Number field search results

Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)

Results (21 matches)

 

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
21.3.736...327.1	$x^{21} - 57 x^{14} + 495 x^{7} + 1$	$21$	[3,9]	$-\,3^{28}\cdot 7^{29}$	$2$	$63.5626248712$	$66.57684419786632$				$C_3\times F_7$ (as 21T9)	$[21]$	$2$	$11$	$10457923589.107075$
21.3.250...375.1	$x^{21} - 2 x^{20} - 23 x^{19} + 36 x^{18} + 232 x^{17} - 215 x^{16} - 1522 x^{15} + 393 x^{14} + 7734 x^{13} + 463 x^{12} - 27458 x^{11} - 5102 x^{10} + 50786 x^{9} + 73668 x^{8} - 119559 x^{7} - 181211 x^{6} + 197536 x^{5} + 208597 x^{4} - 160704 x^{3} - 129353 x^{2} + 50491 x + 35771$	$21$	[3,9]	$-\,3^{24}\cdot 5^{18}\cdot 7^{17}$	$3$	$67.37915579242008$	$87.00158931080732$			?	$C_3\times F_7$ (as 21T9)	$[14]$	$2$	$11$	$4655449641.940092$
21.3.203...375.1	$x^{21} - 6 x^{19} - 96 x^{18} - 6 x^{17} + 648 x^{16} + 2889 x^{15} - 5685 x^{14} - 28155 x^{13} - 9420 x^{12} + 241392 x^{11} + 451815 x^{10} - 1479827 x^{9} - 510537 x^{8} + 7030128 x^{7} - 10608182 x^{6} - 37483542 x^{5} + 47557968 x^{4} + 35144488 x^{3} - 121483152 x^{2} + 50031891 x - 18017937$	$21$	[3,9]	$-\,3^{28}\cdot 5^{18}\cdot 7^{17}$	$3$	$83.0626541583$	$87.00158931080732$			?	$C_3\times F_7$ (as 21T9)	$[42]$	$2$	$11$	$37226343333.12808$
21.3.489...327.1	$x^{21} - 7 x^{20} + 21 x^{19} - 34 x^{18} + 29 x^{17} + 52 x^{16} - 373 x^{15} + 248 x^{14} - 3577 x^{13} + 42918 x^{12} - 170639 x^{11} + 225822 x^{10} + 43556 x^{9} + 105237 x^{8} - 3230632 x^{7} + 5161290 x^{6} + 1287601 x^{5} + 2320101 x^{4} - 14827477 x^{3} + 4310250 x^{2} + 1634962 x + 569387$	$21$	[3,9]	$-\,7^{17}\cdot 29^{18}$	$2$	$86.6185646862$	$90.72612557219027$				$F_7$ (as 21T4)	$[7, 7]$	$2$	$11$	$72630093220.36017$
21.3.489...327.2	$x^{21} - 7 x^{20} + 21 x^{19} - 34 x^{18} + 116 x^{17} + 545 x^{16} - 2200 x^{15} + 3148 x^{14} - 14133 x^{13} - 26711 x^{12} - 65282 x^{11} - 158805 x^{10} + 228083 x^{9} - 139668 x^{8} - 1168123 x^{7} + 426315 x^{6} + 764470 x^{5} - 1534666 x^{4} - 486339 x^{3} + 614026 x^{2} - 225533 x + 15197$	$21$	[3,9]	$-\,7^{17}\cdot 29^{18}$	$2$	$86.6185646862$	$90.72612557219027$			?	$C_3\times D_7$ (as 21T3)	$[7, 7]$	$2$	$11$	$42748360893.35298$
21.3.286...192.3	$x^{21} - 7 x^{20} + 35 x^{19} - 322 x^{18} + 497 x^{17} - 2016 x^{16} - 2968 x^{15} + 27685 x^{14} - 60200 x^{13} - 493206 x^{12} + 4226439 x^{11} - 14076657 x^{10} + 30578695 x^{9} - 34424992 x^{8} - 48912423 x^{7} + 272188826 x^{6} - 537907244 x^{5} + 678810839 x^{4} - 613790093 x^{3} + 392829325 x^{2} - 158183074 x + 30153907$	$21$	[3,9]	$-\,2^{18}\cdot 7^{23}\cdot 43^{12}$	$3$	$130.92416846178918$	$196.20480119263357$			?	$C_3\times F_7$ (as 21T9)	$[14]$	$2$	$11$	$7322114993300.565$
