Number field search results

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

Results (1-50 of 121 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
23.1.831...703.1	$x^{23} - 2 x^{22} - 3 x^{21} + 13 x^{20} - 19 x^{19} + 21 x^{18} - 75 x^{16} + 202 x^{15} - 378 x^{14} + 596 x^{13} - 798 x^{12} + 955 x^{11} - 995 x^{10} + 849 x^{9} - 610 x^{8} + 384 x^{7} - 151 x^{6} + 2 x^{5} + 46 x^{4} - 37 x^{3} + 3 x^{2} + 20 x + 1$	$23$	[1,11]	$-\,647^{11}$	$1$	$22.0976212489$	$25.436194683953808$				$D_{23}$ (as 23T2)	trivial	$2$	$11$	$1561186.27544$
23.1.205...983.1	$x^{23} - x - 1$	$23$	[1,11]	$-\,29\cdot 53264767\cdot 13296646221023838475181$	$3$	$22.9835192023$	$4532001778737922.0$			✓	$S_{23}$ (as 23T7)	trivial	$2$	$11$	$2560615.38998$
23.1.152...439.1	$x^{23} + 4 x^{21} - 14 x^{20} + 25 x^{19} - 6 x^{18} - 14 x^{17} - 26 x^{16} + 31 x^{15} + 48 x^{14} - 62 x^{13} + 19 x^{12} + 19 x^{11} + 24 x^{10} - 17 x^{9} + 34 x^{8} + 40 x^{7} - 228 x^{6} + 76 x^{5} + 4 x^{4} + 28 x^{3} + 45 x^{2} + 49 x + 1$	$23$	[1,11]	$-\,1039^{11}$	$1$	$27.7159120747$	$32.2335229225724$				$D_{23}$ (as 23T2)	trivial	$2$	$11$	$55921894.4803$
23.1.293...047.1	$x^{23} + 5 x^{21} - 17 x^{20} + 33 x^{19} - 14 x^{18} + 53 x^{17} - 34 x^{16} - 19 x^{15} + 140 x^{14} - 19 x^{13} + 257 x^{12} - 106 x^{11} - 16 x^{10} + 274 x^{9} + 165 x^{8} + 515 x^{7} - 28 x^{6} + 129 x^{5} + 89 x^{4} + 524 x^{3} + 244 x^{2} + 50 x - 1$	$23$	[1,11]	$-\,1103^{11}$	$1$	$28.5196906393$	$33.21144381083123$				$D_{23}$ (as 23T2)	trivial	$2$	$11$	$42306743.1121$
23.1.149...079.1	$x^{23} - 7 x^{22} + 15 x^{21} - 6 x^{20} + x^{19} - 21 x^{18} + 17 x^{17} + 2 x^{16} + 46 x^{15} - 10 x^{14} + 108 x^{13} - 129 x^{12} - 98 x^{11} - 144 x^{10} - 85 x^{9} + 8 x^{8} + 187 x^{7} - 82 x^{6} + 363 x^{5} + 216 x^{4} - 128 x^{3} - 51 x^{2} + 77 x - 1$	$23$	[1,11]	$-\,1279^{11}$	$1$	$30.612204664$	$35.76310948449533$				$D_{23}$ (as 23T2)	trivial	$2$	$11$	$195904703.063$
23.1.582...903.1	$x^{23} - 2 x^{22} + 16 x^{21} - 34 x^{20} + 68 x^{19} - 63 x^{18} + 17 x^{17} + 43 x^{16} - 139 x^{15} + 165 x^{14} + 25 x^{13} - 228 x^{12} + 265 x^{11} - 270 x^{10} + 75 x^{9} + 246 x^{8} - 130 x^{7} - 161 x^{6} + 240 x^{5} - 393 x^{4} + 569 x^{3} - 385 x^{2} + 99 x + 1$	$23$	[1,11]	$-\,1447^{11}$	$1$	$32.4734497852$	$38.03945320322047$				$D_{23}$ (as 23T2)	trivial	$2$	$11$	$530761705.173$
