|
? |
$D_{28}$ (as 28T10) |
not computed |
$2$ |
$14$ |
|
| 28.4.267...376.1 |
$x^{28} - 8 x^{27} + 18 x^{26} + 24 x^{25} - 219 x^{24} + 528 x^{23} - 504 x^{22} - 792 x^{21} + 3822 x^{20} - 3720 x^{19} - 10236 x^{18} + 29088 x^{17} - 2226 x^{16} - 73848 x^{15} + 58836 x^{14} + 105792 x^{13} - 134013 x^{12} - 121848 x^{11} + 172362 x^{10} + 170040 x^{9} - 221931 x^{8} - 132624 x^{7} + 164988 x^{6} + 144528 x^{5} - 154173 x^{4} - 76368 x^{3} + 49938 x^{2} + 79840 x - 48347$ |
$28$ |
[4,12] |
$2^{78}\cdot 3^{46}$ |
$2$ |
$41.920419564484185$ |
|
|
|
? |
$G(2,2)$ (as 28T393) |
trivial |
$2$ |
$15$ |
$1704998304150.298$ |
| 28.4.267...376.2 |
$x^{28} - 4 x^{27} + 6 x^{26} - 150 x^{24} + 456 x^{23} + 480 x^{22} - 3168 x^{21} + 1689 x^{20} + 8292 x^{19} - 12618 x^{18} - 4008 x^{17} + 25002 x^{16} - 23280 x^{15} - 6672 x^{14} + 47496 x^{13} - 46584 x^{12} - 30144 x^{11} + 77256 x^{10} - 3408 x^{9} - 64524 x^{8} + 1728 x^{7} + 30720 x^{6} + 11184 x^{5} - 6612 x^{4} - 13968 x^{3} - 9912 x^{2} - 3136 x - 368$ |
$28$ |
[4,12] |
$2^{78}\cdot 3^{46}$ |
$2$ |
$41.920419564484185$ |
|
|
|
|
$G(2,2)$ (as 28T393) |
trivial |
$2$ |
$15$ |
$2744376685978.139$ |
| 28.4.267...376.3 |
$x^{28} - 2 x^{27} + 18 x^{25} - 81 x^{24} + 48 x^{23} - 216 x^{22} - 72 x^{21} + 2442 x^{20} - 2196 x^{19} + 7596 x^{18} - 13428 x^{17} - 10836 x^{16} + 38124 x^{15} - 74064 x^{14} + 115644 x^{13} + 34410 x^{12} - 394320 x^{11} + 529860 x^{10} - 198024 x^{9} - 305028 x^{8} + 686424 x^{7} - 854844 x^{6} + 761592 x^{5} - 483174 x^{4} + 215244 x^{3} - 64248 x^{2} + 11452 x - 926$ |
$28$ |
[4,12] |
$2^{78}\cdot 3^{46}$ |
$2$ |
$41.920419564484185$ |
|
|
|
? |
$G(2,2)$ (as 28T393) |
trivial |
$2$ |
$15$ |
$4784367711537.669$ |
| 28.4.267...376.4 |
$x^{28} - 2 x^{27} - 6 x^{26} + 12 x^{25} - 36 x^{23} + 48 x^{22} + 96 x^{21} + 48 x^{20} - 296 x^{19} - 1160 x^{18} - 2880 x^{17} - 3108 x^{16} + 28248 x^{15} + 13176 x^{14} - 86016 x^{13} - 22524 x^{12} + 75624 x^{11} + 100360 x^{10} + 56848 x^{9} - 223896 x^{8} + 31296 x^{7} + 181824 x^{6} - 95040 x^{5} + 22152 x^{4} - 9744 x^{3} + 2160 x^{2} - 96 x + 48$ |
$28$ |
[4,12] |
$2^{78}\cdot 3^{46}$ |
$2$ |
$41.920419564484185$ |
|
|
|
? |
$G(2,2)$ (as 28T393) |
trivial |
$2$ |
$15$ |
$3061447218892.9146$ |
| 28.4.275...824.1 |
$x^{28} - 4 x^{27} + 18 x^{25} - 45 x^{24} + 162 x^{23} - 306 x^{22} - 288 x^{21} + 2025 x^{20} - 2946 x^{19} + 1362 x^{18} + 3564 x^{17} - 18477 x^{16} + 32868 x^{15} + 16686 x^{14} - 105066 x^{13} + 48096 x^{12} + 155520 x^{11} - 202092 x^{10} + 4308 x^{9} + 224856 x^{8} - 454176 x^{7} + 468000 x^{6} + 648 x^{5} - 559152 x^{4} + 720720 x^{3} - 518400 x^{2} + 242000 x - 50000$ |