21.3.365...727.1	$x^{21} - 7 x^{20} + 21 x^{19} - 100 x^{18} + 425 x^{17} - 2778 x^{16} + 15235 x^{15} - 51069 x^{14} + 124446 x^{13} - 15583 x^{12} - 890873 x^{11} + 3247413 x^{10} - 8124288 x^{9} + 11894816 x^{8} - 25296225 x^{7} + 45735056 x^{6} - 21283165 x^{5} - 14098611 x^{4} + 1879382 x^{3} - 90105883 x^{2} + 4106355 x - 50238131$	$21$	[3,9]	$-\,3^{24}\cdot 7^{17}\cdot 11^{18}$	$3$	$132.4435217278695$	$171.01426618855564$			?	$C_3\times F_7$ (as 21T9)	$[7, 7]$	$2$	$11$	$1454744669741.6125$
21.3.108...592.2	$x^{21} - 2018 x^{14} + 6152 x^{7} - 128$	$21$	[3,9]	$-\,2^{18}\cdot 7^{21}\cdot 43^{14}$	$3$	$155.633369799$	$196.20480119263357$				$C_3\times F_7$ (as 21T9)	$[14]$	$2$	$11$	$263672723097349.6$
21.3.280...952.2	$x^{21} - 224 x^{18} + 2352 x^{16} + 7448 x^{15} + 1764 x^{14} - 197568 x^{13} + 340256 x^{12} + 846720 x^{11} - 5301408 x^{10} + 4466448 x^{9} + 18670176 x^{8} - 25371024 x^{7} - 658560 x^{6} + 24893568 x^{5} - 42674688 x^{4} + 17364032 x^{3} - 11656512 x^{2} - 2286144$	$21$	[3,9]	$-\,2^{18}\cdot 3^{24}\cdot 7^{35}$	$3$	$162.8560428465659$	$210.2836461794035$			?	$C_3\times F_7$ (as 21T9)	$[14]$	$2$	$11$	$53596409492572.82$
21.3.295...887.1	$x^{21} - 21 x^{19} - 11 x^{18} + 189 x^{17} - 978 x^{15} + 693 x^{14} + 3759 x^{13} + 2519 x^{12} + 3213 x^{11} - 30030 x^{10} - 29151 x^{9} + 12474 x^{8} - 95907 x^{7} + 698269 x^{6} + 658350 x^{5} - 1504272 x^{4} - 8525 x^{3} + 557865 x^{2} - 85701 x - 57365$	$21$	[3,9]	$-\,3^{28}\cdot 7^{17}\cdot 11^{18}$	$3$	$163.271716771$	$171.01426618855564$			?	$C_3\times F_7$ (as 21T9)	$[21]$	$2$	$11$	$81427960974978.42$
21.3.489...927.1	$x^{21} - 7 x^{20} + 21 x^{19} - 34 x^{18} - 326 x^{17} - 2633 x^{16} + 6276 x^{15} - 262 x^{14} - 62573 x^{13} - 195159 x^{12} + 556052 x^{11} - 18483 x^{10} + 1794625 x^{9} + 26343578 x^{8} + 40153179 x^{7} - 162134041 x^{6} - 214511808 x^{5} + 867279238 x^{4} + 2465480719 x^{3} + 2567288464 x^{2} + 1206871419 x + 176307053$	$21$	[3,9]	$-\,7^{17}\cdot 71^{18}$	$2$	$186.603530008$	$195.45250324835894$			?	$C_3\times D_7$ (as 21T3)	$[7, 7]$	$2$	$11$	$85935385452559.7$
21.3.674...368.1	$x^{21} - 77856 x^{14} + 263505920 x^{7} + 2097152$	$21$	[3,9]	$-\,2^{18}\cdot 7^{29}\cdot 19^{14}$	$3$	$189.482131588$	$198.46761172329423$				$C_3\times F_7$ (as 21T9)	$[21]$	$2$	$11$	$1793582744855836.2$
21.3.674...368.2	$x^{21} - 830 x^{14} - 181248 x^{7} + 2097152$	$21$	[3,9]	$-\,2^{18}\cdot 7^{29}\cdot 19^{14}$	$3$	$189.482131588$	$198.46761172329423$				$C_3\times F_7$ (as 21T9)	$[21]$	$2$	$11$	$1867922722744152.2$