23.1.697...671.1	$x^{23} - 5 x^{22} + 3 x^{21} + 3 x^{20} + 43 x^{19} - 6 x^{18} - 31 x^{17} - 56 x^{16} - 68 x^{15} - 89 x^{14} + 147 x^{13} + 180 x^{12} + 274 x^{11} + 240 x^{10} - 211 x^{9} - 521 x^{8} - 383 x^{7} - 275 x^{6} + 291 x^{5} + 249 x^{4} + 358 x^{3} - 9 x^{2} + 107 x + 1$	$23$	[1,11]	$-\,1471^{11}$	$1$	$32.7299386538$	$38.353617821530214$				$D_{23}$ (as 23T2)	trivial	$2$	$11$	$492297100.302$
23.1.100...339.1	$x^{23} - 3 x^{21} - 6 x^{20} + x^{19} + 17 x^{18} + 18 x^{17} - 10 x^{16} - 43 x^{15} - 25 x^{14} + 33 x^{13} + 60 x^{12} + 11 x^{11} - 54 x^{10} - 47 x^{9} + 12 x^{8} + 46 x^{7} + 17 x^{6} - 17 x^{5} - 16 x^{4} + 6 x^{2} + x - 1$	$23$	[1,11]	$-\,167\cdot 30727\cdot 499717\cdot 39149185505838967853863$	$4$	$33.2515830019$	$3.168412684878976e+17$			✓	$S_{23}$ (as 23T7)	trivial	$2$	$11$	$139979317.774$
23.1.459...108.1	$x^{23} - 2 x^{22} - x^{21} + 5 x^{20} - x^{19} - 4 x^{18} + 6 x^{15} + 6 x^{14} - 17 x^{13} - 10 x^{12} + 31 x^{11} + 5 x^{10} - 32 x^{9} + 25 x^{7} - 17 x^{5} + 2 x^{4} + 9 x^{3} - 3 x^{2} - 2 x + 1$	$23$	[1,11]	$-\,2^{2}\cdot 1021\cdot 425123\cdot 264472629367076822658099919$	$4$	$35.5239226707$				?	$S_{23}$ (as 23T7)	trivial	$2$	$11$	$583250036.6$
23.1.687...411.1	$x^{23} - 3 x^{22} + 7 x^{21} - 8 x^{20} - 11 x^{19} + 19 x^{18} + 160 x^{17} + 291 x^{16} + 464 x^{15} - 35 x^{14} - 648 x^{13} - 1313 x^{12} - 1101 x^{11} - 240 x^{10} + 1477 x^{9} + 1043 x^{8} + 863 x^{7} - 10 x^{6} - 264 x^{5} - 712 x^{4} - 80 x^{3} - 2304 x^{2} - 2048 x - 1024$	$23$	[1,11]	$-\,1811^{11}$	$1$	$36.1522149922$	$42.555845661906424$				$D_{23}$ (as 23T2)	trivial	$2$	$11$	$9293967260.34$
23.1.167...576.1	$x^{23} - 4 x - 4$	$23$	[1,11]	$-\,2^{22}\cdot 8623\cdot 10045730659\cdot 4597557191821267$	$4$	$37.5755650454$	$1224687438025823.0$			?	$S_{23}$ (as 23T7)	trivial	$2$	$11$	$1131394806.61$
23.1.182...779.1	$x^{23} - 11 x^{22} + 47 x^{21} - 78 x^{20} - 51 x^{19} + 367 x^{18} - 359 x^{17} - 364 x^{16} + 1182 x^{15} - 712 x^{14} - 1586 x^{13} + 3310 x^{12} - 393 x^{11} - 5271 x^{10} + 5059 x^{9} + 3246 x^{8} - 8091 x^{7} - 125 x^{6} + 10047 x^{5} - 6818 x^{4} - 2608 x^{3} + 2872 x^{2} + 1488 x - 2176$	$23$	[1,11]	$-\,1979^{11}$	$1$	$37.7190748431$	$44.48595283907045$				$D_{23}$ (as 23T2)	trivial	$2$	$11$	$15406380217.0$
23.1.286...639.1	$x^{23} + 2 x - 1$	$23$	[1,11]	$-\,127\cdot 5892521806212607\cdot 3827252586261454951$	$3$	$38.4668488198$	$1.6923727437974505e+18$			✓	$S_{23}$ (as 23T7)	trivial	$2$	$11$	$1296440588.69$
23.1.103...168.1	$x^{23} + 4 x - 4$	$23$	[1,11]	$-\,2^{22}\cdot 127\cdot 121259\cdot 78283735681\cdot 2050329605299$	$5$	$40.6796380099$	$3051042090149834.0$			?	$S_{23}$ (as 23T7)	trivial	$2$	$11$	$3908153739.94$
