Number field search results

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

Results (37 matches)

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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
14.4.250058750499647.1	$x^{14} - 2 x^{13} + x^{12} - x^{11} + x^{10} - 4 x^{9} + 9 x^{8} - 9 x^{7} + 9 x^{6} - 4 x^{5} + x^{4} - x^{3} + x^{2} - 2 x + 1$	$14$	[4,5]	$-\,47\cdot 107^{2}\cdot 21557^{2}$	$3$	$10.676565665$	$10412.019640780552$			✓	$C_2^7.S_7$ (as 14T57)	trivial	trivial	$2$	$8$	$31.5102502485$
14.4.270118421833507.1	$x^{14} - x^{13} - 3 x^{12} - x^{11} + x^{10} + 2 x^{8} + 7 x^{7} + 3 x^{6} + 4 x^{5} + 9 x^{4} + 7 x^{3} + x^{2} + 1$	$14$	[4,5]	$-\,13^{4}\cdot 67\cdot 109^{4}$	$3$	$10.7355747516$	$308.1217291915648$			?	$C_2^7.\PSL(2,7)$ (as 14T51)	trivial	trivial	$2$	$8$	$33.079338429$
14.4.297261105546875.1	$x^{14} - 3 x^{12} - x^{11} + 5 x^{10} + 3 x^{9} - 6 x^{8} - 6 x^{7} + 3 x^{6} + 7 x^{5} - 4 x^{3} - 2 x^{2} + x + 1$	$14$	[4,5]	$-\,5^{7}\cdot 89\cdot 971\cdot 44029$	$4$	$10.8092504055$	$137930.09372504608$			✓	$S_7\wr C_2$ (as 14T61)	trivial	trivial	$2$	$8$	$34.9413880804$
14.4.334624313614643.1	$x^{14} - x^{13} - 4 x^{12} + 3 x^{11} + 3 x^{10} + 3 x^{9} + 2 x^{8} - 12 x^{7} + x^{5} + 2 x^{4} + 6 x^{3} - 3 x^{2} + x - 1$	$14$	[4,5]	$-\,13^{4}\cdot 83\cdot 109^{4}$	$3$	$10.9010515249$	$342.94460194031336$			?	$C_2^7.\PSL(2,7)$ (as 14T51)	trivial	trivial	$2$	$8$	$37.8345982696$
14.4.411650990546875.1	$x^{14} - 3 x^{12} - 2 x^{11} + 5 x^{10} + 4 x^{9} - 6 x^{8} - 7 x^{7} + 7 x^{6} + 9 x^{5} - 4 x^{4} - 6 x^{3} + 2 x^{2} + 2 x - 1$	$14$	[4,5]	$-\,5^{7}\cdot 24851\cdot 212029$	$3$	$11.0635611432$	$162313.47262319294$			?	$S_7\wr C_2$ (as 14T61)	trivial	trivial	$2$	$8$	$42.0905477867$
14.4.498897726810659.1	$x^{14} - 2 x^{13} + 3 x^{11} - 7 x^{10} + x^{9} + 14 x^{8} - 2 x^{7} - 13 x^{6} + 2 x^{5} + 4 x^{4} - 4 x^{3} + 3 x + 1$	$14$	[4,5]	$-\,11^{3}\cdot 71^{2}\cdot 8623^{2}$	$3$	$11.2165156356$	$2595.103658815963$			?	$C_2^7.S_7$ (as 14T57)	trivial	trivial	$2$	$8$	$47.3515916708$
14.4.569282687307707.1	$x^{14} - 2 x^{13} + x^{12} + 6 x^{11} - 14 x^{10} + 15 x^{9} - 4 x^{8} - 17 x^{7} + 25 x^{6} - 19 x^{5} + 6 x^{4} + 4 x^{3} - x^{2} - x - 1$	$14$	[4,5]	$-\,107^{3}\cdot 21557^{2}$	$2$	$11.3227520826$	$4884.6336180096205$			?	$C_2^7.S_7$ (as 14T57)	trivial	trivial	$2$	$8$	$50.817635446$
