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 matches 1-50 of 64)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.163840814805078125.1	x^16 - 5x^15 + 15x^14 - 33x^13 + 54x^12 - 69x^11 + 73x^10 - 67x^9 + 57x^8 - 46x^7 + 37x^6 - 29x^5 + 17x^4 - 10x^3 + 6x^2 - x + 1	\( 5^{8}\cdot 11^{2}\cdot 13^{2}\cdot 29^{5} \)	16T1779	Trivial
16.4.163840814805078125.1	x^16 - 2x^15 + 3x^14 + x^13 - 9x^12 + 12x^11 - 5x^10 - 22x^9 + 32x^8 + 10x^7 - 27x^6 - x^5 + 6x^4 + 5x^3 - x^2 - 3x + 1	\( 5^{8}\cdot 11^{2}\cdot 13^{2}\cdot 29^{5} \)	16T1779	Trivial
16.0.1301248124195703125.1	x^16 - 4x^15 + 14x^14 - 26x^13 + 39x^12 - 30x^11 + 11x^10 + 25x^9 - 31x^8 + 25x^7 + 11x^6 - 30x^5 + 39x^4 - 26x^3 + 14x^2 - 4x + 1	\( 5^{8}\cdot 13^{2}\cdot 29^{5}\cdot 31^{2} \)	16T1779	Trivial
16.0.1896792072166637568.3	x^16 + 7x^14 + 24x^12 + 52x^10 + 81x^8 + 91x^6 + 71x^4 + 39x^2 + 13	\( 2^{16}\cdot 3^{8}\cdot 13^{5}\cdot 109^{2} \)	16T1779	Trivial
16.0.1896792072166637568.4	x^16 - 8x^14 + 33x^12 - 85x^10 + 149x^8 - 178x^6 + 141x^4 - 65x^2 + 13	\( 2^{16}\cdot 3^{8}\cdot 13^{5}\cdot 109^{2} \)	16T1779	Trivial
16.2.9499174502400000000.1	x^16 - 2x^15 + 6x^14 - 6x^13 - 7x^12 - 54x^10 - 42x^9 - 50x^8 - 88x^7 - 44x^6 - 52x^5 - 40x^4 + 4x^3 + 12x^2 + 2x + 1	\( -\,2^{24}\cdot 3^{2}\cdot 5^{8}\cdot 11^{5} \)	16T1779	Trivial
16.2.9499174502400000000.2	x^16 - 2x^15 + 4x^14 - 6x^13 + 12x^12 - 18x^11 + 4x^10 - 54x^9 - 26x^8 - 54x^7 + 4x^6 - 18x^5 + 12x^4 - 6x^3 + 4x^2 - 2x + 1	\( -\,2^{24}\cdot 3^{2}\cdot 5^{8}\cdot 11^{5} \)	16T1779	Trivial
16.0.16087543146273828125.1	x^16 + 5x^14 - 4x^13 + 16x^12 - 22x^11 + 38x^10 - 40x^9 + 76x^8 - 59x^7 + 114x^6 + 56x^5 + 146x^4 + 36x^3 + 17x^2 - 2x + 1	\( 5^{8}\cdot 13^{2}\cdot 29^{5}\cdot 109^{2} \)	16T1779	Trivial
16.4.16087543146273828125.1	x^16 - 2x^15 + x^14 + 3x^13 - 12x^12 + 13x^11 - 8x^10 + 10x^9 + 6x^8 - 25x^7 + 18x^6 + x^5 - 22x^4 + 19x^3 - x^2 - 4x + 1	\( 5^{8}\cdot 13^{2}\cdot 29^{5}\cdot 109^{2} \)	16T1779	Trivial
16.4.19824738591414453125.1	x^16 - 2x^15 - 2x^14 + 11x^13 + x^12 - 41x^11 - 16x^10 + 147x^9 - 102x^8 - 260x^7 + 457x^6 + 6x^5 - 403x^4 + 174x^3 + 39x^2 - 10x + 1	\( 5^{8}\cdot 11^{4}\cdot 13^{2}\cdot 29^{5} \)	16T1779	Trivial (GRH)