23.1.761...080.1	$x^{23} - 8 x - 8$	$23$	[1,11]	$-\,2^{22}\cdot 3\cdot 5\cdot 557\cdot 2100359171059\cdot 1034221960670111$	$6$	$44.363145749$	$8267393774442177.0$			?	$S_{23}$ (as 23T7)	trivial	$2$	$11$	$16501892392.2$
23.1.847...296.1	$x^{23} - 2 x - 2$	$23$	[1,11]	$-\,2^{22}\cdot 3\cdot 5519\cdot 1219883568588480577372817507$	$4$	$44.5699078639$	$8721511346792999.0$			✓	$S_{23}$ (as 23T7)	trivial	$2$	$11$	$12211948562.3$
23.1.875...784.1	$x^{23} - x - 2$	$23$	[1,11]	$-\,2^{23}\cdot 7\cdot 24177221\cdot 78687506363\cdot 783971054543$	$5$	$44.6343866189$				✓	$S_{23}$ (as 23T7)	trivial	$2$	$11$	$17404788077.7$
23.1.875...047.1	$x^{23} - x - 4$	$23$	[1,11]	$-\,7901\cdot 159683\cdot 69415968602603755097356934209$	$3$	$44.6343866265$	$9.358366868937871e+18$			?	$S_{23}$ (as 23T7)	trivial	$2$	$11$	$10664511959.7$
23.1.875...368.1	$x^{23} - 2$	$23$	[1,11]	$-\,2^{22}\cdot 23^{23}$	$2$	$44.6343866265$	$50.83747447492002$			✓	$F_{23}$ (as 23T4)	trivial	$2$	$11$	$14787749883.9$
23.1.904...440.1	$x^{23} + 2 x - 2$	$23$	[1,11]	$-\,2^{22}\cdot 5\cdot 9629\cdot 78977\cdot 5671055267529396512759$	$5$	$44.6968791201$	$9011551868163896.0$			✓	$S_{23}$ (as 23T7)	trivial	$2$	$11$	$11760180370.2$
23.1.990...656.1	$x^{23} + 8 x - 8$	$23$	[1,11]	$-\,2^{22}\cdot 19\cdot 2617\cdot 310741\cdot 1528181322635255601073$	$5$	$44.8735986096$	$9429900711203802.0$			?	$S_{23}$ (as 23T7)	trivial	$2$	$11$	$13784529892.7$
23.1.332...679.1	$x^{23} - 9 x - 9$	$23$	[1,11]	$-\,3^{22}\cdot 103\cdot 409\cdot 136973\cdot 1835872831815206461$	$5$	$47.299523925$	$294371594383291.06$			?	$S_{23}$ (as 23T7)	trivial	$2$	$11$	$12917754140.4$
23.1.101...875.1	$x^{23} + 23 x^{21} + 230 x^{19} + 1311 x^{17} + 4692 x^{15} + 10948 x^{13} + 16744 x^{11} + 16445 x^{9} + 9867 x^{7} + 3289 x^{5} + 506 x^{3} + 23 x - 1$	$23$	[1,11]	$-\,5^{11}\cdot 23^{23}$	$2$	$49.6612718765$	$58.57701468324603$			✓	$F_{23}$ (as 23T4)	trivial	$2$	$11$	$53144954646.2$
23.1.140...512.1	$x^{23} - 4 x - 8$	$23$	[1,11]	$-\,2^{26}\cdot 25811015603927\cdot 808975051375354229$	$3$	$50.3526826419$				?	$S_{23}$ (as 23T7)	trivial	$2$	$11$	$61444013102.3$
23.1.224...224.1	$x^{23} + 4 x - 8$	$23$	[1,11]	$-\,2^{30}\cdot 3\cdot 929\cdot 623071\cdot 16280269\cdot 738591239095427$	$6$	$56.8035733437$				?	$S_{23}$ (as 23T7)	trivial	$2$	$11$	$402011657995$
23.1.285...320.1	$x^{23} + 8 x - 4$	$23$	[1,11]	$-\,2^{22}\cdot 5\cdot 24986142523\cdot 54552257894632015274417$	$4$	$57.4067141285$	$1.6020745037248333e+17$			?	$S_{23}$ (as 23T7)	trivial	$2$	$11$	$281108277991$
