| 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 |
| 28.0.327...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 |
$2$ |
$14$ |
$985266200.5138724$ |
| 28.2.119...424.1 |
$x^{28} - 4 x - 1$ |
$28$ |
[2,13] |
$-\,2^{30}\cdot 313\cdot 35\!\cdots\!77$ |
$3$ |
$48.003579789$ |
|
|
|
? |
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$14$ |
$2934730265132.1826$ |
| 28.2.119...904.1 |
$x^{28} - 2 x - 1$ |
$28$ |
[2,13] |
$-\,2^{28}\cdot 5167\cdot 353915647\cdot 3141620149\cdot 77184457201040359$ |
$5$ |
$48.0035802664$ |
|
|
|
✓ |
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$14$ |
$4100907986522.6587$ |
| 28.0.210...736.1 |
$x^{28} - 4 x + 4$ |
$28$ |
[0,14] |
$2^{28}\cdot 78\!\cdots\!81$ |
$2$ |
$53.1903492$ |
|
|
|
? |
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$13$ |
$11321745362544.66$ |
| 28.2.234...072.1 |
$x^{28} - 4 x - 4$ |
$28$ |
[2,13] |
$-\,2^{28}\cdot 1531\cdot 2383\cdot 51031\cdot 46889040281957983714550830849$ |
$5$ |
$53.3942447206$ |
|
|
|
? |
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$14$ |
$25153873098265.008$ |
| 28.0.432...640.1 |
$x^{28} - 2 x + 2$ |
$28$ |
[0,14] |
$2^{28}\cdot 5\cdot 32\!\cdots\!13$ |
$3$ |
$54.5778342357$ |
|
|
|
✓ |
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$13$ |
$19117757369089.4$ |
| 28.0.444...005.1 |
$x^{28} - x + 2$ |
$28$ |
[0,14] |
$5\cdot 6249889\cdot 26339207\cdot 398948659\cdot 13547923849744568758845893$ |
$5$ |
$54.6307239547$ |
$2.1091981427046934e+24$ |
|
|
✓ |
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$13$ |
$35776227834950.36$ |
| 28.2.456...976.1 |
$x^{28} - 2 x - 2$ |
$28$ |
[2,13] |
$-\,2^{28}\cdot 29\cdot 2411\cdot 24\!\cdots\!09$ |
$4$ |
$54.6822662974$ |
|
|
|
✓ |
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$14$ |
$34192757648971.188$ |
| 28.2.101...947.1 |
$x^{28} - 3 x + 1$ |
$28$ |
[2,13] |
$-\,11\cdot 13\cdot 23\cdot 47\cdot 47470777\cdot 13\!\cdots\!17$ |
$6$ |
$72.0053696835$ |
$1.0071829893586881e+26$ |
|
|
✓ |
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$14$ |
$1091720855028220.6$ |
| 28.2.101...419.1 |
$x^{28} - 3 x - 1$ |
$28$ |
[2,13] |
$-\,79\cdot 6399373412031876752263\cdot 20065603237699194720476206747$ |
$3$ |
$72.0053696835$ |
$1.0071829893619791e+26$ |
|
|
✓ |
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$14$ |
$1126285775019767.5$ |
| 28.2.101...491.1 |
$x^{28} - 3 x - 2$ |
$28$ |
[2,13] |
$-\,29\cdot 53\cdot 1231\cdot 53\!\cdots\!53$ |
$4$ |
$72.0064972263$ |
$1.0074038146331297e+26$ |
|
|
✓ |
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$14$ |
$4091490251128624.5$ |
| 28.0.242...749.1 |
$x^{28} - 3 x + 3$ |
$28$ |
[0,14] |
$3^{27}\cdot 13\cdot 45673\cdot 586051\cdot 628025053\cdot 145586123452771747741$ |
