Global number field search results

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Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying all 38 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.43782304297275648.1	x^16 - 7x^15 + 26x^14 - 68x^13 + 140x^12 - 234x^11 + 306x^10 - 280x^9 + 126x^8 + 67x^7 - 156x^6 + 108x^5 - 23x^4 - 17x^3 + 18x^2 - 7x + 1	\( 2^{8}\cdot 3^{8}\cdot 13^{4}\cdot 97^{3} \)	16T1781	Trivial
16.2.125468737884127232.2	x^16 - 4x^15 + 6x^14 - 8x^13 + 19x^12 - 40x^11 + 62x^10 - 76x^9 + 90x^8 - 104x^7 + 80x^6 - 12x^5 - 46x^4 + 52x^3 - 28x^2 + 8x - 1	\( -\,2^{32}\cdot 7^{4}\cdot 23^{3} \)	16T1781	Trivial
16.2.125468737884127232.3	x^16 - 4x^15 + 6x^14 - 19x^12 + 44x^11 - 48x^10 + 8x^9 + 53x^8 - 76x^7 + 36x^6 + 28x^5 - 43x^4 + 12x^3 + 4x^2 - 1	\( -\,2^{32}\cdot 7^{4}\cdot 23^{3} \)	16T1781	Trivial
16.0.1312406091695703125.1	x^16 - 5x^15 + 10x^14 - 6x^13 - 14x^12 + 28x^11 + 4x^10 - 53x^9 + 22x^8 + 69x^7 - 49x^6 - 111x^5 + 131x^4 + 68x^3 - 90x^2 - 75x + 71	\( 5^{8}\cdot 11^{4}\cdot 29^{3}\cdot 97^{2} \)	16T1781	Trivial
16.0.4874651380100000000.1	x^16 - 2x^15 - 2x^14 + 7x^13 + 6x^12 - 30x^11 + 13x^10 + 49x^9 - 50x^8 - 41x^7 + 84x^6 - 9x^5 - 66x^4 + 35x^3 + 29x^2 - 9x + 1	\( 2^{8}\cdot 5^{8}\cdot 29^{4}\cdot 41^{3} \)	16T1781	Trivial
16.0.5664494168027168768.1	x^16 - 3x^12 - 5x^10 + 5x^8 + 18x^6 + 17x^4 + 8x^2 + 2	\( 2^{19}\cdot 7^{8}\cdot 37^{4} \)	16T1781	Trivial
16.0.59626875462487113728.1	x^16 - 4x^15 + 16x^14 - 48x^13 + 118x^12 - 248x^11 + 452x^10 - 696x^9 + 920x^8 - 1036x^7 + 930x^6 - 596x^5 + 229x^4 - 24x^3 - 14x^2 + 4	\( 2^{32}\cdot 17^{3}\cdot 41^{4} \)	16T1781	Trivial
16.4.121866284502500000000.1	x^16 - 8x^15 + 30x^14 - 64x^13 + 63x^12 + 74x^11 - 462x^10 + 1093x^9 - 1698x^8 + 1916x^7 - 1643x^6 + 1088x^5 - 512x^4 + 217x^3 - 100x^2 - 25x + 31	\( 2^{8}\cdot 5^{10}\cdot 29^{4}\cdot 41^{3} \)	16T1781	Trivial
16.4.121866284502500000000.2	x^16 - 5x^15 + 12x^14 - 21x^13 + 15x^12 + x^11 - 39x^10 + 90x^9 - 72x^8 + 60x^7 + 139x^6 - 118x^5 + 135x^4 - 78x^3 + 73x^2 - 25x + 1	\( 2^{8}\cdot 5^{10}\cdot 29^{4}\cdot 41^{3} \)	16T1781	Trivial (GRH)
16.4.646220440309430078125.1	x^16 - 4x^15 + 12x^14 - 30x^13 + 40x^12 - 16x^11 - 102x^10 + 422x^9 - 763x^8 + 531x^7 + 286x^6 - 557x^5 - 120x^4 + 512x^3 - 158x^2 + 18x - 1	\( 5^{8}\cdot 11^{4}\cdot 97^{2}\cdot 229^{3} \)	16T1781	Trivial (GRH)
16.8.954030007399793819648.1	x^16 - 6x^14 + 15x^12 - 38x^10 + 165x^8 - 540x^6 + 948x^4 - 816x^2 + 272	\( 2^{36}\cdot 17^{3}\cdot 41^{4} \)	16T1781	Trivial (GRH)
16.0.1103733523116086328125.1	x^16 - 2x^15 - 10x^14 + 2x^13 + 113x^12 + 12x^11 - 635x^10 - 249x^9 + 2451x^8 + 1121x^7 - 6342x^6 - 2322x^5 + 10279x^4 + 2361x^3 - 9346x^2 - 1034x + 3739	\( 5^{8}\cdot 11^{4}\cdot 29^{5}\cdot 97^{2} \)	16T1781	$[2]$ (GRH)