23.1.321...535.1	$x^{23} + 3 x - 1$	$23$	[1,11]	$-\,5\cdot 22723592653\cdot 282905139402414328282680249319$	$3$	$57.7002549419$	$1.7928498469225808e+20$			✓	$S_{23}$ (as 23T7)	trivial	$2$	$11$	$185847611513$
23.1.322...336.1	$x^{23} + 3 x - 2$	$23$	[1,11]	$-\,2^{23}\cdot 17\cdot 43\cdot 67\cdot 971821\cdot 15873405731\cdot 5085469520371$	$7$	$57.7070814215$				✓	$S_{23}$ (as 23T7)	trivial	$2$	$11$	$407641553662$
23.1.623...335.1	$x^{23} - 3 x - 3$	$23$	[1,11]	$-\,3^{22}\cdot 5\cdot 203008301\cdot 19561943299801571525063$	$4$	$65.6379381689$	$1.274455719527393e+16$			✓	$S_{23}$ (as 23T7)	trivial	$2$	$11$	$933328504105$
23.1.655...231.1	$x^{23} - 2 x - 3$	$23$	[1,11]	$-\,587\cdot 75967200927041\cdot 14694056584644694851886093$	$3$	$65.7816262406$	$8.094741174753032e+20$			✓	$S_{23}$ (as 23T7)	trivial	$2$	$11$	$951514783980$
23.1.655...719.1	$x^{23} - x - 3$	$23$	[1,11]	$-\,41\cdot 263\cdot 455033\cdot 13\!\cdots\!21$	$4$	$65.781638742$	$8.094758865875517e+20$			✓	$S_{23}$ (as 23T7)	trivial	$2$	$11$	$1198293682960$
23.1.655...303.1	$x^{23} - 3$	$23$	[1,11]	$-\,3^{22}\cdot 23^{23}$	$2$	$65.781638742$	$74.92367730844663$			✓	$F_{23}$ (as 23T4)	trivial	$2$	$11$	$1289649122770$
23.1.655...887.1	$x^{23} + x - 3$	$23$	[1,11]	$-\,859\cdot 1733\cdot 44\!\cdots\!21$	$3$	$65.781638742$	$8.094758865879735e+20$			✓	$S_{23}$ (as 23T7)	trivial	$2$	$11$	$813269772507$
23.1.687...271.1	$x^{23} + 3 x - 3$	$23$	[1,11]	$-\,3^{22}\cdot 7\cdot 467399\cdot 10931299891\cdot 612464196024013$	$5$	$65.9187485478$	$1.3385852001185396e+16$			✓	$S_{23}$ (as 23T7)	trivial	$2$	$11$	$993709440615$
23.1.751...207.1	$x^{23} + 9 x - 9$	$23$	[1,11]	$-\,3^{22}\cdot 151\cdot 158631250967721112920032141873$	$3$	$66.175479984$	$1.3997797308565002e+16$			?	$S_{23}$ (as 23T7)	trivial	$2$	$11$	$640542907885$
23.1.222...471.1	$x^{23} + 7 x - 4$	$23$	[1,11]	$-\,3\cdot 661\cdot 102898348801\cdot 10918926580157025647925153137$	$4$	$69.3766818568$	$1.4926415711036585e+21$			?	$S_{23}$ (as 23T7)	trivial	$2$	$11$	$3129530905130$
23.1.367...128.1	$x^{23} - 2 x - 4$	$23$	[1,11]	$-\,2^{42}\cdot 3\cdot 3739\cdot 360193\cdot 400051\cdot 516740936139647$	$6$	$70.901395652$				?	$S_{23}$ (as 23T7)	trivial	$2$	$11$	$4422799153190$
23.1.240...144.1	$x^{23} + 4 x - 2$	$23$	[1,11]	$-\,2^{22}\cdot 3\cdot 13\cdot 449\cdot 32\!\cdots\!01$	$5$	$76.9336854467$	$4.64463898940054e+18$			✓	$S_{23}$ (as 23T7)	trivial	$2$	$11$	$7581209599410$
23.1.246...079.1	$x^{23} + 4 x - 3$	$23$	[1,11]	$-\,114089\cdot 350671093\cdot 18936502114367\cdot 32577747177637381$	$4$	$77.0237298985$	$4.968007867177008e+21$			✓	$S_{23}$ (as 23T7)	trivial	$2$	$11$	$6125748579000$