21.3.276...503.2	$x^{21} - 168 x^{18} - 1134 x^{17} - 2184 x^{16} + 378 x^{15} + 76551 x^{14} + 294588 x^{13} + 522144 x^{12} - 3308760 x^{11} - 31140900 x^{10} - 108938088 x^{9} - 107842392 x^{8} - 68928309 x^{7} - 3010137228 x^{6} - 22383508896 x^{5} - 100315652472 x^{4} - 331515547902 x^{3} - 752768538480 x^{2} - 1042363764666 x - 654447883851$	$21$	[3,9]	$-\,3^{18}\cdot 7^{29}\cdot 19^{12}$	$3$	$202.63645044473785$	$280.94739430472515$				$C_3\times F_7$ (as 21T9)	$[7, 14]$	$2$	$11$	$233430087741712.25$
21.3.684...847.1	$x^{21} - 7 x^{20} + 21 x^{19} + 422 x^{18} - 5728 x^{17} + 42573 x^{16} - 179701 x^{15} + 131177 x^{14} + 4644969 x^{13} - 44789982 x^{12} + 257708881 x^{11} - 1119064122 x^{10} + 3825317289 x^{9} - 10843937506 x^{8} + 25291884804 x^{7} - 51145668311 x^{6} + 85922669412 x^{5} - 131337137580 x^{4} + 154503701941 x^{3} - 179737758235 x^{2} + 104422439682 x - 113349977651$	$21$	[3,9]	$-\,3^{24}\cdot 7^{17}\cdot 19^{18}$	$3$	$211.58405389390046$	$273.20242803730264$				$C_3\times F_7$ (as 21T9)	$[14]$	$2$	$11$	$2037702484097324.2$
21.3.281...367.1	$x^{21} - 7 x^{20} + 133 x^{19} - 406 x^{18} + 5033 x^{17} - 5684 x^{16} + 75607 x^{15} + 93048 x^{14} + 10395 x^{13} + 2418486 x^{12} - 7042581 x^{11} - 35243544 x^{10} - 125410411 x^{9} - 431404694 x^{8} - 2733671896 x^{7} + 546616693 x^{6} + 9128612374 x^{5} + 5611098164 x^{4} - 13076146104 x^{3} - 2234365840 x^{2} + 3147401824 x + 1234150336$	$21$	[3,9]	$-\,3^{18}\cdot 7^{23}\cdot 61^{12}$	$3$	$226.32530810167358$	$350.6597469132496$				$C_3\times F_7$ (as 21T9)	$[42]$	$2$	$11$	$1329129787323514.0$
21.3.318...687.1	$x^{21} - 449 x^{14} - 8521 x^{7} + 1$	$21$	[3,9]	$-\,7^{29}\cdot 61^{14}$	$2$	$227.646008828$	$238.44126784757347$				$C_3\times F_7$ (as 21T9)	$[21]$	$2$	$11$	$2471124664442345.5$
21.3.677...727.1	$x^{21} - 3915 x^{14} - 19657534 x^{7} + 17249876309$	$21$	[3,9]	$-\,7^{29}\cdot 29^{18}$	$2$	$263.344437076$	$275.8325603002433$			?	$C_3\times D_7$ (as 21T3)	$[91]$	$2$	$11$	$1049926002001072.1$
21.3.996...583.1	$x^{21} - 103983 x^{14} + 508304187 x^{7} + 10460353203$	$21$	[3,9]	$-\,3^{18}\cdot 7^{29}\cdot 19^{14}$	$3$	$268.227700605$	$280.94739430472515$				$C_3\times F_7$ (as 21T9)	$[21]$	$2$	$11$	$48743028014176990$
21.3.996...583.2	$x^{21} - 29403 x^{14} + 214879311 x^{7} + 10460353203$	$21$	[3,9]	$-\,3^{18}\cdot 7^{29}\cdot 19^{14}$	$3$	$268.227700605$	$280.94739430472515$				$C_3\times F_7$ (as 21T9)	$[42]$	$2$	$11$	$33794281381556120$
21.3.213...543.2	$x^{21} - 6237 x^{14} - 38795193 x^{7} - 10460353203$	$21$	[3,9]	$-\,3^{18}\cdot 7^{21}\cdot 61^{14}$	$3$	$278.149962353$	$350.6597469132496$				$C_3\times F_7$ (as 21T9)	$[42]$	$2$	$11$	$34675552868967690$