14.4.673916269391159.1	$x^{14} - 3 x^{13} + 4 x^{12} - x^{11} - 7 x^{10} + 13 x^{9} - 10 x^{8} - 5 x^{7} + 15 x^{6} - 10 x^{5} - 2 x^{4} + 7 x^{3} - 2 x^{2} + 1$	$14$	[4,5]	$-\,23^{2}\cdot 29^{2}\cdot 31^{2}\cdot 71\cdot 149^{2}$	$5$	$11.460040136$	$14789.928431199389$			✓	$C_2^7.S_7$ (as 14T57)	trivial	trivial	$2$	$8$	$58.9923614819$
14.4.1157074433824127.1	$x^{14} - 2 x^{13} - x^{12} + 7 x^{11} - 8 x^{10} + 6 x^{9} - 3 x^{8} - 9 x^{7} + 15 x^{6} - 9 x^{5} + 5 x^{4} - 2 x^{3} - 2 x^{2} + 1$	$14$	[4,5]	$-\,7\cdot 13^{4}\cdot 41\cdot 109^{4}$	$4$	$11.9111687749$	$637.7138856885587$			?	$C_2^7.\PSL(2,7)$ (as 14T51)	trivial	trivial	$2$	$8$	$83.2205360651$
14.4.1237706798550547.1	$x^{14} - 3 x^{13} + 3 x^{12} + 4 x^{11} - 14 x^{10} + 16 x^{9} - 5 x^{8} - 6 x^{7} + 12 x^{6} - 16 x^{5} + 17 x^{4} - 11 x^{3} + 2 x^{2} + 2 x - 1$	$14$	[4,5]	$-\,13^{4}\cdot 109^{4}\cdot 307$	$3$	$11.9686213341$	$659.5597016191938$			?	$C_2^7.\PSL(2,7)$ (as 14T51)	trivial	trivial	$2$	$8$	$83.4257736319$
14.4.1237706798550547.2	$x^{14} - 4 x^{13} + 9 x^{12} - 12 x^{11} + x^{10} + 23 x^{9} - 41 x^{8} + 46 x^{7} - 43 x^{6} + 36 x^{5} - 25 x^{4} + 11 x^{3} - 6 x^{2} + 4 x - 1$	$14$	[4,5]	$-\,13^{4}\cdot 109^{4}\cdot 307$	$3$	$11.9686213341$	$659.5597016191938$			?	$C_2^7.\PSL(2,7)$ (as 14T51)	trivial	trivial	$2$	$8$	$84.7144798087$
14.4.1524052425039147.1	$x^{14} - 6 x^{13} + 20 x^{12} - 46 x^{11} + 79 x^{10} - 108 x^{9} + 113 x^{8} - 92 x^{7} + 46 x^{6} - 5 x^{5} - 21 x^{4} + 19 x^{3} - 10 x^{2} + 1$	$14$	[4,5]	$-\,3^{3}\cdot 2741^{4}$	$2$	$12.1478660175$	$90.68075870878012$			?	$C_2^4:\GL(3,2)$ (as 14T43)	trivial	trivial	$2$	$8$	$121.507606686$
14.4.1544109784510943.1	$x^{14} - 2 x^{13} - 2 x^{12} + 6 x^{11} - x^{10} - 3 x^{9} - 2 x^{7} + 10 x^{6} - 2 x^{5} - 11 x^{4} + 4 x^{3} + 4 x^{2} - 2 x - 1$	$14$	[4,5]	$-\,13^{4}\cdot 109^{4}\cdot 383$	$3$	$12.1592162928$	$736.6892153411776$			✓	$C_2^7.\PSL(2,7)$ (as 14T51)	trivial	trivial	$2$	$8$	$90.0508384965$
14.4.1689248041018499.1	$x^{14} - 7 x^{13} + 22 x^{12} - 41 x^{11} + 51 x^{10} - 46 x^{9} + 29 x^{8} - 5 x^{7} - 17 x^{6} + 26 x^{5} - 23 x^{4} + 15 x^{3} - 7 x^{2} + 2 x + 1$	$14$	[4,5]	$-\,13^{4}\cdot 109^{4}\cdot 419$	$3$	$12.2374910567$	$770.5342302584617$			?	$C_2^7.\PSL(2,7)$ (as 14T51)	trivial	trivial	$2$	$8$	$99.3342735188$