$28$ |
[4,12] |
$2^{40}\cdot 3^{70}$ |
$2$ |
$41.961015280007636$ |
|
|
|
|
$G(2,2)$ (as 28T393) |
trivial |
$2$ |
$15$ |
$10226060287587.56$ |
| 28.4.429...416.1 |
$x^{28} - 4 x^{27} + 18 x^{26} - 18 x^{24} + 252 x^{23} - 72 x^{22} - 432 x^{21} + 1881 x^{20} - 552 x^{19} - 3606 x^{18} + 3960 x^{17} - 3159 x^{16} - 3528 x^{15} + 14292 x^{14} - 5040 x^{13} - 6156 x^{12} + 9792 x^{11} - 12480 x^{10} - 1200 x^{9} + 12384 x^{8} - 4320 x^{7} - 72 x^{6} + 2304 x^{5} - 1908 x^{4} + 72 x^{2} - 64 x + 4$ |
$28$ |
[4,12] |
$2^{66}\cdot 3^{54}$ |
$2$ |
$42.63174640915747$ |
|
|
|
? |
$G(2,2)$ (as 28T393) |
trivial |
$2$ |
$15$ |
$2945609402193.5283$ |
| 28.4.528...736.1 |
$x^{28} - 6 x^{26} - 32 x^{25} - 6 x^{24} + 456 x^{23} + 16 x^{22} - 1848 x^{21} + 3 x^{20} - 1640 x^{19} + 4506 x^{18} + 27480 x^{17} - 25916 x^{16} - 51984 x^{15} + 47664 x^{14} + 18832 x^{13} + 3327 x^{12} - 18480 x^{11} - 54530 x^{10} + 75984 x^{9} - 19254 x^{8} + 5704 x^{7} + 55584 x^{6} - 56280 x^{5} - 61019 x^{4} + 65304 x^{3} - 13794 x^{2} - 12936 x + 4968$ |
$28$ |
[4,12] |
$2^{98}\cdot 3^{34}$ |
$2$ |
$42.95033033822286$ |
|
|
|
|
$G(2,2)$ (as 28T393) |
trivial |
$2$ |
$15$ |
$20984051309482.99$ |
| 28.4.543...464.1 |
$x^{28} - 10 x^{27} + 54 x^{26} - 198 x^{25} + 531 x^{24} - 1080 x^{23} + 1404 x^{22} - 468 x^{21} - 990 x^{20} - 684 x^{19} + 6138 x^{18} - 7236 x^{17} - 5238 x^{16} + 16308 x^{15} - 2160 x^{14} - 12528 x^{13} + 3402 x^{12} - 1728 x^{11} + 7776 x^{10} + 10368 x^{9} - 22842 x^{8} + 1944 x^{7} + 14904 x^{6} - 6480 x^{5} - 2106 x^{4} + 324 x^{3} + 1296 x^{2} - 540 x + 54$ |
$28$ |
[4,12] |
$2^{60}\cdot 3^{58}$ |
$2$ |
$42.991923418878145$ |
|
|
|
? |
$G(2,2)$ (as 28T393) |
trivial |
$2$ |
$15$ |
$5244773578660.423$ |
| 28.4.543...464.2 |
$x^{28} - 36 x^{24} - 72 x^{23} + 234 x^{20} + 960 x^{19} - 288 x^{18} - 2160 x^{17} - 2214 x^{16} + 1368 x^{15} + 6840 x^{14} - 6912 x^{13} + 7641 x^{12} - 20232 x^{11} + 31584 x^{10} - 38736 x^{9} + 47034 x^{8} - 69552 x^{7} + 86472 x^{6} - 68976 x^{5} + 46521 x^{4} - 43200 x^{3} + 28584 x^{2} - 6976 x + 144$ |
$28$ |
[4,12] |
$2^{60}\cdot 3^{58}$ |
$2$ |
$42.991923418878145$ |
|
|
|
? |
$G(2,2)$ (as 28T393) |
$[2]$ |
$2$ |
$15$ |
$2677254116490.4404$ |
| 28.4.602...096.1 |