16.0.30061404375930078125.1	x^16 - 2x^15 + 5x^14 - 12x^13 + 21x^12 - 32x^11 + 47x^10 - 41x^9 + 57x^8 - 21x^7 + 34x^6 + 2x^5 + 10x^4 - 18x^3 + 14x^2 - 5x + 1	\( 5^{8}\cdot 13^{2}\cdot 29^{5}\cdot 149^{2} \)	16T1779	Trivial
16.4.30061404375930078125.1	x^16 - x^15 - x^14 - 12x^13 - 8x^12 - 9x^11 + 14x^10 + 17x^9 - 2x^8 - 24x^7 - 64x^6 - 23x^5 - 28x^4 + 19x^3 - 4x^2 + 3x + 1	\( 5^{8}\cdot 13^{2}\cdot 29^{5}\cdot 149^{2} \)	16T1779	Trivial
16.4.38059111970559229952.1	x^16 - 4x^15 + 4x^14 - 7x^12 + 32x^11 - 42x^10 + 16x^9 - 18x^8 + 16x^7 + 14x^6 - 12x^5 + 10x^4 - 24x^3 + 22x^2 - 8x + 1	\( 2^{32}\cdot 17^{5}\cdot 79^{2} \)	16T1779	Trivial
16.8.38059111970559229952.1	x^16 - 8x^14 + 21x^12 - 4x^11 - 38x^10 + 8x^9 + 57x^8 + 8x^7 - 38x^6 - 4x^5 + 21x^4 - 8x^2 + 1	\( 2^{32}\cdot 17^{5}\cdot 79^{2} \)	16T1779	Trivial
16.0.43385318571648828125.1	x^16 - 3x^15 + 7x^14 - 8x^13 + 14x^12 - 12x^11 + 18x^10 - 12x^9 + 19x^8 - 12x^7 + 18x^6 - 12x^5 + 14x^4 - 8x^3 + 7x^2 - 3x + 1	\( 5^{8}\cdot 13^{2}\cdot 29^{5}\cdot 179^{2} \)	16T1779	Trivial
16.4.43385318571648828125.1	x^16 - 3x^15 + 3x^14 - 7x^13 + 15x^12 - 12x^11 - 3x^10 - 29x^9 + 79x^8 - x^7 + 42x^6 - 161x^5 - 45x^4 + 77x^3 + 55x^2 + 13x + 1	\( 5^{8}\cdot 13^{2}\cdot 29^{5}\cdot 179^{2} \)	16T1779	Trivial
16.8.43385318571648828125.1	x^16 - 6x^15 + 7x^14 + 24x^13 - 64x^12 - 5x^11 + 167x^10 - 132x^9 - 161x^8 + 280x^7 - 53x^6 - 152x^5 + 142x^4 - 55x^3 + x^2 + 6x - 1	\( 5^{8}\cdot 13^{2}\cdot 29^{5}\cdot 179^{2} \)	16T1779	Trivial (GRH)
16.4.43385318571648828125.2	x^16 - 3x^14 - 9x^12 - 15x^11 - 28x^10 - 20x^9 - 21x^8 - 20x^7 - 28x^6 - 15x^5 - 9x^4 - 3x^2 + 1	\( 5^{8}\cdot 13^{2}\cdot 29^{5}\cdot 179^{2} \)	16T1779	Trivial
16.0.403122887420429729792.1	x^16 - 3x^15 + 4x^14 + 2x^13 - 7x^12 + 3x^11 + 11x^10 + 5x^9 + 2x^8 - 32x^7 + 99x^6 - 37x^5 + 24x^4 - 28x^3 + 18x^2 - 6x + 8	\( 2^{23}\cdot 17^{8}\cdot 83^{2} \)	16T1779	Trivial
16.2.502174024985600000000.1	x^16 + 10x^14 + 44x^12 + 104x^10 + 125x^8 + 53x^6 - 24x^4 - 33x^2 - 11	\( -\,2^{16}\cdot 5^{8}\cdot 11^{5}\cdot 349^{2} \)	16T1779	Trivial (GRH)
