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 46 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.13156120051417161.1	x^16 - x^15 - x^13 - 3x^12 + 15x^11 - 18x^10 + 10x^9 - 3x^8 - 15x^7 + 57x^6 - 90x^5 + 83x^4 - 50x^3 + 21x^2 - 6x + 1	\( 3^{12}\cdot 7^{4}\cdot 13^{4}\cdot 19^{2} \)	16T919	Trivial
16.0.28102717979654409.1	x^16 - 4x^15 + 9x^14 - 15x^13 + 17x^12 - 9x^11 - 4x^10 + 14x^9 - 18x^8 + 13x^7 + 2x^6 - 15x^5 + 20x^4 - 18x^3 + 12x^2 - 5x + 1	\( 3^{12}\cdot 7^{4}\cdot 13^{2}\cdot 19^{4} \)	16T919	Trivial
16.0.135306265600000000.1	x^16 - 4x^15 + 8x^14 - 16x^13 + 32x^12 - 48x^11 + 50x^10 - 50x^9 + 75x^8 - 86x^7 + 78x^6 - 56x^5 + 39x^4 - 18x^3 + 7x^2 - 2x + 1	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 19^{2} \)	16T919	Trivial
16.0.165035929514868736.1	x^16 - x^14 + x^12 - 3x^10 + 19x^6 + 21x^4 + 8x^2 + 1	\( 2^{16}\cdot 17^{8}\cdot 19^{2} \)	16T919	Trivial (GRH)
16.4.190802976100000000.1	x^16 - 2x^14 - 3x^12 + 2x^10 + 3x^8 + 2x^6 - 3x^4 - 2x^2 + 1	\( 2^{8}\cdot 5^{8}\cdot 11^{4}\cdot 19^{4} \)	16T919	Trivial
16.0.315214873600000000.2	x^16 + 2x^14 + 4x^12 + 5x^10 + 5x^8 + 5x^6 + 4x^4 + 2x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 29^{2} \)	16T919	Trivial
16.0.315214873600000000.3	x^16 - 2x^14 + 4x^12 - 5x^10 + 5x^8 - 5x^6 + 4x^4 - 2x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 29^{2} \)	16T919	Trivial
16.0.1304712217600000000.1	x^16 + 2x^14 + 4x^12 + 8x^10 + 9x^8 + 3x^6 - 3x^4 + 1	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 59^{2} \)	16T919	Trivial
16.4.1304712217600000000.1	x^16 - 2x^14 + 4x^12 - 8x^10 + 9x^8 - 3x^6 - 3x^4 + 1	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 59^{2} \)	16T919	Trivial
16.4.1396521604275503104.1	x^16 - 2x^14 + 3x^12 - 2x^8 - 6x^6 + 8x^4 - 4x^2 + 1	\( 2^{40}\cdot 7^{4}\cdot 23^{2} \)	16T919	Trivial
16.4.1889415193600000000.1	x^16 - 4x^15 + 6x^14 - 12x^13 + 13x^12 - 14x^11 + 18x^10 - 12x^9 + 16x^8 - 6x^7 - 18x^6 + 22x^5 - 47x^4 + 24x^3 - 6x^2 + 2x + 1	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 71^{2} \)	16T919	Trivial
16.0.2190873625600000000.2	x^16 + 3x^14 + 6x^12 + 7x^10 + 5x^8 - 2x^6 - 4x^4 + 2x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 11^{2}\cdot 29^{4} \)	16T919	Trivial
16.0.2805759001600000000.1	x^16 + 3x^14 + 5x^12 + 4x^10 + 3x^8 + 4x^6 + 5x^4 + 3x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 19^{4}\cdot 29^{2} \)	16T919	Trivial