$x^{28} + 72 x^{24} - 72 x^{23} + 936 x^{20} - 1920 x^{19} - 288 x^{18} + 1080 x^{17} + 15930 x^{16} + 5472 x^{15} - 13680 x^{14} - 6912 x^{13} + 8208 x^{12} + 97704 x^{11} + 126336 x^{10} + 77472 x^{9} - 129384 x^{8} - 228960 x^{7} - 135792 x^{6} - 83448 x^{5} - 63639 x^{4} - 43200 x^{3} - 13104 x^{2} - 1216 x + 576$ |
$28$ |
[4,12] |
$2^{76}\cdot 3^{48}$ |
$2$ |
$43.15226217924664$ |
|
|
|
|
$G(2,2)$ (as 28T393) |
$[2]$ |
$2$ |
$15$ |
$2511094585193.796$ |
| 28.4.602...096.2 |
$x^{28} - 8 x^{27} + 18 x^{26} + 12 x^{25} - 87 x^{24} + 144 x^{23} - 732 x^{22} + 1176 x^{21} + 3933 x^{20} - 6888 x^{19} + 6 x^{18} - 34092 x^{17} + 44853 x^{16} + 20832 x^{15} + 197496 x^{14} - 417264 x^{13} + 142635 x^{12} - 309816 x^{11} + 1085166 x^{10} - 484812 x^{9} - 488061 x^{8} + 335568 x^{7} - 99996 x^{6} + 94104 x^{5} - 24537 x^{4} - 6168 x^{3} + 666 x^{2} - 788 x - 977$ |
$28$ |
[4,12] |
$2^{76}\cdot 3^{48}$ |
$2$ |
$43.15226217924664$ |
|
|
|
? |
$G(2,2)$ (as 28T393) |
trivial |
$2$ |
$15$ |
$7222992276658.049$ |
| 28.4.602...096.3 |
$x^{28} + 72 x^{24} - 72 x^{23} + 936 x^{20} - 1920 x^{19} - 288 x^{18} + 1080 x^{17} + 15930 x^{16} + 5472 x^{15} - 13680 x^{14} - 6912 x^{13} + 8208 x^{12} + 97704 x^{11} + 126336 x^{10} + 77472 x^{9} - 129384 x^{8} - 228960 x^{7} - 135792 x^{6} - 83448 x^{5} - 63639 x^{4} - 43200 x^{3} - 13104 x^{2} - 1216 x + 576$ |
$28$ |
[4,12] |
$2^{76}\cdot 3^{48}$ |
$2$ |
$43.15226217924664$ |
|
|
|
|
$G(2,2)$ (as 28T393) |
$[2]$ |
$2$ |
$15$ |
$2511094585193.796$ |
| 28.4.110...296.1 |
$x^{28} - 6 x^{27} + 54 x^{25} - 45 x^{24} - 180 x^{23} + 36 x^{22} + 720 x^{21} - 360 x^{20} - 474 x^{19} + 1080 x^{18} - 4032 x^{17} - 1197 x^{16} + 2466 x^{15} + 28674 x^{14} - 29340 x^{13} + 6876 x^{12} - 53028 x^{11} + 87204 x^{10} - 29664 x^{9} + 62604 x^{8} - 145584 x^{7} + 115128 x^{6} - 58032 x^{5} + 32472 x^{4} - 14688 x^{3} - 2880 x^{2} + 2560 x + 768$ |
$28$ |
[4,12] |
$2^{42}\cdot 3^{70}$ |
$2$ |
$44.090815370097204$ |
|
|
|
? |
$G(2,2)$ (as 28T393) |
trivial |
$2$ |
$15$ |
$6499859640645.487$ |
| 28.4.118...656.1 |
$x^{28} - 8 x^{27} + 6 x^{26} + 96 x^{25} - 117 x^{24} - 1152 x^{23} + 3468 x^{22} + 1176 x^{21} - 20814 x^{20} + 33024 x^{19} + 12588 x^{18} - 108864 x^{17} + 139134 x^{16} - 3744 x^{15} - 209712 x^{14} + 288384 x^{13} - 172812 x^{12} + 16128 x^{11} + 18552 x^{10} + 4032 x^{9} - 3444 x^{8} - 15360 x^{7} + 21264 x^{6} - 7968 x^{5} - 312 x^{4} + 576 x^{3} - 336 x^{2} - 128 x - 8$ |
$28$ |
[4,12] |
$2^{96}\cdot 3^{36}$ |
$2$ |
$44.21243715343166$ |
|
|
|
|
$G(2,2)$ (as 28T393) |
trivial |
$2$ |
$15$ |
$23365454965436.94$ |
| 28.4.118...656.2 |
