| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Narrow class group |
Unit group torsion |
Unit group rank |
Regulator |
Unit signature rank |
Max $p$ |
| 20.8.795...000.1 |
$x^{20} + 60 x^{18} - 14670 x^{16} + 6300 x^{14} + 8907525 x^{12} + 9479160 x^{10} - 1206365400 x^{8} - 8973601200 x^{6} - 20752297200 x^{4} - 9703281600 x^{2} + 8398080$ |
$20$ |
(8, 6) |
$2^{28}\cdot 3^{12}\cdot 5^{35}\cdot 61^{8}$ |
$4$ |
$441.61537830368036$ |
|
|
|
|
$C_2^9.D_5^2$ (as 20T640) |
$[2, 2]$ |
$[2, 2, 2, 2]$ |
$2$ |
$13$ |
$9993062688952732000$ |
$6$ |
$61$ |
| 20.8.127...000.1 |
$x^{20} - 300 x^{18} + 24600 x^{16} + 50400 x^{14} - 54349200 x^{12} + 281232000 x^{10} + 32361552000 x^{8} + 251851680000 x^{6} + 416340000000 x^{4} + 255674880000 x^{2} + 53747712000$ |
$20$ |
(8, 6) |
$2^{32}\cdot 3^{12}\cdot 5^{35}\cdot 61^{8}$ |
$4$ |
$507.282858599$ |
|
|
|
|
$C_2^9.D_5^2$ (as 20T640) |
$[2]$ |
$[2, 2, 2, 2]$ |
$2$ |
$13$ |
$54178729239200000000$ |
$5$ |
$61$ |
| 20.12.203...000.1 |
$x^{20} + 300 x^{18} + 24600 x^{16} - 50400 x^{14} - 54349200 x^{12} - 281232000 x^{10} + 32361552000 x^{8} - 251851680000 x^{6} + 416340000000 x^{4} - 255674880000 x^{2} + 53747712000$ |
$20$ |
(12, 4) |
$2^{36}\cdot 3^{12}\cdot 5^{35}\cdot 61^{8}$ |
$4$ |
$582.714985191$ |
|
|
|
|
$C_2^9.D_5^2$ (as 20T640) |
$[2, 2]$ |
$[2, 2, 2, 2, 2]$ |
$2$ |
$15$ |
$311000769114000000000$ |
$9$ |
$61$ |
| 20.12.701...000.1 |
$x^{20} - 3650 x^{18} + 4985975 x^{16} - 3003647250 x^{14} + 596325225125 x^{12} + 118592596976000 x^{10} - 47719566530765000 x^{8} - 726809692619550000 x^{6} + 797406243903991450000 x^{4} + 1467217083171997000000 x^{2} + 571417316953056800000$ |
$20$ |
(12, 4) |
$2^{28}\cdot 3^{8}\cdot 5^{35}\cdot 61^{8}\cdot 26725861^{2}$ |
$5$ |
$1960.2574268275625$ |
|
|
|
|
$C_2^9.D_5^2$ (as 20T640) |
not computed |
not computed |
$2$ |
$15$ |
|
|
$26725861$ |
| 24.4.186...125.1 |
$x^{24} - 9 x^{23} - 129 x^{22} + 1211 x^{21} + 8551 x^{20} - 98302 x^{19} - 66467 x^{18} + 2667418 x^{17} - 521357 x^{16} - 60872932 x^{15} + 196445499 x^{14} - 200669426 x^{13} - 463307536 x^{12} + 6551088054 x^{11} - 17314933831 x^{10} - 11196389533 x^{9} + 117153213977 x^{8} - 157646184848 x^{7} - 555881744908 x^{6} + 514483693607 x^{5} + 1859100826211 x^{4} - 4026938526854 x^{3} - 15514494343439 x^{2} - 12648105196784 x - 2575207541579$ |
$24$ |
(4, 10) |
$5^{38}\cdot 29^{21}$ |
$2$ |
$243.388892784999$ |
$318.27003782911316$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
$[4, 8]$ |
$[8, 4, 2, 2]$ |
$2$ |
$13$ |
$728335178324237000$ |
$2$ |
$29$ |
| 24.4.186...125.4 |
$x^{24} - 8 x^{23} + 44 x^{22} - 152 x^{21} + 406 x^{20} - 2120 x^{19} + 4955 x^{18} - 6815 x^{17} - 115930 x^{16} + 800065 x^{15} - 2050700 x^{14} + 6714325 x^{13} - 24335475 x^{12} + 195023675 x^{11} - 450118525 x^{10} - 59389000 x^{9} + 326959875 x^{8} - 1930375250 x^{7} - 5810533625 x^{6} - 2815047250 x^{5} + 4774353125 x^{4} - 16413408125 x^{3} + 15563724375 x^{2} + 10921208125 x + 3071200625$ |
$24$ |
(4, 10) |
$5^{38}\cdot 29^{21}$ |
$2$ |
$243.388892784999$ |
$318.27003782911316$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
$[4, 8]$ |
$[8, 4, 2, 2]$ |
$2$ |
$13$ |
$769270320970123600$ |
$2$ |
$29$ |
| 24.4.186...125.5 |
$x^{24} - 8 x^{23} + 44 x^{22} - 152 x^{21} + 406 x^{20} + 490 x^{19} - 8675 x^{18} + 39150 x^{17} - 184950 x^{16} + 408565 x^{15} - 1002350 x^{14} + 5610875 x^{13} - 34315100 x^{12} + 77350375 x^{11} + 159799325 x^{10} - 269128600 x^{9} - 1538476000 x^{8} + 4841462600 x^{7} + 4074604300 x^{6} - 27610097275 x^{5} - 35457813195 x^{4} + 9506519710 x^{3} - 30480445480 x^{2} - 25848971110 x + 4925124805$ |
$24$ |
(4, 10) |
$5^{38}\cdot 29^{21}$ |
$2$ |
