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 34 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.4.1133799040000000000.3	x^16 - 2x^15 - 4x^14 + 18x^13 - 16x^12 - 28x^11 + 72x^10 - 36x^9 - 67x^8 + 122x^7 - 42x^6 - 76x^5 + 69x^4 - 6x^3 - x^2 - 4x + 1	\( 2^{16}\cdot 5^{10}\cdot 11^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T542)	Trivial
16.0.2528149687744140625.1	x^16 - 6x^15 + 18x^14 - 34x^13 + 45x^12 - 35x^11 + 9x^10 + 12x^9 + x^8 - 33x^7 + 99x^6 - 92x^5 + 108x^4 - 46x^3 + 24x^2 + 9x + 1	\( 5^{12}\cdot 11^{4}\cdot 29^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T542)	$[2]$
16.4.2528149687744140625.1	x^16 - 6x^15 + 16x^14 - 26x^13 + 37x^12 - 67x^11 + 108x^10 - 129x^9 + 151x^8 - 178x^7 + 161x^6 - 95x^5 + x^4 + 36x^3 - 10x^2 + 1	\( 5^{12}\cdot 11^{4}\cdot 29^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T542)	Trivial
16.0.3596249992978515625.1	x^16 - 3x^15 + 3x^14 + 5x^13 - 15x^12 + 14x^11 + 11x^10 - 38x^9 + 50x^8 - 47x^7 + 46x^6 - 26x^5 + 23x^4 - 17x^3 + 10x^2 + x + 1	\( 5^{10}\cdot 19^{4}\cdot 41^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T542)	Trivial
16.4.5856400000000000000.1	x^16 - 4x^15 + x^14 + 24x^13 - 57x^12 + 36x^11 + 74x^10 - 198x^9 + 163x^8 + 56x^7 - 314x^6 + 402x^5 - 302x^4 + 142x^3 - 36x^2 + 2x + 1	\( 2^{16}\cdot 5^{14}\cdot 11^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T542)	Trivial (GRH)
16.4.5856400000000000000.2	x^16 - x^14 + 2x^12 - 8x^10 + 10x^8 + 43x^6 + 2x^4 - 34x^2 + 1	\( 2^{16}\cdot 5^{14}\cdot 11^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T542)	Trivial (GRH)
16.0.8455691280628842496.1	x^16 - 7x^15 + 20x^14 - 25x^13 + 4x^12 + 7x^11 + 67x^10 - 226x^9 + 376x^8 - 472x^7 + 524x^6 - 476x^5 + 336x^4 - 196x^3 + 108x^2 - 56x + 16	\( 2^{22}\cdot 17^{10} \)	$C_2^4.C_2^3.C_2$ (as 16T542)	Trivial
16.0.21351792640000000000.2	x^16 - 2x^15 - 2x^14 + 2x^13 + 28x^12 - 58x^11 + 58x^10 - 38x^9 + 38x^8 - 38x^7 + 58x^6 - 58x^5 + 28x^4 + 2x^3 - 2x^2 - 2x + 1	\( 2^{24}\cdot 5^{10}\cdot 19^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T542)	Trivial
16.8.290252554240000000000.1	x^16 - 4x^15 + 18x^13 - 36x^12 + 84x^10 - 86x^9 - 50x^8 + 142x^7 - 64x^6 - 50x^5 + 69x^4 - 6x^3 - 20x^2 + 2x + 1	\( 2^{24}\cdot 5^{10}\cdot 11^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T542)	Trivial (GRH)
16.0.290252554240000000000.3	x^16 + 12x^14 + 46x^12 + 112x^10 + 335x^8 + 608x^6 + 126x^4 - 12x^2 + 1	\( 2^{24}\cdot 5^{10}\cdot 11^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T542)	$[2]$ (GRH)
16.0.305906112217041015625.1	x^16 - 3x^15 + 8x^14 + x^13 - 13x^12 + 50x^11 - 18x^10 + 52x^9 + 105x^8 - 138x^7 + 572x^6 - 400x^5 + 592x^4 - 64x^3 + 448x^2 - 128x + 256	\( 5^{12}\cdot 11^{6}\cdot 29^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T542)	$[2]$ (GRH)