14.4.2837756470349143.1	$x^{14} - x^{13} + x^{12} - x^{11} - x^{10} - 3 x^{8} + x^{7} - 3 x^{6} - x^{4} - x^{3} + x^{2} - x + 1$	$14$	[4,5]	$-\,7\cdot 71^{2}\cdot 283583^{2}$	$3$	$12.6994214839$	$11871.846991938533$			✓	$C_2^7.S_7$ (as 14T57)	trivial	trivial	$2$	$8$	$138.726849555$
14.4.3222197555141171.1	$x^{14} - 7 x^{13} + 22 x^{12} - 41 x^{11} + 46 x^{10} - 21 x^{9} - 25 x^{8} + 61 x^{7} - 63 x^{6} + 38 x^{5} - 9 x^{4} - 6 x^{3} + 9 x^{2} - 5 x + 1$	$14$	[4,5]	$-\,17^{4}\cdot 131^{5}$	$2$	$12.8151931004$	$239.6719487328181$			?	$C_2^7.A_7$ (as 14T56)	trivial	trivial	$2$	$8$	$135.312709358$
14.4.3808955502493696.1	$x^{14} - 2 x^{13} + x^{12} + 8 x^{11} - 16 x^{10} + 10 x^{9} + 18 x^{8} - 32 x^{7} + 18 x^{6} + 10 x^{5} - 16 x^{4} + 8 x^{3} + x^{2} - 2 x + 1$	$14$	[4,5]	$-\,2^{16}\cdot 491^{4}$	$2$	$12.969245375$	$66.4005340773643$			?	$C_2^4:\GL(3,2)$ (as 14T43)	trivial	trivial	$2$	$8$	$303.97833566$
14.4.7488261696523347.1	$x^{14} - x^{10} - x^{8} - x^{7} - x^{6} - x^{4} + 1$	$14$	[4,5]	$-\,3^{3}\cdot 16653619^{2}$	$2$	$13.6108221164$	$9302.405211217323$			✓	$C_2^7.S_7$ (as 14T57)	trivial	trivial	$2$	$8$	$290.172352012$
14.4.7651638724807467.1	$x^{14} - x^{13} - 5 x^{12} - 2 x^{11} + 8 x^{10} + 7 x^{9} - 3 x^{8} - 9 x^{7} - 12 x^{6} - 11 x^{5} + 8 x^{4} + 16 x^{3} + 5 x^{2} - 2 x - 1$	$14$	[4,5]	$-\,3^{13}\cdot 13^{2}\cdot 73^{4}$	$3$	$13.6318214716$	$289.63785703021404$			?	$C_2^7.A_7$ (as 14T56)	trivial	trivial	$2$	$8$	$325.982887322$
14.4.922101103923347456.1	$x^{14} - 2 x^{11} - 10 x^{10} - 4 x^{9} - 6 x^{8} + 2 x^{7} + 15 x^{6} + 12 x^{5} + 16 x^{4} + 10 x^{3} + 4 x^{2} + 2 x - 1$	$14$	[4,5]	$-\,2^{14}\cdot 56280584956259$	$2$	$19.1954574926$				?	$S_{14}$ (as 14T63)	trivial	$[2]$	$2$	$8$	$4299.69142191$
14.4.129...115.1	$x^{14} - x^{13} - 3 x^{12} + 7 x^{11} - 9 x^{10} + x^{9} + 8 x^{8} - 15 x^{7} + 8 x^{6} + x^{5} - 9 x^{4} + 7 x^{3} - 3 x^{2} - x + 1$	$14$	[4,5]	$-\,5\cdot 7\cdot 577^{6}$	$3$	$19.6630841298$	$142.10911300827965$			?	$C_2\wr D_7$ (as 14T38)	trivial	$[2]$	$2$	$8$	$3481.95645948$
