| 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 |
| 24.0.131...209.1 |
$x^{24} - x + 1$ |
$24$ |
[0,12] |
$6361\cdot 61167766669\cdot 3374184647743911301$ |
$3$ |
$23.984225717$ |
$3.623334526165692e+16$ |
|
|
✓ |
$S_{24}$ (as 24T25000) |
trivial |
$2$ |
$11$ |
$9163307.175032053$ |
| 24.2.135...343.1 |
$x^{24} - x - 1$ |
$24$ |
[2,11] |
$-\,101\cdot 2347\cdot 5714547093403974893094772369$ |
$3$ |
$24.015539369$ |
$3.680511166740474e+16$ |
|
|
✓ |
$S_{24}$ (as 24T25000) |
trivial |
$2$ |
$12$ |
$6241504.123318238$ |
| 24.2.350...008.1 |
$x^{24} - 4 x - 1$ |
$24$ |
[2,11] |
$-\,2^{24}\cdot 1301\cdot 916880537\cdot 17504518859356095299$ |
$4$ |
$40.366321221$ |
|
|
|
? |
$S_{24}$ (as 24T25000) |
trivial |
$2$ |
$12$ |
$3181555749.175104$ |
| 24.2.350...248.1 |
$x^{24} - 2 x - 1$ |
$24$ |
[2,11] |
$-\,2^{24}\cdot 31\cdot 41\cdot 271\cdot 60621550560749490987423583$ |
$5$ |
$40.3663276245$ |
|
|
|
✓ |
$S_{24}$ (as 24T25000) |
trivial |
$2$ |
$12$ |
$8976744012.609863$ |
| 24.0.524...432.1 |
$x^{24} - 4 x + 4$ |
$24$ |
[0,12] |
$2^{24}\cdot 787\cdot 11677\cdot 13863011\cdot 2453357022296255093$ |
$5$ |
$45.1840521438$ |
|
|
|
? |
$S_{24}$ (as 24T25000) |
trivial |
$2$ |
$11$ |
$28183484862.370083$ |
| 24.2.594...376.1 |
$x^{24} - 4 x - 4$ |
$24$ |
[2,11] |
$-\,2^{24}\cdot 173\cdot 1231\cdot 1663736950608410583747530797$ |
$4$ |
$45.4207739105$ |
|
|
|
? |
$S_{24}$ (as 24T25000) |
trivial |
$2$ |
$12$ |
$41394490764.6542$ |
| 24.0.108...336.1 |
$x^{24} - 2 x + 2$ |
$24$ |
[0,12] |
$2^{24}\cdot 7\cdot 109\cdot 53165777879\cdot 15924556660524315773$ |
$5$ |
$46.5717615163$ |
|
|
|
✓ |
$S_{24}$ (as 24T25000) |
trivial |
$2$ |
$11$ |
$34023168882.135223$ |
| 24.0.111...241.1 |
$x^{24} - x + 2$ |
$24$ |
[0,12] |
$7\cdot 11777\cdot 45920781197\cdot 2955409859759798105958427$ |
$4$ |
$46.6335331717$ |
$1.0577422458563353e+20$ |
|
|
✓ |
$S_{24}$ (as 24T25000) |
trivial |
$2$ |
$11$ |
$65656267224.95359$ |
| 24.2.115...280.1 |
$x^{24} - 2 x - 2$ |
$24$ |
[2,11] |
$-\,2^{24}\cdot 5\cdot 67\cdot 2753\cdot 610126757\cdot 1222245568857186613$ |
$6$ |
$46.6934783744$ |
|
|
|
✓ |
$S_{24}$ (as 24T25000) |
trivial |
$2$ |
$12$ |
$83113137628.73575$ |
| 24.0.478...441.1 |
$x^{24} - 3 x + 3$ |
$24$ |
[0,12] |
$3^{24}\cdot 8147\cdot 5301617770571\cdot 392383198581553$ |
$4$ |
$60.0253144144$ |
|
|
|
? |
$S_{24}$ (as 24T25000) |
$[2]$ |
$2$ |
$11$ |
$222384104690.3615$ |
| 24.2.589...951.1 |
$x^{24} - 3 x + 1$ |
$24$ |
[2,11] |
$-\,3^{24}\cdot 205151\cdot 13244784701\cdot 7684607440855021$ |