16.0.6536408089600000000.1	x^16 + 5x^14 + 12x^12 + 20x^10 + 23x^8 + 15x^6 + 7x^4 + 5x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 19^{2}\cdot 29^{4} \)	16T919	Trivial
16.8.12207024382173773824.1	x^16 - 14x^12 + 55x^8 - 32x^6 + 46x^4 - 16x^2 + 1	\( 2^{44}\cdot 7^{4}\cdot 17^{2} \)	16T919	Trivial (GRH)
16.0.16372058137600000000.1	x^16 - 2x^15 + 4x^14 - 8x^13 + 30x^12 - 74x^11 + 184x^10 - 330x^9 + 415x^8 - 330x^7 + 184x^6 - 74x^5 + 30x^4 - 8x^3 + 4x^2 - 2x + 1	\( 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 19^{2} \)	16T919	Trivial
16.8.16372058137600000000.1	x^16 - 6x^15 + 13x^14 - 6x^13 - 34x^12 + 88x^11 - 61x^10 - 86x^9 + 113x^8 + 40x^7 - 39x^6 - 70x^5 + 34x^4 + 30x^3 - 13x^2 - 4x + 1	\( 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 19^{2} \)	16T919	Trivial (GRH)
16.0.16372058137600000000.2	x^16 - 4x^15 + 6x^14 - 6x^13 + 15x^12 - 36x^10 - 28x^9 + 129x^8 + 28x^7 - 36x^6 + 15x^4 + 6x^3 + 6x^2 + 4x + 1	\( 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 19^{2} \)	16T919	Trivial
16.4.23087160108100000000.1	x^16 - 3x^15 + 6x^14 - 2x^13 - 2x^12 - x^11 + 38x^10 - 61x^9 - 19x^8 + 251x^7 - 482x^6 + 547x^5 - 412x^4 + 202x^3 - 80x^2 + 17x - 1	\( 2^{8}\cdot 5^{8}\cdot 11^{6}\cdot 19^{4} \)	16T919	Trivial (GRH)
16.4.23087160108100000000.2	x^16 - 3x^15 + 20x^13 - 32x^12 - 7x^11 + 29x^10 + 35x^9 - 112x^8 + 125x^7 - 69x^6 + 6x^5 + 8x^4 - 5x^3 + 4x + 1	\( 2^{8}\cdot 5^{8}\cdot 11^{6}\cdot 19^{4} \)	16T919	Trivial (GRH)
16.8.26426179609600000000.1	x^16 - 4x^15 + 4x^14 + 20x^13 - 98x^12 + 218x^11 - 316x^10 + 304x^9 - 177x^8 + 38x^7 + 74x^6 - 52x^5 - 67x^4 + 62x^3 + 3x^2 - 10x + 1	\( 2^{16}\cdot 5^{8}\cdot 19^{4}\cdot 89^{2} \)	16T919	Trivial (GRH)
16.8.32040757882594140625.1	x^16 - x^15 - 7x^14 - 6x^13 + 37x^12 + 53x^11 - 95x^10 - 167x^9 + 88x^8 + 325x^7 - 18x^6 - 298x^5 - 61x^4 + 80x^3 + 120x^2 - 25x - 25	\( 5^{8}\cdot 11^{4}\cdot 29^{4}\cdot 89^{2} \)	16T919	Trivial (GRH)
16.8.34601093000062890625.1	x^16 - 7x^15 + 17x^14 - 10x^13 - 39x^12 + 133x^11 - 241x^10 + 252x^9 - 43x^8 - 270x^7 + 415x^6 - 383x^5 + 303x^4 - 182x^3 + 67x^2 - 13x + 1	\( 5^{8}\cdot 19^{4}\cdot 29^{4}\cdot 31^{2} \)	16T919	Trivial (GRH)
16.0.48845561881600000000.2	x^16 + 4x^14 - x^12 + 4x^10 + 4x^6 - x^4 + 4x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 19^{4} \)	16T919	$[2]$
16.0.68879874372100000000.1	x^16 - 8x^15 + 36x^14 - 112x^13 + 272x^12 - 540x^11 + 912x^10 - 1326x^9 + 1648x^8 - 1716x^7 + 1476x^6 - 1036x^5 + 663x^4 - 414x^3 + 186x^2 - 42x + 71	\( 2^{8}\cdot 5^{8}\cdot 11^{4}\cdot 19^{6} \)	16T919	Trivial