16.6.502174024985600000000.1	x^16 - 10x^12 - 5x^10 - x^8 + 5x^6 + 20x^4 - 11	\( -\,2^{16}\cdot 5^{8}\cdot 11^{5}\cdot 349^{2} \)	16T1779	Trivial (GRH)
16.2.502174024985600000000.2	x^16 - 7x^14 + 6x^12 + 42x^10 - 68x^8 - 24x^6 + 71x^4 - 11x^2 - 11	\( -\,2^{16}\cdot 5^{8}\cdot 11^{5}\cdot 349^{2} \)	16T1779	Trivial (GRH)
16.6.502174024985600000000.2	x^16 - 10x^14 + 44x^12 - 104x^10 + 125x^8 - 53x^6 - 24x^4 + 33x^2 - 11	\( -\,2^{16}\cdot 5^{8}\cdot 11^{5}\cdot 349^{2} \)	16T1779	Trivial (GRH)
16.0.6449966198726875676672.1	x^16 + 5x^14 - x^12 - 31x^10 + 102x^8 + 32x^6 + 48x^4 + 48x^2 + 32	\( 2^{27}\cdot 17^{8}\cdot 83^{2} \)	16T1779	Trivial (GRH)
16.4.6586671438233600000000.1	x^16 - 2x^15 + 2x^14 - 10x^13 + 27x^12 - 102x^11 + 276x^10 - 572x^9 + 1169x^8 - 1920x^7 + 2868x^6 - 3894x^5 + 4173x^4 - 3826x^3 + 2394x^2 - 334x - 251	\( 2^{24}\cdot 5^{8}\cdot 7^{2}\cdot 29^{5} \)	16T1779	Trivial (GRH)
16.8.6586671438233600000000.1	x^16 - 2x^15 - 2x^14 - 12x^13 + 51x^12 - 16x^11 - 152x^10 + 386x^9 - 608x^8 + 630x^7 - 232x^6 - 286x^5 + 354x^4 - 78x^3 - 62x^2 + 28x - 1	\( 2^{24}\cdot 5^{8}\cdot 7^{2}\cdot 29^{5} \)	16T1779	Trivial (GRH)
16.4.11657421285094400000000.1	x^16 - 2x^14 - 15x^12 + 34x^10 + 55x^8 - 163x^6 - 61x^4 + 261x^2 + 29	\( 2^{16}\cdot 5^{8}\cdot 29^{5}\cdot 149^{2} \)	16T1779	Trivial (GRH)
16.4.11657421285094400000000.2	x^16 - x^14 - 29x^12 - 81x^10 - 55x^8 + 108x^6 + 224x^4 + 145x^2 + 29	\( 2^{16}\cdot 5^{8}\cdot 29^{5}\cdot 149^{2} \)	16T1779	Trivial (GRH)
16.12.22717295368601600000000.1	x^16 - 4x^15 - 18x^14 + 90x^13 + 31x^12 - 516x^11 + 332x^10 + 1036x^9 - 1307x^8 - 408x^7 + 1384x^6 - 580x^5 - 231x^4 + 246x^3 - 58x^2 + 1	\( 2^{24}\cdot 5^{8}\cdot 13^{2}\cdot 29^{5} \)	16T1779	Trivial (GRH)
16.12.22717295368601600000000.2	x^16 - 8x^15 + 18x^14 + 10x^13 - 109x^12 + 198x^11 - 42x^10 - 492x^9 + 697x^8 + 128x^7 - 880x^6 + 456x^5 + 273x^4 - 342x^3 + 62x^2 + 50x - 19	\( 2^{24}\cdot 5^{8}\cdot 13^{2}\cdot 29^{5} \)	16T1779	Trivial (GRH)
16.0.22717295368601600000000.3	x^16 - 4x^15 + 16x^14 - 44x^13 + 160x^12 - 420x^11 + 968x^10 - 1764x^9 + 3170x^8 - 4780x^7 + 6608x^6 - 7604x^5 + 8216x^4 - 6732x^3 + 5336x^2 - 3452x + 1301	\( 2^{24}\cdot 5^{8}\cdot 13^{2}\cdot 29^{5} \)	16T1779	$[2]$ (GRH)