$4$ |
$60.549481831$ |
|
|
|
✓ |
$S_{24}$ (as 24T25000) |
trivial |
$2$ |
$12$ |
$752679838190.7345$ |
| 24.2.589...503.1 |
$x^{24} - 3 x - 1$ |
$24$ |
[2,11] |
$-\,3^{25}\cdot 36151\cdot 192530109859296455766319771$ |
$3$ |
$60.5494818321$ |
|
|
|
✓ |
$S_{24}$ (as 24T25000) |
trivial |
$2$ |
$12$ |
$1209366106979.0007$ |
| 24.2.590...535.1 |
$x^{24} - 3 x - 2$ |
$24$ |
[2,11] |
$-\,3^{24}\cdot 5\cdot 11\cdot 265483\cdot 154229507\cdot 9289589167754417$ |
$6$ |
$60.5542638809$ |
|
|
|
✓ |
$S_{24}$ (as 24T25000) |
trivial |
$2$ |
$12$ |
$2807992408743.26$ |
| 24.0.125...280.1 |
$x^{24} - 2 x + 3$ |
$24$ |
[0,12] |
$2^{24}\cdot 5\cdot 1093\cdot 297427638587\cdot 4604325971243997318451$ |
$5$ |
$68.7784514863$ |
|
|
|
✓ |
$S_{24}$ (as 24T25000) |
trivial |
$2$ |
$11$ |
$10082557825933.582$ |
| 24.0.125...185.1 |
$x^{24} - x + 3$ |
$24$ |
[0,12] |
$5\cdot 73019\cdot 92849\cdot 117957311\cdot 31401520670424842716043857$ |
$5$ |
$68.7784594817$ |
$1.1205450715966904e+22$ |
|
|
✓ |
$S_{24}$ (as 24T25000) |
trivial |
$2$ |
$11$ |
$4571458691448.702$ |
| 24.2.125...319.1 |
$x^{24} - x - 3$ |
$24$ |
[2,11] |
$-\,13\cdot 53\cdot 137\cdot 6991493\cdot 138367970479\cdot 1375033795802777653789$ |
$6$ |
$68.7784594817$ |
$1.1205450715968766e+22$ |
|
|
✓ |
$S_{24}$ (as 24T25000) |
trivial |
$2$ |
$12$ |
$8106076389384.166$ |
| 24.2.131...479.1 |
$x^{24} - 3 x - 3$ |
$24$ |
[2,11] |
$-\,3^{24}\cdot 13\cdot 113\cdot 3889\cdot 11933731\cdot 235812503\cdot 28952007143$ |
$7$ |
$68.9101163834$ |
|
|
|
✓ |
$S_{24}$ (as 24T25000) |
trivial |
$2$ |
$12$ |
$5389501630891.528$ |
| 24.2.587...144.1 |
$x^{24} - 4 x + 2$ |
$24$ |
[2,11] |
$-\,2^{48}\cdot 7\cdot 19973360963\cdot 149344836212483380939$ |
$4$ |
$80.7326360385$ |
|
|
|
✓ |
$S_{24}$ (as 24T25000) |
trivial |
$2$ |
$12$ |
$40611569080398.21$ |
| 24.2.587...176.1 |
$x^{24} - 4 x + 1$ |
$24$ |
[2,11] |
$-\,2^{48}\cdot 20\!\cdots\!71$ |
$2$ |
$80.732642442$ |
|
|
|
✓ |
$S_{24}$ (as 24T25000) |
trivial |
$2$ |
$12$ |
$82507073507256.89$ |
| 24.2.587...760.1 |
$x^{24} - 4 x - 2$ |
$24$ |
[2,11] |
$-\,2^{48}\cdot 5\cdot 53\cdot 4104279709\cdot 19198099166735406971$ |
$5$ |
$80.7326488455$ |
|
|
|
✓ |
$S_{24}$ (as 24T25000) |
trivial |
$2$ |
$12$ |
$67542832354583.086$ |
| 24.2.600...704.1 |
$x^{24} - 4 x - 3$ |
$24$ |
[2,11] |
$-\,2^{48}\cdot 13\cdot 6961573\cdot 235651364354358546904391$ |
$4$ |
$80.8037817311$ |
|
|
|
✓ |
$S_{24}$ (as 24T25000) |
trivial |
$2$ |
$12$ |
$108007643285877.9$ |
| 24.0.234...448.1 |
$x^{24} - 2 x + 4$ |