23.1.918...736.1	$x^{23} + 2 x - 4$	$23$	[1,11]	$-\,2^{42}\cdot 40227185812367\cdot 519063606886319927$	$3$	$81.5520316455$				?	$S_{23}$ (as 23T7)	trivial	$2$	$11$	$23343019188400$
23.1.367...904.1	$x^{23} - 3 x - 4$	$23$	[1,11]	$-\,2^{22}\cdot 10301\cdot 19433\cdot 437464575526593257842019918297$	$4$	$86.6182995535$				✓	$S_{23}$ (as 23T7)	trivial	$2$	$11$	$50747738605900$
23.1.367...747.1	$x^{23} - 5 x - 8$	$23$	[1,11]	$-\,3\cdot 41\cdot 567183743783102484853\cdot 5265383449191308483213$	$4$	$86.6186191608$	$1.916591003191362e+22$			?	$S_{23}$ (as 23T7)	trivial	$2$	$11$	$38061010516000$
23.1.367...551.1	$x^{23} - x - 8$	$23$	[1,11]	$-\,13\cdot 251\cdot 3046418117488903\cdot 36953319274301480913105359$	$4$	$86.6186291097$	$1.916593534758477e+22$				$S_{23}$ (as 23T7)	trivial	$2$	$11$	$71078272346100$
23.1.367...456.1	$x^{23} + x - 4$	$23$	[1,11]	$-\,2^{22}\cdot 3\cdot 859\cdot 887\cdot 31627\cdot 276929\cdot 4374572903952274742317$	$7$	$86.6186291097$				✓	$S_{23}$ (as 23T7)	trivial	$2$	$11$	$37961073776200$
23.1.367...339.1	$x^{23} + 3 x - 8$	$23$	[1,11]	$-\,23036001684392168053\cdot 15946043188751196471887063$	$2$	$86.6186291098$	$1.9165935347784695e+22$			?	$S_{23}$ (as 23T7)	trivial	$2$	$11$	$30244259988400$
23.1.865...983.1	$x^{23} - 23 x^{20} + 184 x^{19} - 1334 x^{18} + 3680 x^{17} - 7567 x^{16} + 3381 x^{15} + 48346 x^{14} - 105455 x^{13} + 165048 x^{12} - 1033942 x^{11} + 3237457 x^{10} - 6694426 x^{9} + 24074675 x^{8} - 57748676 x^{7} + 58090042 x^{6} - 24771506 x^{5} + 67771087 x^{4} - 75769360 x^{3} + 19385596 x^{2} - 386078 x + 1437601$	$23$	[1,11]	$-\,23^{33}$	$1$	$89.9049112995$	$96.24677714683362$				$D_{23}$ (as 23T2)	trivial	$2$	$11$	$35038470243900$
23.1.101...592.1	$x^{23} + 5 x - 2$	$23$	[1,11]	$-\,2^{22}\cdot 31\cdot 97\cdot 31026973\cdot 2773405960861\cdot 937568290656913$	$6$	$90.5419744001$				?	$S_{23}$ (as 23T7)	trivial	$2$	$11$	$75394975727600$
23.1.407...567.1	$x^{23} + 5 x - 1$	$23$	[1,11]	$-\,7\cdot 17\cdot 53\cdot 1307\cdot 188072810621797\cdot 2625334491870023904395339$	$6$	$96.1670915672$	$6.379762902602266e+22$			✓	$S_{23}$ (as 23T7)	trivial	$2$	$11$	$58039635942200$
23.1.407...303.1	$x^{23} + 5 x - 3$	$23$	[1,11]	$-\,509\cdot 79\!\cdots\!67$	$2$	$96.167764643$	$6.380276420777516e+22$			✓	$S_{23}$ (as 23T7)	trivial	$2$	$11$	$105050188582000$
23.1.443...872.1	$x^{23} + 5 x - 4$	$23$	[1,11]	$-\,2^{22}\cdot 29\cdot 43\cdot 1669\cdot 8233\cdot 15257051\cdot 4046914931701778759797$	$7$	$96.5290572105$				✓	$S_{23}$ (as 23T7)	trivial	$2$	$11$	$219237939880000$