21.3.448...872.2	$x^{21} - 7 x^{20} + 7 x^{19} - 280 x^{18} + 4403 x^{17} - 23828 x^{16} + 99162 x^{15} - 859625 x^{14} + 6446132 x^{13} - 29048264 x^{12} + 105517069 x^{11} - 473510191 x^{10} + 2056439077 x^{9} - 4338445622 x^{8} - 10749550753 x^{7} + 111533743006 x^{6} - 378996395624 x^{5} + 564078479069 x^{4} + 267199120419 x^{3} - 1987375160323 x^{2} + 1867600797202 x + 453135147361$	$21$	[3,9]	$-\,2^{18}\cdot 3^{24}\cdot 7^{23}\cdot 19^{12}$	$4$	$288.14232462113256$	$492.4869576249633$			?	$C_3\times F_7$ (as 21T9)	$[14]$	$2$	$11$	$25783062726976052$
21.3.151...407.1	$x^{21} - 7 x^{20} + 7 x^{19} - 70 x^{18} - 1204 x^{17} + 3913 x^{16} - 1400 x^{15} + 89118 x^{14} + 1009281 x^{13} + 782649 x^{12} + 7427259 x^{11} - 5117742 x^{10} - 236661397 x^{9} - 824813360 x^{8} - 2340038521 x^{7} - 8431442474 x^{6} - 26770340051 x^{5} - 77676034786 x^{4} - 152941898529 x^{3} - 312904408180 x^{2} - 491213223158 x - 441236002901$	$21$	[3,9]	$-\,3^{18}\cdot 7^{23}\cdot 103^{12}$	$3$	$305.3074085359798$	$497.2302113029612$				$C_3\times F_7$ (as 21T9)	$[14]$	$2$	$11$	$111309098972736110$
21.3.108...432.1	$x^{21} - 7 x^{20} + 7 x^{19} - 280 x^{18} + 4739 x^{17} - 27076 x^{16} + 111146 x^{15} - 962441 x^{14} + 7752276 x^{13} - 37414328 x^{12} + 138632445 x^{11} - 624064959 x^{10} + 2980887749 x^{9} - 8065257382 x^{8} - 6878480417 x^{7} + 150046770846 x^{6} - 588950687752 x^{5} + 985703360061 x^{4} + 249631431427 x^{3} - 3175827536707 x^{2} + 3257326872786 x + 776107661057$	$21$	[3,9]	$-\,2^{18}\cdot 7^{23}\cdot 223^{12}$	$3$	$335.3495835660136$	$587.8509650190412$			?	$C_3\times F_7$ (as 21T9)	$[7, 7]$	$2$	$11$	$34552175541474750$
21.3.336...263.1	$x^{21} - 7 x^{20} + 7 x^{19} - 406 x^{18} + 4025 x^{17} - 9380 x^{16} + 52556 x^{15} - 606982 x^{14} + 1266902 x^{13} + 6632094 x^{12} - 27094340 x^{11} + 153715394 x^{10} - 1675209480 x^{9} + 7569710484 x^{8} - 8720691939 x^{7} - 45813941663 x^{6} + 213901573039 x^{5} - 389289261130 x^{4} + 217905977793 x^{3} + 634011046900 x^{2} - 1736664797420 x + 1617352418408$	$21$	[3,9]	$-\,7^{23}\cdot 11^{18}\cdot 19^{12}$	$3$	$353.93394155193204$	$490.7153595356438$				$C_3\times F_7$ (as 21T9)	$[7, 7]$	$2$	$11$	$130857147506779580$
21.3.267...248.2	$x^{21} - 6432 x^{14} - 3778560 x^{7} + 2097152$	$21$	[3,9]	$-\,2^{18}\cdot 3^{28}\cdot 7^{21}\cdot 19^{14}$	$4$	$390.649995982$	$492.4869576249633$				$C_3\times F_7$ (as 21T9)	$[42]$	$2$	$11$	$1946448298516030700$
21.3.327...487.1	$x^{21} - 5205 x^{14} + 1057239 x^{7} - 2187$	$21$	[3,9]	$-\,3^{18}\cdot 7^{21}\cdot 103^{14}$	$3$	$394.412434766$	$497.2302113029612$				$C_3\times F_7$ (as 21T9)	$[14]$	$2$	$11$	$4996966218921501000$
21.21.724...889.4	$x^{21} - 903 x^{19} - 2408 x^{18} + 322371 x^{17} + 1567608 x^{16} - 57217692 x^{15} - 384550677 x^{14} + 5297604816 x^{13} + 46019992039 x^{12} - 239871482424 x^{11} - 2894978733948 x^{10} + 3238401809699 x^{9} + 94345678493136 x^{8} + 111760681819143 x^{7} - 1405026978142459 x^{6} - 4000967262399996 x^{5} + 5000920037348550 x^{4} + 31976002108505938 x^{3} + 39769563390498270 x^{2} + 15884115372049848 x + 1731927086090117$	$21$	[21,0]	$3^{28}\cdot 7^{14}\cdot 43^{20}$	$3$	$569.173418786$	$569.1734187861515$		✓	?	$C_{21}$ (as 21T1)	$[6, 6]$	$2$	$20$	$1538134121593772200000$