16.4.1247910753305600000000.1	x^16 - 4x^15 + 5x^14 + 6x^13 - 42x^12 + 90x^11 - 112x^10 + 78x^9 - 53x^8 + 156x^7 - 448x^6 + 720x^5 - 672x^4 + 192x^3 + 320x^2 - 512x + 256	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 41^{3} \)	16T1781	Trivial (GRH)
16.8.1247910753305600000000.1	x^16 - x^14 - x^12 - 17x^10 + 8x^8 + 49x^6 + x^4 - 82x^2 + 41	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 41^{3} \)	16T1781	Trivial (GRH)
16.10.8192699220747100000000.1	x^16 - 9x^14 + 29x^12 - 32x^10 - 35x^8 + 148x^6 - 194x^4 + 124x^2 - 31	\( -\,2^{8}\cdot 5^{8}\cdot 31^{3}\cdot 229^{4} \)	16T1781	Trivial (GRH)
16.4.12348428916764870703125.1	x^16 - 2x^14 + 13x^12 + 126x^10 - 128x^8 - 211x^6 + 105x^4 - 174x^2 + 29	\( 5^{8}\cdot 11^{4}\cdot 29^{3}\cdot 97^{4} \)	16T1781	Trivial (GRH)
16.10.14139411419216276881408.1	x^16 - 10x^14 + 37x^12 - 64x^10 + 50x^8 - 2x^6 - 32x^4 + 28x^2 - 7	\( -\,2^{32}\cdot 7^{3}\cdot 313^{4} \)	16T1781	Trivial (GRH)
16.2.14139411419216276881408.1	x^16 + 10x^14 + 37x^12 + 64x^10 + 50x^8 + 2x^6 - 32x^4 - 28x^2 - 7	\( -\,2^{32}\cdot 7^{3}\cdot 313^{4} \)	16T1781	Trivial
16.4.15264480118396701114368.1	x^16 - 8x^15 + 44x^14 - 168x^13 + 486x^12 - 1096x^11 + 1884x^10 - 2424x^9 + 2051x^8 - 568x^7 - 1300x^6 + 2376x^5 - 2174x^4 + 1264x^3 - 464x^2 + 96x - 7	\( 2^{40}\cdot 17^{3}\cdot 41^{4} \)	16T1781	Trivial
16.2.40704820494617600000000.3	x^16 + 12x^14 + 52x^12 + 79x^10 - 94x^8 - 527x^6 - 787x^4 - 524x^2 - 131	\( -\,2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 131^{3} \)	16T1781	Trivial (GRH)
16.6.40704820494617600000000.3	x^16 + 3x^14 - 33x^12 - 186x^10 - 245x^8 + 189x^6 + 463x^4 - 131	\( -\,2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 131^{3} \)	16T1781	Trivial (GRH)
16.6.40704820494617600000000.4	x^16 - 7x^14 - 6x^12 + 79x^10 - 88x^6 + 250x^4 + 131x^2 - 131	\( -\,2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 131^{3} \)	16T1781	Trivial (GRH)
16.6.40704820494617600000000.5	x^16 + 4x^14 - 25x^12 - 47x^10 + 300x^8 - 24x^6 - 994x^4 + 917x^2 - 131	\( -\,2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 131^{3} \)	16T1781	Trivial (GRH)
16.6.40704820494617600000000.6	x^16 - 3x^14 - 33x^12 + 186x^10 - 245x^8 - 189x^6 + 463x^4 - 131	\( -\,2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 131^{3} \)	16T1781	Trivial (GRH)
16.12.244231681894347217829888.1	x^16 - 4x^15 - 8x^14 + 40x^13 - 16x^12 - 12x^11 + 48x^10 - 172x^9 - 193x^8 + 252x^7 + 336x^6 - 68x^5 - 192x^4 - 32x^3 + 32x^2 + 12x + 1	\( 2^{44}\cdot 17^{3}\cdot 41^{4} \)	16T1781	Trivial (GRH)
16.8.244231681894347217829888.1	x^16 - 4x^15 - 12x^14 + 60x^13 - 10x^12 - 92x^11 - 76x^10 + 52x^9 + 158x^8 + 52x^7 - 76x^6 - 92x^5 - 10x^4 + 60x^3 - 12x^2 - 4x + 1	\( 2^{44}\cdot 17^{3}\cdot 41^{4} \)	16T1781	Trivial (GRH)
16.8.244231681894347217829888.2	x^16 - 8x^15 + 20x^14 - 28x^13 + 118x^12 - 356x^11 + 456x^10 - 656x^9 + 1731x^8 - 2164x^7 + 1152x^6 - 2272x^5 + 4616x^4 - 3540x^3 + 996x^2 - 60x + 1	\( 2^{44}\cdot 17^{3}\cdot 41^{4} \)	16T1781	Trivial (GRH)