$6$ |
$80.6499119411$ |
$5.1451594315704736e+20$ |
|
|
✓ |
$S_{28}$ (as 28T1854) |
$[2]$ |
$2$ |
$13$ |
$2120141623302227.5$ |
| 28.0.252...264.1 |
$x^{28} - 2 x + 3$ |
$28$ |
[0,14] |
$2^{28}\cdot 3^{27}\cdot 13\cdot 6553\cdot 20327\cdot 42022097279\cdot 1696876609651$ |
$7$ |
$80.7679823424$ |
|
|
|
✓ |
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$13$ |
$10505974365221896$ |
| 28.0.252...629.1 |
$x^{28} - x + 3$ |
$28$ |
[0,14] |
$3^{27}\cdot 11\cdot 23\cdot 83\cdot 3121\cdot 20446009\cdot 38719859\cdot 223913377\cdot 2853054979$ |
$9$ |
$80.7679837008$ |
|
|
|
✓ |
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$13$ |
$5281401797704566.0$ |
| 28.2.252...235.1 |
$x^{28} - x - 3$ |
$28$ |
[2,13] |
$-\,3^{27}\cdot 5\cdot 97\cdot 149\cdot 241\cdot 1657\cdot 1777\cdot 4297\cdot 210101\cdot 715939655803727309$ |
$10$ |
$80.7679837008$ |
|
|
|
✓ |
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$14$ |
$6368679128119342.0$ |
| 28.2.262...115.1 |
$x^{28} - 3 x - 3$ |
$28$ |
[2,13] |
$-\,3^{27}\cdot 5\cdot 101\cdot 313\cdot 15581\cdot 2849857\cdot 4912021661444396106058349$ |
$7$ |
$80.8815714913$ |
$5.3559732890485857e+20$ |
|
|
✓ |
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$14$ |
$4704673349371942.0$ |
| 28.2.863...272.1 |
$x^{28} + 216 x^{14} - 864 x^{13} + 729 x^{12} + 512 x - 432$ |
$28$ |
[2,13] |
$-\,2^{92}\cdot 3^{55}$ |
$2$ |
$84.39194996048609$ |
|
|
|
|
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$14$ |
$116823531035928140$ |
| 28.2.127...432.1 |
$x^{28} - 4 x + 2$ |
$28$ |
[2,13] |
$-\,2^{56}\cdot 191\cdot 115262593309109\cdot 805674854468579152273$ |
$4$ |
$85.5809671258$ |
|
|
|
? |
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$14$ |
$12889353279181418$ |
| 28.2.319...872.1 |
$x^{28} - 4 x + 1$ |
$28$ |
[2,13] |
$-\,2^{57}\cdot 2873098703\cdot 77168683376597053505702878367$ |
$3$ |
$96.007159578$ |
|
|
|
✓ |
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$14$ |
$144037020966621000$ |
| 28.2.319...416.1 |
$x^{28} - 4 x - 2$ |
$28$ |
[2,13] |
$-\,2^{56}\cdot 11\cdot 29\cdot 13\!\cdots\!49$ |
$4$ |
$96.0071600554$ |
|
|
|
✓ |
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$14$ |
$116349621534817800$ |
| 28.2.322...040.1 |
$x^{28} - 4 x - 3$ |
$28$ |
[2,13] |
$-\,2^{57}\cdot 3^{27}\cdot 5\cdot 5860972353958479965136697$ |
$4$ |
$96.0341799908$ |
|
|
|
✓ |
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$14$ |
$209536747833216320$ |
| 28.0.149...264.1 |
$x^{28} - 2 x + 4$ |
$28$ |
[0,14] |
$2^{26}\cdot 11\cdot 937\cdot 1021\cdot 6553\cdot 10285417\cdot 46704961\cdot 67146234212046428719403$ |
$8$ |
$101.441050397$ |
$2.907254952056253e+24$ |
|
|
? |