16.8.69416922866203515625.1	x^16 - 4x^15 + x^14 + 9x^13 - x^12 - 21x^11 - 8x^10 + 63x^9 - 4x^8 - 88x^7 - 2x^6 + 69x^5 + 35x^4 - 21x^3 - 14x^2 + 3x + 1	\( 5^{8}\cdot 11^{4}\cdot 29^{4}\cdot 131^{2} \)	16T919	Trivial (GRH)
16.0.80695007641600000000.3	x^16 - 4x^15 + 16x^14 - 36x^13 + 85x^12 - 150x^11 + 274x^10 - 378x^9 + 479x^8 - 442x^7 + 434x^6 - 490x^5 + 725x^4 - 834x^3 + 686x^2 - 336x + 101	\( 2^{24}\cdot 5^{8}\cdot 11^{4}\cdot 29^{2} \)	16T919	Trivial (GRH)
16.0.94465412096391015625.1	x^16 - 3x^15 + 2x^14 + 11x^13 - 19x^12 - 8x^11 + 50x^10 - 79x^8 + 200x^6 - 64x^5 - 304x^4 + 352x^3 + 128x^2 - 384x + 256	\( 5^{8}\cdot 11^{2}\cdot 29^{4}\cdot 41^{4} \)	16T919	Trivial (GRH)
16.4.265095708697600000000.5	x^16 - 12x^14 + 65x^12 - 205x^10 + 413x^8 - 560x^6 + 540x^4 - 374x^2 + 121	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 29^{4} \)	16T919	Trivial (GRH)
16.12.781528990105600000000.1	x^16 - 8x^14 + 19x^12 - 19x^10 + 36x^8 - 81x^6 + 69x^4 - 17x^2 + 1	\( 2^{20}\cdot 5^{8}\cdot 11^{4}\cdot 19^{4} \)	16T919	Trivial (GRH)
16.4.781528990105600000000.2	x^16 - 4x^14 - x^12 - 4x^10 - 4x^6 - x^4 - 4x^2 + 1	\( 2^{20}\cdot 5^{8}\cdot 11^{4}\cdot 19^{4} \)	16T919	$[2]$ (GRH)
16.12.2097478042876266015625.1	x^16 - 2x^15 - 12x^14 + 31x^13 - x^12 - 44x^10 - 227x^9 + 539x^8 + 26x^7 - 802x^6 + 463x^5 + 240x^4 - 246x^3 + 20x^2 + 16x - 1	\( 5^{8}\cdot 11^{2}\cdot 29^{4}\cdot 89^{4} \)	16T919	Trivial (GRH)
16.0.6183971315830687890625.1	x^16 - x^15 + 9x^14 + 5x^13 + 48x^12 - 19x^11 + 110x^10 - 43x^9 + 267x^8 - 116x^7 + 195x^6 + 8x^5 + 53x^4 - 5x^3 + 6x^2 + 2x + 1	\( 5^{8}\cdot 29^{4}\cdot 41^{4}\cdot 89^{2} \)	16T919	Trivial
16.0.6183971315830687890625.2	x^16 - 3x^15 + 11x^14 - 5x^13 + 18x^12 - 7x^11 + 100x^10 + 19x^9 + 97x^8 + 12x^7 + 125x^6 - 4x^5 + 53x^4 + 5x^3 + 24x^2 + 4x + 1	\( 5^{8}\cdot 29^{4}\cdot 41^{4}\cdot 89^{2} \)	16T919	$[2]$
16.8.29139343719628125390625.1	x^16 - 5x^15 + 10x^13 - 12x^12 + 115x^11 + 15x^10 - 20x^9 - 312x^8 + 20x^7 + 15x^6 - 115x^5 - 12x^4 - 10x^3 + 5x + 1	\( 5^{8}\cdot 29^{4}\cdot 41^{2}\cdot 89^{4} \)	16T919	Trivial (GRH)
16.8.29139343719628125390625.2	x^16 - 12x^14 + 52x^12 - 262x^10 + 1068x^8 - 2196x^6 + 2373x^4 - 1264x^2 + 256	\( 5^{8}\cdot 29^{4}\cdot 41^{2}\cdot 89^{4} \)	16T919	Trivial (GRH)
16.0.95699550839833600000000.1	x^16 + 18x^14 + 136x^12 + 522x^10 + 1345x^8 + 3008x^6 + 3301x^4 + 1177x^2 + 121	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 19^{2}\cdot 29^{4} \)	16T919	$[2, 4]$