16.8.305906112217041015625.1	x^16 - x^15 - 7x^14 + 11x^13 - 10x^12 - 15x^11 + 74x^10 - 88x^9 + 106x^8 - 38x^7 + 69x^6 + 78x^5 - 232x^4 - 61x^3 - 186x^2 - 151x + 1	\( 5^{12}\cdot 11^{6}\cdot 29^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T542)	Trivial (GRH)
16.0.453519616000000000000.1	x^16 + 19x^12 + 40x^10 + 56x^8 + 40x^6 + 19x^4 + 1	\( 2^{20}\cdot 5^{12}\cdot 11^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T542)	$[2]$ (GRH)
16.8.453519616000000000000.1	x^16 - 17x^14 + 105x^12 - 317x^10 + 504x^8 - 423x^6 + 175x^4 - 28x^2 + 1	\( 2^{20}\cdot 5^{12}\cdot 11^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T542)	Trivial (GRH)
16.8.487941178183837890625.1	x^16 - 4x^15 + 6x^14 - 11x^13 + 16x^12 - 8x^11 - 37x^10 + 87x^9 + 132x^8 - 51x^7 - 493x^6 - 59x^5 + 436x^4 + 128x^3 - 36x^2 - 7x + 1	\( 5^{12}\cdot 29^{4}\cdot 41^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T542)	Trivial (GRH)
16.0.487941178183837890625.5	x^16 + 4x^14 - 15x^13 + 51x^12 - 50x^11 + 124x^10 - 230x^9 + 206x^8 - 360x^7 + 380x^6 - 190x^5 + 195x^4 - 50x^3 - 50x^2 - 25x + 25	\( 5^{12}\cdot 29^{4}\cdot 41^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T542)	$[2]$
16.8.529843992560511483904.1	x^16 + 4x^14 - 26x^12 - 96x^10 + 199x^8 + 24x^6 + 26x^4 - 12x^2 + 1	\( 2^{52}\cdot 7^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T542)	Trivial (GRH)
16.0.529843992560511483904.5	x^16 - 4x^14 + 22x^12 - 56x^10 + 139x^8 - 264x^6 + 542x^4 - 436x^2 + 289	\( 2^{52}\cdot 7^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T542)	Trivial
16.8.718749457809384765625.1	x^16 - 6x^15 + 7x^14 + 27x^13 - 95x^12 + 83x^11 + 143x^10 - 409x^9 + 287x^8 + 177x^7 - 321x^6 + 31x^5 + 95x^4 - 21x^3 - x^2 + 4x - 1	\( 5^{10}\cdot 29^{4}\cdot 101^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T542)	Trivial (GRH)
16.0.4996517664602500000000.1	x^16 - 2x^15 + 4x^14 - 6x^13 + 6x^12 - 34x^11 + 48x^10 + 38x^9 - 52x^8 - 192x^7 + 78x^6 + 336x^5 + 385x^4 + 550x^3 + 622x^2 + 360x + 79	\( 2^{8}\cdot 5^{10}\cdot 29^{4}\cdot 41^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T542)	$[2]$
16.0.4996517664602500000000.2	x^16 - 4x^15 + 5x^14 - 12x^13 + 60x^12 - 124x^11 + 129x^10 - 199x^9 + 494x^8 - 645x^7 + 195x^6 + 451x^5 - 467x^4 + 425x^3 - 660x^2 + 123x + 779	\( 2^{8}\cdot 5^{10}\cdot 29^{4}\cdot 41^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T542)	$[2]$
16.0.17968736445234619140625.5	x^16 - 4x^15 + 9x^14 - 14x^13 + 19x^12 - 6x^11 - 67x^10 - 7x^9 - 29x^8 + 55x^7 + 738x^6 - 322x^5 + 624x^4 - 775x^3 - 20x^2 + 753x + 261	\( 5^{12}\cdot 29^{4}\cdot 101^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T542)	$[8]$
16.0.2316751136283220221362176.1	x^16 + 22x^14 + 183x^12 + 730x^10 + 1484x^8 + 1494x^6 + 631x^4 + 58x^2 + 1	\( 2^{46}\cdot 7^{6}\cdot 23^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T542)	$[2, 2, 4]$ (GRH)