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$13$ |
$291259593669693100$ |
| 28.2.149...848.1 |
$x^{28} - 2 x - 4$ |
$28$ |
[2,13] |
$-\,2^{26}\cdot 13\cdot 103\cdot 4093\cdot 5179\cdot 78\!\cdots\!79$ |
$6$ |
$101.441050398$ |
$2.907254952635815e+24$ |
|
|
? |
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$14$ |
$244508645159324580$ |
| 28.0.597...541.1 |
$x^{28} - 3 x + 4$ |
$28$ |
[0,14] |
$3954528313281695204366070899\cdot 150988049822851039060206430559$ |
$2$ |
$106.589792463$ |
$2.44353538544391e+28$ |
|
|
✓ |
$S_{28}$ (as 28T1854) |
$[2]$ |
$2$ |
$13$ |
$290572268488061700$ |
| 28.0.597...421.1 |
$x^{28} - x + 4$ |
$28$ |
[0,14] |
$3288658789096196137\cdot 18\!\cdots\!33$ |
$2$ |
$106.589857137$ |
$2.4435561425254633e+28$ |
|
|
✓ |
$S_{28}$ (as 28T1854) |
$[2]$ |
$2$ |
$13$ |
$285381791382834720$ |
| 28.2.597...027.1 |
$x^{28} - x - 4$ |
$28$ |
[2,13] |
$-\,7219\cdot 82\!\cdots\!33$ |
$2$ |
$106.589857137$ |
$2.4435561425254633e+28$ |
|
|
✓ |
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$14$ |
$663385170558089600$ |
| 28.2.183...827.1 |
$x^{28} - 5 x + 3$ |
$28$ |
[2,13] |
$-\,3^{25}\cdot 229\cdot 17569\cdot 99894127\cdot 116259097\cdot 59955224737\cdot 773258618963$ |
$7$ |
$110.95153298$ |
$1.3385082513950918e+23$ |
|
|
? |
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$14$ |
$548121537161173060$ |
| 28.2.165...067.1 |
$x^{28} - 5 x + 2$ |
$28$ |
[2,13] |
$-\,43335783497980753391\cdot 38\!\cdots\!37$ |
$2$ |
$120.008949471$ |
$1.2852596602585616e+29$ |
|
|
✓ |
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$14$ |
$4251152018811512000$ |
| 28.2.165...139.1 |
$x^{28} - 5 x + 1$ |
$28$ |
[2,13] |
$-\,888001\cdot 1600259\cdot 7353593029\cdot 1516584409801007\cdot 1042345851554496448307$ |
$5$ |
$120.008949472$ |
$1.2852596604316284e+29$ |
|
|
✓ |
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$14$ |
$1070001860755087100$ |
| 28.2.165...611.1 |
$x^{28} - 5 x - 1$ |
$28$ |
[2,13] |
$-\,193\cdot 2448937\cdot 2988196213\cdot 677107855741\cdot 17273481068834805096620450587$ |
$5$ |
$120.008949472$ |
$1.2852596604316284e+29$ |
|
|
✓ |
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$14$ |
$1659276372080273700$ |
| 28.2.165...683.1 |
$x^{28} - 5 x - 2$ |
$28$ |
[2,13] |
$-\,29\cdot 1465423\cdot 424913013227713\cdot 91\!\cdots\!73$ |
$4$ |
$120.008949474$ |
$1.2852596606046952e+29$ |
|
|
✓ |
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$14$ |
$5434263021164631000$ |
| 28.2.165...307.1 |
$x^{28} - 5 x - 3$ |
$28$ |
[2,13] |
$-\,3^{27}\cdot 269\cdot 1117661\cdot 124354849\cdot 8019930101\cdot 7224683677751168621$ |
$6$ |
$120.009015052$ |
|
|
|
✓ |
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$14$ |
$1516369186301694500$ |