16.4.22717295368601600000000.3	x^16 - 4x^15 + 8x^14 - 22x^13 + 75x^12 - 196x^11 + 382x^10 - 722x^9 + 1331x^8 - 2762x^7 + 4086x^6 - 2658x^5 + 89x^4 + 468x^3 - 384x^2 + 466x - 109	\( 2^{24}\cdot 5^{8}\cdot 13^{2}\cdot 29^{5} \)	16T1779	Trivial (GRH)
16.8.22717295368601600000000.3	x^16 - 2x^15 + 2x^14 - 26x^13 + 64x^12 - 74x^11 - 62x^10 + 606x^9 - 682x^8 - 62x^7 + 598x^6 - 1318x^5 + 760x^4 - 262x^3 - 58x^2 + 18x + 1	\( 2^{24}\cdot 5^{8}\cdot 13^{2}\cdot 29^{5} \)	16T1779	Trivial (GRH)
16.4.22717295368601600000000.4	x^16 - 2x^15 - 10x^14 + 52x^13 - 113x^12 + 130x^11 - 40x^10 - 48x^9 - 180x^8 + 690x^7 - 714x^6 + 90x^5 + 128x^4 + 596x^3 - 936x^2 + 308x + 49	\( 2^{24}\cdot 5^{8}\cdot 13^{2}\cdot 29^{5} \)	16T1779	Trivial (GRH)
16.8.22717295368601600000000.4	x^16 - 4x^15 + 16x^13 - 41x^12 + 174x^11 - 508x^10 + 624x^9 + 574x^8 - 3206x^7 + 4190x^6 - 656x^5 - 4280x^4 + 5470x^3 - 3222x^2 + 1018x - 149	\( 2^{24}\cdot 5^{8}\cdot 13^{2}\cdot 29^{5} \)	16T1779	Trivial (GRH)
16.8.22717295368601600000000.5	x^16 - 4x^15 - 6x^14 + 66x^13 - 137x^12 - 32x^11 + 582x^10 - 890x^9 + 247x^8 + 774x^7 - 1330x^6 + 1298x^5 - 819x^4 + 432x^3 - 166x^2 + 26x - 1	\( 2^{24}\cdot 5^{8}\cdot 13^{2}\cdot 29^{5} \)	16T1779	Trivial (GRH)
16.8.191136100120879351953125.1	x^16 - 5x^15 + 4x^14 + 6x^13 - 36x^12 + 157x^11 - 593x^10 + 1578x^9 - 1738x^8 + 365x^7 + 2276x^6 - 4207x^5 - 2289x^4 + 4217x^3 + 2610x^2 - 376x - 331	\( 5^{8}\cdot 13^{2}\cdot 29^{5}\cdot 109^{4} \)	16T1779	Trivial (GRH)
16.8.667393238550023664453125.1	x^16 - x^15 - 19x^14 + 29x^13 + 128x^12 - 368x^11 - 433x^10 + 2559x^9 + 177x^8 - 10032x^7 + 7526x^6 + 17399x^5 - 28818x^4 + 595x^3 + 27473x^2 - 21306x + 5119	\( 5^{8}\cdot 13^{2}\cdot 29^{5}\cdot 149^{4} \)	16T1779	Trivial (GRH)
16.4.1686187888187801600000000.1	x^16 - 58x^12 - 358x^10 - 1602x^8 - 3748x^6 - 3037x^4 + 812x^2 + 1421	\( 2^{32}\cdot 5^{8}\cdot 7^{2}\cdot 29^{5} \)	16T1779	Trivial (GRH)
16.8.1686187888187801600000000.1	x^16 - 58x^12 + 358x^10 - 1602x^8 + 3748x^6 - 3037x^4 - 812x^2 + 1421	\( 2^{32}\cdot 5^{8}\cdot 7^{2}\cdot 29^{5} \)	16T1779	Trivial (GRH)