16.0.2363875125336827353515625.1	x^16 - 2x^15 + 15x^14 - 5x^13 + 2x^12 + 176x^11 - 202x^10 + 210x^9 + 849x^8 - 987x^7 + 485x^6 + 2039x^5 - 1991x^4 - 3700x^3 + 2434x^2 + 6172x + 4729	\( 5^{10}\cdot 41^{4}\cdot 541^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T542)	$[6]$ (GRH)
16.0.11518796833836013415010304.3	x^16 - 4x^15 + 12x^14 - 57x^13 + 213x^12 - 522x^11 + 1409x^10 - 3725x^9 + 7312x^8 - 11699x^7 + 19307x^6 - 26434x^5 + 17738x^4 + 2345x^3 - 5696x^2 - 3872x + 3928	\( 2^{12}\cdot 13^{6}\cdot 17^{12} \)	$C_2^4.C_2^3.C_2$ (as 16T542)	$[8]$ (GRH)
16.16.14973015908212458290937856.1	x^16 - 32x^14 + 360x^12 - 1920x^10 + 5281x^8 - 7488x^6 + 5064x^4 - 1280x^2 + 16	\( 2^{40}\cdot 17^{4}\cdot 113^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T542)	Trivial (GRH)
16.0.15686332680774922119140625.1	x^16 - 4x^15 + 62x^14 - 162x^13 + 1357x^12 - 2204x^11 + 13752x^10 - 12451x^9 + 72905x^8 - 32084x^7 + 221779x^6 - 14352x^5 + 393392x^4 + 80477x^3 + 366837x^2 + 106495x + 130321	\( 3^{8}\cdot 5^{12}\cdot 29^{4}\cdot 61^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T542)	$[2, 4, 16]$ (GRH)
16.0.31977713053456000000000000.1	x^16 + 23x^14 + 185x^12 + 663x^10 + 1094x^8 + 827x^6 + 265x^4 + 32x^2 + 1	\( 2^{16}\cdot 5^{12}\cdot 29^{4}\cdot 41^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T542)	$[2, 4, 8]$ (GRH)
16.16.31977713053456000000000000.1	x^16 - 23x^14 + 185x^12 - 663x^10 + 1094x^8 - 827x^6 + 265x^4 - 32x^2 + 1	\( 2^{16}\cdot 5^{12}\cdot 29^{4}\cdot 41^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T542)	Trivial (GRH)
16.0.42415313391616000000000000.1	x^16 - 22x^14 + 157x^12 - 310x^10 - 304x^8 - 570x^6 + 6233x^4 - 2866x^2 + 39601	\( 2^{24}\cdot 5^{12}\cdot 11^{4}\cdot 29^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T542)	$[2, 2, 4]$ (GRH)
16.8.42415313391616000000000000.1	x^16 - 4x^15 - 6x^14 + 126x^13 - 374x^12 - 262x^11 + 2066x^10 - 512x^9 - 1818x^8 - 5738x^7 + 5006x^6 + 12712x^5 - 7819x^4 - 8906x^3 + 3584x^2 + 2244x - 409	\( 2^{24}\cdot 5^{12}\cdot 11^{4}\cdot 29^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T542)	$[2, 2]$ (GRH)
16.0.42415313391616000000000000.2	x^16 + 22x^14 + 157x^12 + 310x^10 - 304x^8 + 570x^6 + 6233x^4 + 2866x^2 + 39601	\( 2^{24}\cdot 5^{12}\cdot 11^{4}\cdot 29^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T542)	$[2, 2, 8]$ (GRH)
16.8.42415313391616000000000000.2	x^16 - 4x^15 - 14x^14 - 26x^13 + 178x^12 + 626x^11 - 1106x^10 - 3108x^9 + 4018x^8 + 6806x^7 - 9894x^6 - 7148x^5 + 12953x^4 + 2582x^3 - 7136x^2 - 88x + 1271	\( 2^{24}\cdot 5^{12}\cdot 11^{4}\cdot 29^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T542)	$[2]$ (GRH)
16.0.42415313391616000000000000.3	x^16 - 8x^15 + 34x^14 - 58x^13 + 41x^12 + 94x^11 + 352x^10 - 364x^9 + 2127x^8 + 1968x^7 + 11658x^6 + 26428x^5 + 341x^4 + 14486x^3 + 203666x^2 + 156354x + 33121	\( 2^{24}\cdot 5^{12}\cdot 11^{4}\cdot 29^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T542)	$[2, 2, 4]$ (GRH)