$243.388892784999$ |
$318.27003782911316$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
$[4, 8]$ |
$[8, 4, 2, 2]$ |
$2$ |
$13$ |
$828985398887129300$ |
$2$ |
$29$ |
| 24.4.186...125.7 |
$x^{24} - 10 x^{23} + 165 x^{22} - 1270 x^{21} + 9525 x^{20} - 49082 x^{19} + 211985 x^{18} - 743590 x^{17} + 1989805 x^{16} - 2969085 x^{15} - 14254441 x^{14} + 122830875 x^{13} - 601044450 x^{12} + 2118914560 x^{11} - 5953584660 x^{10} + 11866554302 x^{9} - 9242593415 x^{8} - 26666679140 x^{7} + 117276965265 x^{6} - 247919402970 x^{5} + 418820539501 x^{4} - 523800522565 x^{3} + 305694639485 x^{2} - 158367839275 x + 213552840595$ |
$24$ |
(4, 10) |
$5^{38}\cdot 29^{21}$ |
$2$ |
$243.388892784999$ |
$318.27003782911316$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
$[4, 8]$ |
$[8, 4, 2, 2]$ |
$2$ |
$13$ |
$842326962907535000$ |
$2$ |
$29$ |
| 24.4.157...125.2 |
$x^{24} - 5 x^{23} + 15 x^{22} + 1270 x^{21} - 11240 x^{20} - 126 x^{19} + 686495 x^{18} - 5659825 x^{17} - 3104680 x^{16} + 224752475 x^{15} - 1183567299 x^{14} + 2159700990 x^{13} + 17718110360 x^{12} - 125681766785 x^{11} + 313424789165 x^{10} - 181868274741 x^{9} - 3689201772175 x^{8} + 10249619753205 x^{7} - 112322043325 x^{6} - 53575992032780 x^{5} + 104765502965411 x^{4} - 76179334639865 x^{3} - 17166928029195 x^{2} - 101897265535390 x - 12329799538105$ |
$24$ |
(4, 10) |
$5^{38}\cdot 29^{23}$ |
$2$ |
$322.2309523456089$ |
$421.3686837523139$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
$[2, 2, 12]$ |
$[2, 4, 12]$ |
$2$ |
$13$ |
$28092508916296163000$ |
$3$ |
$29$ |
| 24.4.157...125.3 |
$x^{24} - 10 x^{23} - 85 x^{22} + 1025 x^{21} - 2650 x^{20} - 11920 x^{19} + 306050 x^{18} - 1511525 x^{17} - 2716150 x^{16} + 41977400 x^{15} - 130518860 x^{14} - 200216500 x^{13} + 3120702450 x^{12} - 9362797725 x^{11} + 7647548225 x^{10} + 41401918275 x^{9} - 230464198375 x^{8} - 83725633750 x^{7} + 7234481326400 x^{6} - 13916001590025 x^{5} - 19960260364770 x^{4} - 20932025753950 x^{3} - 45017259679625 x^{2} - 21997768381750 x - 3597474181775$ |
$24$ |
(4, 10) |
$5^{38}\cdot 29^{23}$ |
$2$ |
$322.2309523456089$ |
$421.3686837523139$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
$[2, 2, 12]$ |
$[2, 4, 12]$ |
$2$ |
$13$ |
$30087975734784110000$ |
$3$ |
$29$ |
| 24.4.157...125.7 |
$x^{24} - 2 x^{23} + 14 x^{22} - 73 x^{21} + 1636 x^{20} - 8356 x^{19} - 29848 x^{18} + 866826 x^{17} - 3107957 x^{16} - 19962726 x^{15} + 197478646 x^{14} - 924701922 x^{13} + 4712245199 x^{12} - 18038078643 x^{11} + 15844347301 x^{10} + 130731357269 x^{9} - 19105139243 x^{8} - 1397555993204 x^{7} - 2392334984497 x^{6} + 17479252050429 x^{5} + 1483008498796 x^{4} - 119605157350952 x^{3} - 199806387582796 x^{2} + 101895780970722 x + 625804792534271$ |
$24$ |
(4, 10) |
$5^{38}\cdot 29^{23}$ |
$2$ |
$322.2309523456089$ |
$421.3686837523139$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
$[2, 2, 12]$ |
$[2, 4, 12]$ |
$2$ |
$13$ |
$41195165712353920000$ |
$3$ |
$29$ |
| 24.4.157...125.8 |
$x^{24} - x^{23} - 69 x^{22} + 9 x^{21} + 2241 x^{20} + 14692 x^{19} - 145267 x^{18} - 355123 x^{17} - 920327 x^{16} + 55689152 x^{15} - 173727566 x^{14} + 210860316 x^{13} - 4526932771 x^{12} + 22681660486 x^{11} - 19625717186 x^{10} - 389058166387 x^{9} + 4996994520737 x^{8} - 31631386774447 x^{7} + 101086353291682 x^{6} - 123070867806182 x^{5} - 156279888146759 x^{4} + 545975427554284 x^{3} + 8407552774271 x^{2} - 1457240468479166 x + 1213221837016091$ |
$24$ |
(4, 10) |
$5^{38}\cdot 29^{23}$ |
$2$ |
$322.2309523456089$ |
$421.3686837523139$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
$[2, 2, 12]$ |
$[2, 4, 12]$ |
$2$ |
$13$ |
$48781967469228510000$ |
$3$ |
$29$ |