$24$ |
[0,12] |
$2^{22}\cdot 19\cdot 29\!\cdots\!23$ |
$3$ |
$85.5262769282$ |
$1.4514650638714769e+20$ |
|
|
? |
$S_{24}$ (as 24T25000) |
trivial |
$2$ |
$11$ |
$111450066234983.11$ |
| 24.2.234...184.1 |
$x^{24} - 2 x - 4$ |
$24$ |
[2,11] |
$-\,2^{22}\cdot 372336599\cdot 227464000434709\cdot 66051290459897581$ |
$4$ |
$85.5262769548$ |
$1.4514650692892038e+20$ |
|
|
? |
$S_{24}$ (as 24T25000) |
trivial |
$2$ |
$12$ |
$150930172541315.38$ |
| 24.2.253...583.1 |
$x^{24} - 5 x + 2$ |
$24$ |
[2,11] |
$-\,144848223006701985217\cdot 175352142619907793902441399$ |
$2$ |
$85.8092969402$ |
$1.59372037255321e+23$ |
|
|
? |
$S_{24}$ (as 24T25000) |
trivial |
$2$ |
$12$ |
$118848582374841.58$ |
| 24.0.938...537.1 |
$x^{24} - 3 x + 4$ |
$24$ |
[0,12] |
$3^{24}\cdot 19\cdot 41\cdot 195136097417\cdot 2185934406093696137939$ |
$5$ |
$90.6116967774$ |
|
|
|
✓ |
$S_{24}$ (as 24T25000) |
$[2]$ |
$2$ |
$11$ |
$84166454940372.39$ |
| 24.0.938...697.1 |
$x^{24} - x + 4$ |
$24$ |
[0,12] |
$11\cdot 41\cdot 1771657\cdot 3075314907797831527\cdot 38194763189910060973$ |
$5$ |
$90.6119340174$ |
$3.063548786648836e+23$ |
|
|
✓ |
$S_{24}$ (as 24T25000) |
$[2]$ |
$2$ |
$11$ |
$183463873500541.94$ |
| 24.2.938...831.1 |
$x^{24} - x - 4$ |
$24$ |
[2,11] |
$-\,31\cdot 297479359\cdot 9490442482783\cdot 1072369884939912452511833$ |
$4$ |
$90.6119340174$ |
$3.0635487866488375e+23$ |
|
|
✓ |
$S_{24}$ (as 24T25000) |
trivial |
$2$ |
$12$ |
$380849659753706.3$ |
| 24.2.124...623.1 |
$x^{24} - 5 x + 3$ |
$24$ |
[2,11] |
$-\,251\cdot 1237\cdot 40\!\cdots\!29$ |
$3$ |
$100.915378817$ |
$1.1155479889942422e+24$ |
|
|
✓ |
$S_{24}$ (as 24T25000) |
$[2]$ |
$2$ |
$12$ |
$335513062717685.1$ |
| 24.2.124...599.1 |
$x^{24} - 5 x + 1$ |
$24$ |
[2,11] |
$-\,12\!\cdots\!99$ |
$1$ |
$100.915803053$ |
$1.1156042658016528e+24$ |
|
|
✓ |
$S_{24}$ (as 24T25000) |
trivial |
$2$ |
$12$ |
$355324534613542.8$ |
| 24.2.124...151.1 |
$x^{24} - 5 x - 1$ |
$24$ |
[2,11] |
$-\,59\cdot 48589\cdot 40950871734274681\cdot 10601497338051375177525121$ |
$4$ |
$100.915803053$ |
$1.115604265801654e+24$ |
|
|
✓ |
$S_{24}$ (as 24T25000) |
trivial |
$2$ |
$12$ |
$1037181214790456.0$ |
| 24.2.124...183.1 |
$x^{24} - 5 x - 2$ |
$24$ |
[2,11] |
$-\,83\cdot 32797\cdot 20931701251\cdot 1505093099737\cdot 14512433137983197059$ |
$5$ |
$100.91580309$ |
$1.1156042708160598e+24$ |
|
|
✓ |
$S_{24}$ (as 24T25000) |
trivial |
$2$ |
$12$ |
$1153554151610021.8$ |
| 24.2.124...127.1 |
$x^{24} - 5 x - 3$ |
$24$ |
[2,11] |
$-\,13\cdot 281\cdot 2213\cdot 2909\cdot 931789\cdot 56\!\cdots\!43$ |