16.0.506594602613920781640625.1	x^16 - 3x^15 + 19x^14 - 57x^13 + 185x^12 - 506x^11 + 1189x^10 - 2364x^9 + 4508x^8 - 5714x^7 + 9497x^6 - 10979x^5 + 15984x^4 - 25718x^3 + 25462x^2 - 30794x + 27359	\( 5^{8}\cdot 11^{4}\cdot 19^{4}\cdot 29^{4}\cdot 31^{2} \)	16T919	$[2, 4, 4]$ (GRH)
16.0.506594602613920781640625.2	x^16 - 3x^15 + 21x^14 - 43x^13 + 110x^12 - 182x^11 + 272x^10 - 5x^9 + 1366x^8 + 1365x^7 + 1260x^6 + 1443x^5 + 5170x^4 + 18803x^3 + 30766x^2 + 27872x + 13009	\( 5^{8}\cdot 11^{4}\cdot 19^{4}\cdot 29^{4}\cdot 31^{2} \)	16T919	$[2, 2, 4]$ (GRH)
16.0.578879207029700203515625.1	x^16 - 5x^15 + 24x^14 - 60x^13 + 130x^12 - 181x^11 + 317x^10 - 457x^9 + 515x^8 + 7x^7 - 574x^6 - 285x^5 + 1718x^4 - 3238x^3 + 3065x^2 - 4655x + 4519	\( 5^{8}\cdot 11^{4}\cdot 19^{4}\cdot 29^{2}\cdot 31^{4} \)	16T919	$[2, 4]$ (GRH)
16.16.2267617230852121600000000.1	x^16 - 30x^14 + 360x^12 - 2233x^10 + 7653x^8 - 14245x^6 + 13116x^4 - 4902x^2 + 361	\( 2^{16}\cdot 5^{8}\cdot 19^{4}\cdot 29^{4}\cdot 31^{2} \)	16T919	Trivial (GRH)
16.16.2591177358916633600000000.1	x^16 - 21x^14 + 156x^12 - 500x^10 + 735x^8 - 535x^6 + 191x^4 - 29x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 19^{4}\cdot 29^{2}\cdot 31^{4} \)	16T919	Trivial (GRH)
16.8.9973971226107582891015625.1	x^16 - 3x^15 - 3x^14 - 12x^13 + 65x^12 + 152x^11 - 822x^10 + 1053x^9 + 1338x^8 - 6995x^7 + 9186x^6 + 1526x^5 - 28323x^4 + 36788x^3 + 14567x^2 - 42445x + 7031	\( 5^{8}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2}\cdot 101^{4} \)	16T919	$[2]$ (GRH)
16.0.68681261305082905600000000.1	x^16 - 2x^15 + 17x^14 - 54x^13 + 222x^12 - 336x^11 + 990x^10 - 958x^9 - 575x^8 + 15076x^7 - 25976x^6 + 14764x^5 + 64476x^4 - 130456x^3 + 170781x^2 - 134890x + 40229	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 29^{4}\cdot 509^{2} \)	16T919	$[2, 24]$ (GRH)
16.8.68681261305082905600000000.1	x^16 - 6x^15 + 7x^14 + 56x^13 - 334x^12 + 710x^11 - 391x^10 - 924x^9 + 1113x^8 + 5494x^7 - 13121x^6 + 17400x^5 - 40356x^4 + 35986x^3 + 21513x^2 - 27786x - 191	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 29^{4}\cdot 509^{2} \)	16T919	Trivial (GRH)
16.0.68681261305082905600000000.2	x^16 - 2x^15 - 15x^14 + 22x^13 + 174x^12 - 348x^11 - 882x^10 + 2208x^9 + 6324x^8 - 19298x^7 - 15085x^6 + 79098x^5 + 9355x^4 - 215170x^3 + 93272x^2 + 207856x + 227821	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 29^{4}\cdot 509^{2} \)	16T919	$[2, 30]$ (GRH)