$x^{28} - 8 x^{27} + 30 x^{26} - 72 x^{25} + 21 x^{24} + 456 x^{23} - 2196 x^{22} + 7128 x^{21} - 16215 x^{20} + 34272 x^{19} - 55590 x^{18} + 90336 x^{17} - 113655 x^{16} + 154704 x^{15} - 150696 x^{14} + 187296 x^{13} - 114147 x^{12} + 148584 x^{11} + 12726 x^{10} + 43416 x^{9} + 169761 x^{8} - 39192 x^{7} + 255972 x^{6} - 33144 x^{5} + 149445 x^{4} + 83040 x^{3} + 10866 x^{2} + 41264 x + 16421$ |
$28$ |
[4,12] |
$2^{96}\cdot 3^{36}$ |
$2$ |
$44.21243715343166$ |
|
|
|
|
$G(2,2)$ (as 28T393) |
trivial |
$2$ |
$15$ |
$14216710617882.553$ |
| 28.28.146...821.1 |
$x^{28} - x^{27} - 28 x^{26} + 28 x^{25} + 349 x^{24} - 349 x^{23} - 2551 x^{22} + 2551 x^{21} + 12123 x^{20} - 12123 x^{19} - 39236 x^{18} + 39236 x^{17} + 88045 x^{16} - 88045 x^{15} - 136763 x^{14} + 136763 x^{13} + 144247 x^{12} - 144247 x^{11} - 99295 x^{10} + 99295 x^{9} + 41703 x^{8} - 41703 x^{7} - 9569 x^{6} + 9569 x^{5} + 987 x^{4} - 987 x^{3} - 28 x^{2} + 28 x + 1$ |
$28$ |
[28,0] |
$3^{14}\cdot 29^{27}$ |
$2$ |
$44.537939945$ |
$44.53793994501929$ |
|
✓ |
✓ |
$C_{28}$ (as 28T1) |
trivial |
$2$ |
$27$ |
$114482618238342.14$ |
| 28.4.167...536.1 |
$x^{28} - 12 x^{27} + 66 x^{26} - 252 x^{25} + 855 x^{24} - 2760 x^{23} + 8292 x^{22} - 22248 x^{21} + 51651 x^{20} - 108588 x^{19} + 220410 x^{18} - 408540 x^{17} + 617625 x^{16} - 735120 x^{15} + 756744 x^{14} - 746832 x^{13} + 508599 x^{12} + 206172 x^{11} - 683370 x^{10} - 1085940 x^{9} + 6210633 x^{8} - 11620008 x^{7} + 11623572 x^{6} - 5359560 x^{5} - 587211 x^{4} + 1555740 x^{3} - 194994 x^{2} - 25844 x - 163209$ |
$28$ |
[4,12] |
$2^{106}\cdot 3^{30}$ |
$2$ |
$44.752252495537704$ |
|
|
|
|
$G(2,2)$ (as 28T393) |
trivial |
$2$ |
$15$ |
$19660631807398.406$ |
| 28.4.167...536.2 |
$x^{28} - 4 x^{27} + 114 x^{24} - 384 x^{23} + 36 x^{22} + 3048 x^{21} - 10707 x^{20} + 17652 x^{19} - 5556 x^{18} - 45144 x^{17} + 131832 x^{16} - 218112 x^{15} + 204000 x^{14} + 46224 x^{13} - 448863 x^{12} + 815100 x^{11} - 1018896 x^{10} + 1095936 x^{9} - 710154 x^{8} + 300960 x^{7} + 235860 x^{6} + 416280 x^{5} + 163233 x^{4} - 76476 x^{3} - 92004 x^{2} - 26072 x - 3676$ |
$28$ |
[4,12] |
$2^{106}\cdot 3^{30}$ |
$2$ |
$44.752252495537704$ |
|
|
|
|
$G(2,2)$ (as 28T393) |
trivial |
$2$ |
$15$ |
$18370103601317.53$ |
| 28.0.204...801.1 |
$x^{28} - 6 x^{27} + 18 x^{26} + 6 x^{25} - 69 x^{24} + 47 x^{23} + 257 x^{22} - 674 x^{21} + 321 x^{20} + 545 x^{19} - 15 x^{18} - 692 x^{17} + 1854 x^{16} - 6800 x^{15} + 5094 x^{14} + 6261 x^{13} - 5929 x^{12} + 6262 x^{11} - 14458 x^{10} - 7839 x^{9} + 27851 x^{8} - 6775 x^{7} + 6005 x^{6} - 1487 x^{5} - 35142 x^{4} + 22011 x^{3} + 18446 x^{2} - 12525 x + 2675$ |