16.12.319465152846233600000000.1	x^16 - 2x^15 - 8x^14 + 36x^13 - 46x^12 - 186x^11 + 482x^10 + 214x^9 - 1390x^8 + 470x^7 + 1610x^6 - 1142x^5 - 649x^4 + 690x^3 + 26x^2 - 124x + 19	\( 2^{24}\cdot 5^{8}\cdot 29^{4}\cdot 41^{3} \)	16T1781	Trivial (GRH)
16.4.6080288122871427605078125.1	x^16 - 8x^15 + 25x^14 - 35x^13 - 16x^12 + 187x^11 - 569x^10 + 1250x^9 - 1872x^8 + 1759x^7 - 1592x^6 + 2131x^5 - 10001x^4 + 16868x^3 - 7231x^2 - 897x + 4351	\( 5^{8}\cdot 11^{4}\cdot 97^{4}\cdot 229^{3} \)	16T1781	Trivial (GRH)
16.4.10385028718999256261328125.1	x^16 - 4x^15 + 5x^14 + 12x^13 - 111x^12 + 224x^11 - 912x^9 + 2211x^8 - 2451x^7 + 2040x^6 - 341x^5 + 799x^4 + 1398x^3 + 81x^2 - 594x + 81	\( 5^{8}\cdot 11^{4}\cdot 29^{5}\cdot 97^{4} \)	16T1781	$[2]$ (GRH)
16.0.503321711393409725500489728.1	x^16 + 30x^14 + 176x^12 - 334x^10 - 718x^8 + 15068x^6 + 58335x^4 + 68248x^2 + 6137	\( 2^{32}\cdot 3^{4}\cdot 13^{8}\cdot 17^{3}\cdot 19^{2} \)	16T1781	$[2]$ (GRH)
16.8.503321711393409725500489728.1	x^16 - 30x^14 + 176x^12 + 334x^10 - 718x^8 - 15068x^6 + 58335x^4 - 68248x^2 + 6137	\( 2^{32}\cdot 3^{4}\cdot 13^{8}\cdot 17^{3}\cdot 19^{2} \)	16T1781	Trivial (GRH)
16.0.503321711393409725500489728.2	x^16 + 24x^14 + 252x^12 + 1512x^10 + 5666x^8 + 13560x^6 + 20183x^4 + 16986x^2 + 6137	\( 2^{32}\cdot 3^{4}\cdot 13^{8}\cdot 17^{3}\cdot 19^{2} \)	16T1781	$[2]$ (GRH)
16.8.503321711393409725500489728.2	x^16 - 24x^14 + 252x^12 - 1512x^10 + 5666x^8 - 13560x^6 + 20183x^4 - 16986x^2 + 6137	\( 2^{32}\cdot 3^{4}\cdot 13^{8}\cdot 17^{3}\cdot 19^{2} \)	16T1781	Trivial (GRH)
16.0.3480707415024772072868946116608.1	x^16 - 4x^15 + 88x^14 - 216x^13 + 3132x^12 - 6396x^11 + 57440x^10 - 119824x^9 + 605820x^8 - 1276532x^7 + 3801328x^6 - 6196184x^5 + 10434076x^4 - 11087660x^3 + 11409096x^2 - 6736240x + 3398063	\( 2^{40}\cdot 41^{4}\cdot 73^{3}\cdot 1697^{2} \)	16T1781	$[2, 2, 4646]$ (GRH)
16.16.3480707415024772072868946116608.1	x^16 - 4x^15 - 96x^14 + 280x^13 + 3166x^12 - 8072x^11 - 45496x^10 + 115204x^9 + 281019x^8 - 778400x^7 - 563604x^6 + 2047852x^5 + 251748x^4 - 2123820x^3 + 106928x^2 + 664268x + 79889	\( 2^{40}\cdot 41^{4}\cdot 73^{3}\cdot 1697^{2} \)	16T1781	Trivial (GRH)
16.0.3657406027372345478303568625664.1	x^16 + 78x^14 - 32x^13 + 2501x^12 - 1720x^11 + 42462x^10 - 35572x^9 + 409672x^8 - 334160x^7 + 2239790x^6 - 1357128x^5 + 6371904x^4 - 1825304x^3 + 9659452x^2 - 1797280x + 9287425	\( 2^{32}\cdot 41^{4}\cdot 569^{3}\cdot 1279^{2} \)	16T1781	$[2, 2, 6174]$ (GRH)
16.16.3657406027372345478303568625664.1	x^16 - 86x^14 - 32x^13 + 2911x^12 + 1912x^11 - 49502x^10 - 41020x^9 + 449959x^8 + 384176x^7 - 2184304x^6 - 1509840x^5 + 5524811x^4 + 2012224x^3 - 6145068x^2 + 249908x + 1038527	\( 2^{32}\cdot 41^{4}\cdot 569^{3}\cdot 1279^{2} \)	16T1781	Trivial (GRH)