| 28.2.171...099.1 |
$x^{28} - 5 x - 4$ |
$28$ |
[2,13] |
$-\,3919\cdot 86709047461\cdot 761271819518919587911\cdot 66164246109160600014751$ |
$4$ |
$120.161235675$ |
$1.3082821029692196e+29$ |
|
|
✓ |
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$14$ |
$3468757552663005700$ |
| 28.0.617...208.1 |
$x^{28} - 2 x + 5$ |
$28$ |
[0,14] |
$2^{26}\cdot 53\cdot 137\cdot 5167\cdot 182453\cdot 1981277\cdot 67\!\cdots\!51$ |
$7$ |
$125.79479702$ |
$7.425367777949566e+25$ |
|
|
? |
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$13$ |
$7257941571662790000$ |
| 28.0.230...125.1 |
$x^{28} - 5 x + 5$ |
$28$ |
[0,14] |
$5^{27}\cdot 11\cdot 4561\cdot 12116329\cdot 1438499340367\cdot 35369086293605957$ |
$6$ |
$131.853292798$ |
$8.302052036154199e+20$ |
|
|
✓ |
$S_{28}$ (as 28T1854) |
not computed |
$2$ |
$13$ |
|
| 28.0.246...392.1 |
$x^{28} - 4 x + 5$ |
$28$ |
[0,14] |
$2^{57}\cdot 110435929\cdot 188707927\cdot 5531159309503\cdot 14863885345789$ |
$5$ |
$132.179107247$ |
|
|
|
✓ |
$S_{28}$ (as 28T1854) |
not computed |
$2$ |
$13$ |
|
| 28.0.246...317.1 |
$x^{28} - 3 x + 5$ |
$28$ |
[0,14] |
$77863\cdot 12137505614692991779271\cdot 26\!\cdots\!29$ |
$3$ |
$132.179717883$ |
$4.969440423612302e+29$ |
|
|
✓ |
$S_{28}$ (as 28T1854) |
$[2]$ |
$2$ |
$13$ |
$3076474280246141400$ |
| 28.0.246...197.1 |
$x^{28} - x + 5$ |
$28$ |
[0,14] |
$179\cdot 2277922373\cdot 16187864551193\cdot 37\!\cdots\!87$ |
$4$ |
$132.179718077$ |
$4.969440525677874e+29$ |
|
|
✓ |
$S_{28}$ (as 28T1854) |
not computed |
$2$ |
$13$ |
|
| 28.2.246...803.1 |
$x^{28} - x - 5$ |
$28$ |
[2,13] |
$-\,1193\cdot 23057\cdot 89\!\cdots\!03$ |
$3$ |
$132.179718077$ |
$4.969440525677874e+29$ |
|
|
✓ |
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$14$ |
$5556575275752251000$ |
| 28.2.246...168.1 |
$x^{28} - 2 x - 5$ |
$28$ |
[2,13] |
$-\,2^{28}\cdot 347\cdot 10313\cdot 7313389\cdot 4719485717\cdot 5637211457\cdot 1321243754190655553$ |
$7$ |
$132.179718077$ |
|
|
|
✓ |
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$14$ |
$18376264601489019000$ |
| 28.2.246...683.1 |
$x^{28} - 3 x - 5$ |
$28$ |
[2,13] |
$-\,40699\cdot 233417\cdot 25\!\cdots\!01$ |
$3$ |
$132.179718271$ |
$4.969440627743445e+29$ |
|
|
✓ |
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$14$ |
$4907206336505339000$ |
| 28.2.263...875.1 |
$x^{28} - 5 x - 5$ |
$28$ |
[2,13] |
$-\,5^{27}\cdot 35\!\cdots\!51$ |
$2$ |
$132.485731115$ |
$8.877265835889468e+20$ |
|
|
✓ |
$S_{28}$ (as 28T1854) |
$[2]$ |
$2$ |
$14$ |
$3583647500752635400$ |
| 28.2.482...952.1 |
$x^{28} - 14 x^{27} + 81 x^{26} - 234 x^{25} + 252 x^{24} + 486 x^{23} - 2097 x^{22} + 2574 x^{21} + 1215 x^{20} - 8124 x^{19} + 9624 x^{18} + 1620 x^{17} - 17937 x^{16} + 19566 x^{15} + 1215 x^{14} - 24714 x^{13} + 24156 x^{12} + 486 x^{11} - 21759 x^{10} + 18642 x^{9} + 81 x^{8} - 11952 x^{7} + 8784 x^{6} - 3744 x^{4} + 2304 x^{3} + 512 x - 256$ |