14.4.335...632.1	$x^{14} - 4 x^{13} + 10 x^{11} + 16 x^{10} - 28 x^{9} - 76 x^{8} + 38 x^{7} + 164 x^{6} + 48 x^{5} - 188 x^{4} - 244 x^{3} + 150 x^{2} + 124 x - 34$	$14$	[4,5]	$-\,2^{20}\cdot 317^{5}$	$2$	$21.0512700131$	$47.92614331002722$			?	$C_2\times \GL(3,2)$ (as 14T17)	trivial	$[2]$	$2$	$8$	$9005.22781695$
14.4.335...632.2	$x^{14} - 4 x^{13} - 2 x^{12} + 22 x^{11} - 8 x^{10} - 66 x^{9} + 150 x^{8} - 190 x^{7} + 138 x^{6} - 40 x^{5} - 22 x^{4} + 52 x^{3} - 44 x^{2} + 16 x - 2$	$14$	[4,5]	$-\,2^{20}\cdot 317^{5}$	$2$	$21.0512700131$	$47.92614331002722$			?	$C_2\times \GL(3,2)$ (as 14T17)	trivial	$[2]$	$2$	$8$	$9005.22781695$
14.4.370...103.1	$x^{14} - 3 x^{13} - 9 x^{12} + 31 x^{11} + 27 x^{10} - 119 x^{9} - 27 x^{8} + 211 x^{7} - 7 x^{6} - 175 x^{5} + 24 x^{4} + 59 x^{3} - 10 x^{2} - 5 x + 3$	$14$	[4,5]	$-\,3704349534869766103$	$1$	$21.2000345403$	$1924668681.8436482$			?	$S_{14}$ (as 14T63)	trivial	trivial	$2$	$8$	$11913.6860087$
14.4.390...364.1	$x^{14} - 2 x^{13} - 2 x^{12} + x^{11} - 5 x^{10} - 3 x^{9} - 4 x^{8} - 4 x^{7} - 4 x^{6} - 3 x^{5} - 5 x^{4} + x^{3} - 2 x^{2} - 2 x + 1$	$14$	[4,5]	$-\,2^{2}\cdot 149^{4}\cdot 211^{4}$	$3$	$21.2811625523$	$1992.2437733580762$				$C_2^7.A_7$ (as 14T56)	trivial	$[2]$	$2$	$8$	$36664.5333907$
14.4.390...364.2	$x^{14} - 2 x^{13} - x^{11} + 2 x^{10} + 2 x^{8} + 2 x^{6} + 2 x^{4} - x^{3} - 2 x + 1$	$14$	[4,5]	$-\,2^{2}\cdot 149^{4}\cdot 211^{4}$	$3$	$21.2811625523$	$1992.2437733580762$			?	$C_2^7.A_7$ (as 14T56)	trivial	$[2]$	$2$	$8$	$13480.7995717$
14.4.405...664.1	$x^{14} - 2 x^{13} + 5 x^{12} - 20 x^{11} + 23 x^{10} - 22 x^{9} + 29 x^{8} + 50 x^{7} - 153 x^{6} + 100 x^{5} + 49 x^{4} - 44 x^{3} + 53 x^{2} - 30 x + 14$	$14$	[4,5]	$-\,2^{14}\cdot 3967^{4}$	$2$	$21.3384098751$	$211.85249966774654$			?	$C_2^7.\PSL(2,7)$ (as 14T51)	trivial	trivial	$2$	$8$	$17481.1798237$
14.4.645...575.1	$x^{14} - 5 x^{13} + 9 x^{12} - 5 x^{11} - 20 x^{10} + 55 x^{9} - 66 x^{8} + 65 x^{7} - 2 x^{6} + 16 x^{5} + 54 x^{4} + 8 x^{3} + 25 x^{2} - 6 x - 1$	$14$	[4,5]	$-\,5^{2}\cdot 7\cdot 577^{6}$	$3$	$22.0586061347$	$142.10911300827965$			?	$C_2\wr D_7$ (as 14T38)	trivial	$[2]$	$2$	$8$	$8505.32096967$
14.4.710...912.1	$x^{14} - 2 x^{13} - 6 x^{12} - 8 x^{11} - 10 x^{10} + 4 x^{9} + 4 x^{8} + 18 x^{7} + 4 x^{6} + 4 x^{5} - 10 x^{4} - 8 x^{3} - 6 x^{2} - 2 x + 1$	$14$	[4,5]	$-\,2^{12}\cdot 7\cdot 3967^{4}$	$3$	$22.2086374062$	$471.3300329917456$			?	$C_2^7.\PSL(2,7)$ (as 14T51)	trivial	trivial	$2$	$8$	$33305.5237228$