16.4.1686187888187801600000000.2	x^16 + 2x^14 - 67x^12 - 356x^10 - 719x^8 - 1610x^6 - 3201x^4 - 812x^2 + 1421	\( 2^{32}\cdot 5^{8}\cdot 7^{2}\cdot 29^{5} \)	16T1779	Trivial (GRH)
16.8.1686187888187801600000000.2	x^16 - 2x^14 - 67x^12 + 356x^10 - 719x^8 + 1610x^6 - 3201x^4 + 812x^2 + 1421	\( 2^{32}\cdot 5^{8}\cdot 7^{2}\cdot 29^{5} \)	16T1779	Trivial (GRH)
16.12.27382351547454726374162432.1	x^16 - 8x^15 + 8x^14 + 76x^13 - 188x^12 - 32x^11 + 368x^10 - 468x^9 + 1526x^8 - 1972x^7 - 1520x^6 + 4244x^5 - 2803x^4 + 1692x^3 - 1168x^2 + 252x + 41	\( 2^{32}\cdot 17^{5}\cdot 113^{2}\cdot 593^{2} \)	16T1779	Trivial (GRH)
16.4.27382351547454726374162432.1	x^16 - 8x^15 + 40x^14 - 124x^13 + 252x^12 - 400x^11 + 504x^10 - 44x^9 - 1976x^8 + 4932x^7 - 5212x^6 + 380x^5 + 6037x^4 - 8328x^3 + 5130x^2 - 648x - 567	\( 2^{32}\cdot 17^{5}\cdot 113^{2}\cdot 593^{2} \)	16T1779	$[2]$ (GRH)
16.0.99576130242170943648828125.1	x^16 - 4x^15 + 23x^14 - 47x^13 + 139x^12 - 164x^11 + 401x^10 - 258x^9 + 694x^8 - 58x^7 + 838x^6 + 230x^5 + 818x^4 + 354x^3 + 320x^2 + 13x + 1	\( 5^{8}\cdot 13^{2}\cdot 29^{5}\cdot 271181^{2} \)	16T1779	$[15]$ (GRH)
16.8.120030321490089906705334272.1	x^16 + 8x^14 - 6x^12 - 124x^10 - 29x^8 + 396x^6 - 30x^4 - 132x^2 + 33	\( 2^{16}\cdot 3^{13}\cdot 11^{5}\cdot 84457^{2} \)	16T1779	Trivial (GRH)
16.8.120030321490089906705334272.2	x^16 - 4x^15 - 4x^14 + 22x^13 + 17x^12 - 44x^11 - 60x^10 + 24x^9 + 85x^8 + 24x^7 - 60x^6 - 44x^5 + 17x^4 + 22x^3 - 4x^2 - 4x + 1	\( 2^{16}\cdot 3^{13}\cdot 11^{5}\cdot 84457^{2} \)	16T1779	Trivial (GRH)
16.12.132281136233566814225825792.1	x^16 - 4x^15 - 6x^14 + 28x^13 + 29x^12 - 72x^11 - 106x^10 + 52x^9 + 173x^8 + 52x^7 - 106x^6 - 72x^5 + 29x^4 + 28x^3 - 6x^2 - 4x + 1	\( 2^{32}\cdot 17^{5}\cdot 31^{2}\cdot 4751^{2} \)	16T1779	Trivial (GRH)
16.4.132281136233566814225825792.1	x^16 + 12x^14 + 30x^12 - 92x^10 - 341x^8 + 4x^6 + 282x^4 + 136x^2 + 17	\( 2^{32}\cdot 17^{5}\cdot 31^{2}\cdot 4751^{2} \)	16T1779	Trivial (GRH)
16.0.2927827744400742809600000000.1	x^16 + 46x^14 + 801x^12 + 6620x^10 + 27110x^8 + 55350x^6 + 56336x^4 + 27144x^2 + 4901	\( 2^{24}\cdot 5^{8}\cdot 13^{2}\cdot 29^{5}\cdot 359^{2} \)	16T1779	$[2, 92]$ (GRH)