21.21.326...329.2	$x^{21} - 3 x^{20} - 234 x^{19} + 373 x^{18} + 22227 x^{17} - 11901 x^{16} - 1094568 x^{15} - 107259 x^{14} + 30750441 x^{13} + 11716858 x^{12} - 518275467 x^{11} - 210631296 x^{10} + 5345836461 x^{9} + 1384500363 x^{8} - 33101161890 x^{7} - 481181304 x^{6} + 113556752970 x^{5} - 28704806013 x^{4} - 175186581586 x^{3} + 80675421420 x^{2} + 58460165631 x - 20341937701$	$21$	[21,0]	$3^{28}\cdot 7^{14}\cdot 71^{18}$	$3$	$611.439141265$	$611.4391412650907$		✓	?	$C_{21}$ (as 21T1)	$[21]$	$2$	$20$	$1039550977839431700000$
21.3.589...343.1	$x^{21} - 7 x^{20} + 21 x^{19} - 34 x^{18} + 29 x^{17} - 17000 x^{16} + 76879 x^{15} + 25168 x^{14} - 3960985 x^{13} - 7944166 x^{12} + 40651037 x^{11} + 81259502 x^{10} - 506512648 x^{9} - 2778664855 x^{8} - 84195862092 x^{7} + 400745644202 x^{6} + 655623718393 x^{5} - 7349761489371 x^{4} + 529795117999 x^{3} + 53152215171034 x^{2} - 12893672008602 x - 131863811763929$	$21$	[3,9]	$-\,7^{17}\cdot 293^{18}$	$2$	$628.904851644$	$658.7283078391205$				$F_7$ (as 21T4)	$[7, 7]$	$2$	$11$	$77992079112627040000$
21.3.704...463.1	$x^{21} - 560857 x^{14} + 65329261371 x^{7} - 93206534790699$	$21$	[3,9]	$-\,7^{29}\cdot 11^{18}\cdot 13^{14}$	$3$	$634.295095853$	$664.3741641833503$				$C_3\times F_7$ (as 21T9)	$[2, 6]$	$2$	$11$	$864787995831793200000$
21.3.130...207.1	$x^{21} - 7 x^{20} + 7 x^{19} - 1498 x^{18} + 9191 x^{17} + 16954 x^{16} + 632618 x^{15} - 3311890 x^{14} - 30137282 x^{13} + 4453736 x^{12} + 415435706 x^{11} + 8958755176 x^{10} - 24037899620 x^{9} - 185523188466 x^{8} + 432686836125 x^{7} + 1059833884669 x^{6} - 1689206914423 x^{5} - 1712305095956 x^{4} + 4298110230057 x^{3} + 7431181180906 x^{2} - 4919283323668 x + 24328896128216$	$21$	[3,9]	$-\,3^{24}\cdot 7^{23}\cdot 37^{18}$	$3$	$653.1875644619487$	$843.4115203419918$				$C_3\times F_7$ (as 21T9)	$[14]$	$2$	$11$	$340133338764480350000$
21.13.393...848.1	$x^{21} - 6 x^{20} - 196 x^{19} + 908 x^{18} + 16298 x^{17} - 38657 x^{16} - 805846 x^{15} - 121733 x^{14} + 23579189 x^{13} + 60920978 x^{12} - 321396183 x^{11} - 1963423184 x^{10} - 1073818319 x^{9} + 21446736466 x^{8} + 79483877862 x^{7} + 59509268311 x^{6} - 426733627582 x^{5} - 1804226819510 x^{4} - 3692869755195 x^{3} - 4543444380349 x^{2} - 3247488161475 x - 1051284118606$	$21$	[13,4]	$2^{12}\cdot 7^{14}\cdot 19^{2}\cdot 79^{2}\cdot 173^{9}\cdot 967^{2}\cdot 2202121^{2}$	$7$	$768.240749101$	$20887380124.94724$				$C_3^7.C_2^6:F_7$ (as 21T133)	$[3, 3, 3]$	$2$	$16$	$25075218690200000000000$