14.4.132...743.1	$x^{14} - 2 x^{13} + x^{12} + 17 x^{11} - 48 x^{10} + 56 x^{9} + 15 x^{8} - 256 x^{7} + 331 x^{6} - 302 x^{5} - 332 x^{4} + 488 x^{3} - 417 x^{2} - 144 x + 353$	$14$	[4,5]	$-\,23^{3}\cdot 239^{3}\cdot 431^{3}$	$3$	$23.2266383959$	$60388.22372501204$			?	$C_2^6.S_7$ (as 14T54)	trivial	$[2]$	$2$	$8$	$7817.03714643$
14.4.179...719.1	$x^{14} - 6 x^{13} + 24 x^{12} - 62 x^{11} + 103 x^{10} - 80 x^{9} - 122 x^{8} + 280 x^{7} - 148 x^{6} - 546 x^{5} + 819 x^{4} - 146 x^{3} - 595 x^{2} + 418 x + 299$	$14$	[4,5]	$-\,61^{3}\cdot 42899^{3}$	$2$	$23.7267322483$	$65062.800507367334$			?	$C_2^6.S_7$ (as 14T54)	trivial	trivial	$2$	$8$	$12732.6472741$
14.4.254...363.1	$x^{14} - 3 x^{13} - 2 x^{12} + x^{11} + 30 x^{10} + 45 x^{9} - 200 x^{8} - 45 x^{7} + 257 x^{6} - 121 x^{5} + 614 x^{4} + 323 x^{3} - 1565 x^{2} - 559 x + 523$	$14$	[4,5]	$-\,7^{3}\cdot 13^{6}\cdot 109^{5}$	$3$	$24.3303889493$	$189.11230288198414$			?	$C_2^4.\PSL(2,7)$ (as 14T42)	trivial	trivial	$2$	$8$	$11131.4204258$
14.4.529...123.1	$x^{14} - 7 x^{13} + 14 x^{12} + 7 x^{11} - 49 x^{10} + 14 x^{9} + 168 x^{8} - 393 x^{7} + 420 x^{6} - 203 x^{5} - 91 x^{4} + 224 x^{3} - 203 x^{2} + 98 x - 7$	$14$	[4,5]	$-\,3^{13}\cdot 7^{16}$	$2$	$25.637017305340915$	$40.08236355961002$			?	$C_2\times \GL(3,2)$ (as 14T17)	trivial	trivial	$2$	$8$	$44170.17753740919$
14.4.619...408.1	$x^{14} - 7 x^{13} + 30 x^{12} - 89 x^{11} + 199 x^{10} - 346 x^{9} + 477 x^{8} - 525 x^{7} + 469 x^{6} - 344 x^{5} + 217 x^{4} - 119 x^{3} + 48 x^{2} - 11 x + 1$	$14$	[4,5]	$-\,2^{12}\cdot 3^{5}\cdot 53^{8}$	$3$	$25.92547102608315$	$44.26939474722475$			?	$C_2\times \GL(3,2)$ (as 14T17)	trivial	$[2]$	$2$	$8$	$50557.30370830211$
14.4.619...408.2	$x^{14} - 7 x^{13} + 28 x^{12} - 77 x^{11} + 155 x^{10} - 236 x^{9} + 313 x^{8} - 397 x^{7} + 427 x^{6} - 336 x^{5} + 267 x^{4} - 237 x^{3} + 124 x^{2} - 25 x + 1$	$14$	[4,5]	$-\,2^{12}\cdot 3^{5}\cdot 53^{8}$	$3$	$25.92547102608315$	$44.26939474722475$			?	$C_2\times \GL(3,2)$ (as 14T17)	trivial	trivial	$2$	$8$	$50557.30370830211$