$28$ |
[0,14] |
$7^{14}\cdot 449^{13}$ |
$2$ |
$45.07638783702266$ |
$56.06246516163912$ |
|
|
|
$D_{28}$ (as 28T10) |
trivial |
$2$ |
$13$ |
$4093870424302.4214$ |
| 28.4.211...944.1 |
$x^{28} - 8 x^{27} + 12 x^{26} + 96 x^{25} - 492 x^{24} + 528 x^{23} + 2880 x^{22} - 12720 x^{21} + 17154 x^{20} + 29184 x^{19} - 182400 x^{18} + 406032 x^{17} - 473316 x^{16} + 112896 x^{15} + 596544 x^{14} - 1104192 x^{13} + 1042860 x^{12} - 815712 x^{11} + 1003056 x^{10} - 1327872 x^{9} + 1135584 x^{8} - 519744 x^{7} + 110208 x^{6} - 50880 x^{5} + 11928 x^{4} + 83712 x^{3} - 96960 x^{2} + 45248 x - 7120$ |
$28$ |
[4,12] |
$2^{100}\cdot 3^{34}$ |
$2$ |
$45.13034473523645$ |
|
|
|
|
$G(2,2)$ (as 28T393) |
trivial |
$2$ |
$15$ |
$38756724514773.875$ |
| 28.4.211...944.2 |
$x^{28} - 8 x^{27} + 24 x^{26} - 48 x^{25} + 18 x^{24} - 48 x^{23} + 288 x^{22} - 240 x^{21} - 1242 x^{20} + 528 x^{19} + 3504 x^{18} + 576 x^{17} - 9312 x^{16} - 1344 x^{15} + 16704 x^{14} + 9600 x^{13} - 25056 x^{12} - 24192 x^{11} + 18816 x^{10} + 28416 x^{9} - 21408 x^{8} - 55296 x^{7} - 25344 x^{6} + 14592 x^{5} + 5088 x^{4} - 17664 x^{3} - 16128 x^{2} - 5120 x - 512$ |
$28$ |
[4,12] |
$2^{100}\cdot 3^{34}$ |
$2$ |
$45.13034473523645$ |
|
|
|
|
$G(2,2)$ (as 28T393) |
trivial |
$2$ |
$15$ |
$17445632490941.885$ |
| 28.4.211...944.3 |
$x^{28} - 4 x^{27} - 6 x^{26} + 36 x^{25} + 33 x^{24} - 48 x^{23} - 624 x^{22} - 1152 x^{21} + 6498 x^{20} + 13776 x^{19} - 42768 x^{18} - 93984 x^{17} + 212112 x^{16} + 410352 x^{15} - 795648 x^{14} - 1155648 x^{13} + 2150847 x^{12} + 2060532 x^{11} - 4016202 x^{10} - 2133348 x^{9} + 4975275 x^{8} + 920160 x^{7} - 3936144 x^{6} + 350160 x^{5} + 1794336 x^{4} - 567432 x^{3} - 357444 x^{2} + 188216 x - 3806$ |
$28$ |
[4,12] |
$2^{100}\cdot 3^{34}$ |
$2$ |
$45.13034473523645$ |
|
|
|
|
$G(2,2)$ (as 28T393) |
trivial |
$2$ |
$15$ |
$24722969331194.223$ |
| 28.4.241...384.1 |
$x^{28} - 30 x^{26} + 435 x^{24} - 24 x^{23} - 4188 x^{22} - 264 x^{21} + 27636 x^{20} + 7704 x^{19} - 124692 x^{18} - 65112 x^{17} + 386874 x^{16} + 342888 x^{15} - 720768 x^{14} - 1044312 x^{13} + 494301 x^{12} + 1421112 x^{11} + 107106 x^{10} - 1284312 x^{9} - 1365645 x^{8} - 901152 x^{7} - 403908 x^{6} - 54384 x^{5} - 157638 x^{4} + 9024 x^{3} - 33096 x^{2} + 5920 x - 4452$ |
$28$ |
[4,12] |
$2^{78}\cdot 3^{48}$ |
$2$ |
$45.34252595774765$ |
|
|
|
|
$G(2,2)$ (as 28T393) |
$[2]$ |
$2$ |
$15$ |
$18467350329198.566$ |