$6$ |
$100.916227247$ |
$1.1156605397703165e+24$ |
|
|
✓ |
$S_{24}$ (as 24T25000) |
trivial |
$2$ |
$12$ |
$576915300893602.8$ |
| 24.2.133...639.1 |
$x^{24} - 5 x - 4$ |
$24$ |
[2,11] |
$-\,31\cdot 71\cdot 7507597\cdot 80\!\cdots\!87$ |
$4$ |
$101.221965894$ |
$1.1569037079881029e+24$ |
|
|
✓ |
$S_{24}$ (as 24T25000) |
trivial |
$2$ |
$12$ |
$1234241610433508.0$ |
| 24.0.176...697.1 |
$x^{24} - 3 x + 5$ |
$24$ |
[0,12] |
$3^{24}\cdot 50404800560027\cdot 124095266579974970283331$ |
$3$ |
$102.399393553$ |
|
|
|
? |
$S_{24}$ (as 24T25000) |
$[2]$ |
$2$ |
$11$ |
$495897271669831.3$ |
| 24.0.397...632.1 |
$x^{24} - 2 x + 5$ |
$24$ |
[0,12] |
$2^{22}\cdot 977\cdot 96\!\cdots\!29$ |
$3$ |
$105.918461261$ |
|
|
|
? |
$S_{24}$ (as 24T25000) |
trivial |
$2$ |
$11$ |
$1980769078036230.2$ |
| 24.0.146...625.1 |
$x^{24} - 5 x + 5$ |
$24$ |
[0,12] |
$5^{23}\cdot 11\cdot 5225198203\cdot 21388200184274766461077$ |
$4$ |
$111.836223005$ |
$1.639385544323901e+17$ |
|
|
✓ |
$S_{24}$ (as 24T25000) |
$[4]$ |
$2$ |
$11$ |
$257534976053667.44$ |
| 24.0.158...048.1 |
$x^{24} - 4 x + 5$ |
$24$ |
[0,12] |
$2^{48}\cdot 1211669\cdot 7338719\cdot 6350022778305321759403$ |
$4$ |
$112.214972003$ |
|
|
|
✓ |
$S_{24}$ (as 24T25000) |
$[2]$ |
$2$ |
$11$ |
$1101020765730115.5$ |
| 24.0.158...433.1 |
$x^{24} - x + 5$ |
$24$ |
[0,12] |
$75883\cdot 20\!\cdots\!51$ |
$2$ |
$112.216700718$ |
$3.9874013393033525e+24$ |
|
|
✓ |
$S_{24}$ (as 24T25000) |
trivial |
$2$ |
$11$ |
$921859768909376.0$ |
| 24.2.158...567.1 |
$x^{24} - x - 5$ |
$24$ |
[2,11] |
$-\,7\cdot 29\cdot 3359\cdot 16263817\cdot 927461970881683907\cdot 1545806997710456209$ |
$6$ |
$112.216700718$ |
$3.9874013393033525e+24$ |
|
|
✓ |
$S_{24}$ (as 24T25000) |
trivial |
$2$ |
$12$ |
$2237965179429101.5$ |
| 24.2.158...472.1 |
$x^{24} - 2 x - 5$ |
$24$ |
[2,11] |
$-\,2^{24}\cdot 7\cdot 14327\cdot 94\!\cdots\!03$ |
$4$ |
$112.216700718$ |
|
|
|
✓ |
$S_{24}$ (as 24T25000) |
trivial |
$2$ |
$12$ |
$5310063018231026.0$ |
| 24.2.158...727.1 |
$x^{24} - 3 x - 5$ |
$24$ |
[2,11] |
$-\,3^{24}\cdot 7\cdot 211\cdot 195518711\cdot 8911198202359\cdot 21875854421579$ |
$6$ |
$112.216702452$ |
|
|
|
✓ |
$S_{24}$ (as 24T25000) |
trivial |
$2$ |
$12$ |
$1426161988272566.2$ |
| 24.2.171...375.1 |
$x^{24} - 5 x - 5$ |
$24$ |
[2,11] |
$-\,5^{23}\cdot 7\cdot 43\cdot 12491\cdot 382504803285481476130151021$ |
$5$ |
$112.569640473$ |
$1.7731543944372083e+17$ |
|
|
✓ |
$S_{24}$ (as 24T25000) |
$[2]$ |
$2$ |
$12$ |
$922356456292242.2$ |