14.4.145...144.1	$x^{14} - x^{12} - 2 x^{11} - 3 x^{10} - 2 x^{9} - 3 x^{8} - 2 x^{7} - 3 x^{6} - 2 x^{5} - 3 x^{4} - 2 x^{3} - x^{2} + 1$	$14$	[4,5]	$-\,2^{14}\cdot 11\cdot 73^{8}$	$3$	$27.5531405473$				✓	$C_2\wr C_7:C_3$ (as 14T44)	trivial	$[2]$	$2$	$8$	$71790.485415$
14.4.162...367.1	$x^{14} - 6 x^{13} + 9 x^{12} + 25 x^{11} - 80 x^{10} + 104 x^{9} - 425 x^{8} + 1261 x^{7} + 5 x^{6} - 4607 x^{5} + 6299 x^{4} + 754 x^{3} - 5512 x^{2} + 702 x + 1453$	$14$	[4,5]	$-\,3^{7}\cdot 13^{6}\cdot 109^{5}$	$3$	$27.772644937$	$123.80306325772969$			?	$C_2^4.\PSL(2,7)$ (as 14T42)	trivial	$[2]$	$2$	$8$	$49614.4197132$
14.4.303...392.1	$x^{14} - 2 x^{13} - 7 x^{12} + 32 x^{11} - 83 x^{10} + 146 x^{9} - 199 x^{8} + 222 x^{7} - 199 x^{6} + 146 x^{5} - 83 x^{4} + 32 x^{3} - 7 x^{2} - 2 x + 1$	$14$	[4,5]	$-\,2^{14}\cdot 23\cdot 73^{8}$	$3$	$29.0437165562$				?	$C_2\wr C_7:C_3$ (as 14T44)	trivial	$[2]$	$2$	$8$	$151032.821175$
14.4.463...867.1	$x^{14} - 9 x^{12} - 6 x^{11} + 36 x^{10} + 32 x^{9} - 34 x^{8} - 54 x^{7} - 116 x^{6} - 143 x^{5} + 192 x^{4} + 289 x^{3} + 125 x^{2} - 24 x - 21$	$14$	[4,5]	$-\,3\cdot 7^{8}\cdot 173^{6}$	$3$	$29.9333877161$	$83.36473467247461$			?	$C_2\wr F_7$ (as 14T48)	trivial	trivial	$2$	$8$	$688484.776641$
14.4.170...179.1	$x^{14} - 7 x^{13} + 28 x^{12} - 77 x^{11} + 136 x^{10} - 141 x^{9} + 5 x^{8} + 265 x^{7} - 464 x^{6} + 419 x^{5} - 140 x^{4} - 99 x^{3} + 153 x^{2} - 79 x + 18$	$14$	[4,5]	$-\,7^{8}\cdot 11\cdot 173^{6}$	$3$	$32.8443728152$	$159.63131361268375$			?	$C_2\wr F_7$ (as 14T48)	trivial	trivial	$2$	$8$	$1070462.31054$
14.4.167...344.1	$x^{14} - 4 x^{13} + 19 x^{12} - 30 x^{11} + 74 x^{10} - 180 x^{9} + 422 x^{8} - 418 x^{7} - 1198 x^{6} + 4720 x^{5} - 11626 x^{4} + 16794 x^{3} - 6181 x^{2} - 8990 x + 6319$	$14$	[4,5]	$-\,2^{16}\cdot 797^{6}$	$2$	$38.68266783366515$	$84.59797881758502$			?	$C_2^4:\GL(3,2)$ (as 14T43)	trivial	$[2]$	$2$	$8$	$831962.935116158$
14.4.177...003.1	$x^{14} - 3 x^{13} + 36 x^{12} - 47 x^{11} + 335 x^{10} + 217 x^{9} - 257 x^{8} + 4394 x^{7} - 12210 x^{6} + 5860 x^{5} - 45417 x^{4} + 9232 x^{3} - 36073 x^{2} + 144078 x + 175213$	$14$	[4,5]	$-\,3^{7}\cdot 13^{6}\cdot 109^{6}$	$3$	$38.82824006018023$	$65.19969325081216$			?	$C_2\times \GL(3,2)$ (as 14T17)	trivial	$[2]$	$2$	$8$	$389544.5992650786$

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