$28$ |
[2,13] |
$-\,2^{80}\cdot 3^{83}$ |
$2$ |
$188.10893353562017$ |
|
|
|
|
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$14$ |
$7398078170458682000000$ |
| 28.2.482...952.2 |
$x^{28} - 14 x^{27} + 81 x^{26} - 234 x^{25} + 252 x^{24} + 486 x^{23} - 2097 x^{22} + 2574 x^{21} + 1215 x^{20} - 8124 x^{19} + 9624 x^{18} + 1620 x^{17} - 17937 x^{16} + 19566 x^{15} + 1215 x^{14} - 24714 x^{13} + 24156 x^{12} + 486 x^{11} - 21759 x^{10} + 18642 x^{9} + 81 x^{8} - 11952 x^{7} + 8784 x^{6} - 3744 x^{4} + 2304 x^{3} - 256 x + 128$ |
$28$ |
[2,13] |
$-\,2^{80}\cdot 3^{83}$ |
$2$ |
$188.10893353562017$ |
|
|
|
? |
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$14$ |
$3691537686599014000000$ |
| 28.2.300...272.1 |
$x^{28} - 8 x^{27} + 144 x^{25} - 180 x^{24} - 1296 x^{23} + 2088 x^{22} + 7920 x^{21} - 12474 x^{20} - 36960 x^{19} + 46200 x^{18} + 136080 x^{17} - 104580 x^{16} - 388080 x^{15} + 100440 x^{14} + 816336 x^{13} + 181377 x^{12} - 1163160 x^{11} - 823416 x^{10} + 913440 x^{9} + 1325808 x^{8} - 25344 x^{7} - 979200 x^{6} - 580608 x^{5} + 126720 x^{4} + 313344 x^{3} + 165888 x^{2} + 8192 x + 45056$ |
$28$ |
[2,13] |
$-\,2^{108}\cdot 3^{67}$ |
$2$ |
$200.81617926802772$ |
|
|
|
? |
$S_{28}$ (as 28T1854) |
not computed |
$2$ |
$14$ |
|
| 28.2.192...408.1 |
$x^{28} + 1728 x^{14} - 6912 x^{13} + 5832 x^{12} + 32768 x - 27648$ |
$28$ |
[2,13] |
$-\,2^{114}\cdot 3^{67}$ |
$2$ |
$232.9727507852462$ |
|
|
|
? |
$S_{28}$ (as 28T1854) |
not computed |
$2$ |
$14$ |
|
| 28.2.641...408.1 |
$x^{28} - 14 x^{27} + 81 x^{26} - 234 x^{25} + 252 x^{24} + 486 x^{23} - 2097 x^{22} + 2574 x^{21} + 1215 x^{20} - 8124 x^{19} + 9624 x^{18} + 1620 x^{17} - 17937 x^{16} + 19566 x^{15} + 1215 x^{14} - 24714 x^{13} + 24156 x^{12} + 486 x^{11} - 21759 x^{10} + 18642 x^{9} + 81 x^{8} - 11952 x^{7} + 8784 x^{6} - 3744 x^{4} + 2304 x^{3} + 1024 x - 512$ |
$28$ |
[2,13] |
$-\,2^{62}\cdot 3^{103}$ |
$2$ |
$264.05295653960326$ |
|
|
|
|
$S_{28}$ (as 28T1854) |
not computed |
$2$ |
$14$ |
|
| 28.2.231...688.1 |
$x^{28} + 648 x^{14} - 2592 x^{13} + 2187 x^{12} + 4608 x - 3888$ |
$28$ |
[2,13] |
$-\,2^{64}\cdot 3^{105}$ |
$2$ |
$300.10502454659996$ |
|
|
|
|
$S_{28}$ (as 28T1854) |
trivial |
$2$ |
$14$ |
$2837936502821238400000000$ |
| 28.2.519...048.1 |
$x^{28} - 243 x^{24} + 15309 x^{20} + 373977 x^{16} - 49424013 x^{12} - 387420489 x^{8} + 52301766015 x^{4} - 417942208512 x + 847288609443$ |
$28$ |
[2,13] |
$-\,2^{62}\cdot 3^{107}$ |
$2$ |
$308.92369005571226$ |
|
|
|
|
$S_{28}$ (as 28T1854) |
not computed |
$2$ |
$14$ |
|
