Global number field search results

Further refine search

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 74)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.332115825597087744.1	x^16 - 2x^15 + 10x^14 - 18x^13 + 45x^12 - 68x^11 + 114x^10 - 138x^9 + 169x^8 - 158x^7 + 142x^6 - 100x^5 + 66x^4 - 36x^3 + 20x^2 - 8x + 4	\( 2^{24}\cdot 3^{12}\cdot 193^{2} \)	16T1445	Trivial
16.0.332115825597087744.2	x^16 - 4x^15 + 16x^14 - 42x^13 + 93x^12 - 172x^11 + 264x^10 - 354x^9 + 400x^8 - 388x^7 + 322x^6 - 218x^5 + 126x^4 - 54x^3 + 20x^2 - 4x + 1	\( 2^{24}\cdot 3^{12}\cdot 193^{2} \)	16T1445	Trivial
16.4.1410963865600000000.1	x^16 - 8x^14 + 18x^12 + 4x^10 - 49x^8 + 20x^6 + 14x^4 + 28x^2 + 1	\( 2^{32}\cdot 5^{8}\cdot 29^{2} \)	16T1445	Trivial
16.4.1410963865600000000.2	x^16 - 8x^14 + 24x^12 - 24x^10 - 34x^8 + 24x^6 + 24x^4 + 8x^2 + 1	\( 2^{32}\cdot 5^{8}\cdot 29^{2} \)	16T1445	Trivial
16.4.2760584326875390625.1	x^16 - x^15 - 2x^14 + 8x^13 + 4x^12 - 17x^11 - 16x^10 - 6x^9 - x^8 + 17x^7 + 19x^6 - 3x^5 - 16x^4 - 16x^3 - 13x^2 - 6x - 1	\( 5^{8}\cdot 29^{6}\cdot 109^{2} \)	16T1445	Trivial
16.4.2760584326875390625.2	x^16 + 4x^14 - 4x^11 - 14x^10 + x^9 - 10x^8 - 4x^7 + 32x^6 + 39x^5 + 15x^4 - 28x^3 - 35x^2 - 9x + 1	\( 5^{8}\cdot 29^{6}\cdot 109^{2} \)	16T1445	Trivial
16.0.4489289603531640625.1	x^16 - 5x^15 + 9x^14 - 20x^12 + 12x^11 + 42x^10 - 70x^9 + 11x^8 + 53x^7 - 15x^6 - 67x^5 + 77x^4 - 28x^3 - x^2 + x + 1	\( 5^{8}\cdot 29^{6}\cdot 139^{2} \)	16T1445	Trivial
16.4.4489289603531640625.2	x^16 - 5x^15 + 11x^14 - 15x^13 + 15x^12 - 19x^11 + 33x^10 - 15x^9 - 29x^8 + 14x^7 + 20x^6 + x^5 - 28x^4 + 11x^3 + 6x^2 - 3x + 1	\( 5^{8}\cdot 29^{6}\cdot 139^{2} \)	16T1445	Trivial
16.0.5158465839656640625.1	x^16 - 7x^15 + 28x^14 - 75x^13 + 149x^12 - 224x^11 + 267x^10 - 253x^9 + 208x^8 - 159x^7 + 129x^6 - 98x^5 + 66x^4 - 31x^3 + 11x^2 - 2x + 1	\( 5^{8}\cdot 29^{6}\cdot 149^{2} \)	16T1445	Trivial
16.0.5158465839656640625.2	x^16 - 3x^15 + 9x^14 - 17x^13 + 33x^12 - 50x^11 + 75x^10 - 95x^9 + 113x^8 - 114x^7 + 108x^6 - 95x^5 + 77x^4 - 49x^3 + 23x^2 - 6x + 1	\( 5^{8}\cdot 29^{6}\cdot 149^{2} \)	16T1445	Trivial
16.4.7444817979750390625.1	x^16 - 4x^15 + 3x^14 + 6x^13 - 13x^12 + 11x^11 + 11x^10 - 28x^9 - 20x^8 + 78x^7 - 78x^6 + 62x^5 - 52x^4 + 30x^3 - 10x^2 + 5x - 1	\( 5^{8}\cdot 29^{6}\cdot 179^{2} \)	16T1445	Trivial
16.8.7444817979750390625.1	x^16 - 5x^15 + 4x^14 + 21x^13 - 48x^12 - 3x^11 + 118x^10 - 110x^9 - 81x^8 + 191x^7 - 51x^6 - 105x^5 + 79x^4 + 9x^3 - 23x^2 + x + 1	\( 5^{8}\cdot 29^{6}\cdot 179^{2} \)	16T1445	Trivial
16.0.15227477017600000000.1	x^16 - 2x^15 - 2x^14 + 4x^13 + 13x^12 - 14x^11 - 29x^10 + 4x^9 + 76x^8 - 16x^7 - 71x^6 + 8x^5 + 84x^4 - 54x^3 + 2x^2 + 6x + 1	\( 2^{16}\cdot 5^{8}\cdot 29^{6} \)	16T1445	Trivial
16.8.15227477017600000000.1	x^16 - 3x^14 - 6x^13 - 21x^12 - 22x^11 + 22x^10 + 120x^9 + 267x^8 + 366x^7 + 357x^6 + 276x^5 + 177x^4 + 96x^3 + 40x^2 + 10x + 1	\( 2^{16}\cdot 5^{8}\cdot 29^{6} \)	16T1445	Trivial
16.4.15227477017600000000.2	x^16 - 8x^15 + 28x^14 - 52x^13 + 44x^12 + 14x^11 - 77x^10 + 92x^9 - 69x^8 + 40x^7 - x^6 - 22x^5 + 8x^4 - 2x^3 + 4x + 1	\( 2^{16}\cdot 5^{8}\cdot 29^{6} \)	16T1445	Trivial
16.4.15227477017600000000.3	x^16 - 2x^15 - 5x^14 + 8x^13 + 17x^12 - 34x^11 - 16x^10 + 74x^9 + 6x^8 - 114x^7 + 109x^6 - 56x^5 + 45x^4 - 16x^3 + 15x^2 - 1	\( 2^{16}\cdot 5^{8}\cdot 29^{6} \)	16T1445	Trivial
16.0.92866056756088140625.1	x^16 - x^15 + 5x^14 - 10x^13 + 10x^12 - 25x^11 + 26x^10 - 13x^9 + 43x^8 - 7x^7 + 23x^6 + 11x^5 + 8x^4 + 24x^3 + 2x^2 + 5x + 5	\( 5^{6}\cdot 29^{8}\cdot 109^{2} \)	16T1445	Trivial
16.4.92866056756088140625.1	x^16 - x^15 + 6x^14 - 20x^13 + 24x^12 - 67x^11 + 132x^10 - 135x^9 + 204x^8 - 285x^7 + 186x^6 - 36x^5 - 7x^4 - 12x^3 + 17x^2 - 7x + 1	\( 5^{6}\cdot 29^{8}\cdot 109^{2} \)	16T1445	Trivial
16.0.205744042618125390625.1	x^16 - 5x^15 + 20x^14 - 53x^13 + 122x^12 - 230x^11 + 402x^10 - 602x^9 + 784x^8 - 809x^7 + 677x^6 - 431x^5 + 232x^4 - 87x^3 + 23x^2 + 4x + 1	\( 5^{8}\cdot 29^{6}\cdot 941^{2} \)	16T1445	Trivial
16.8.205744042618125390625.1	x^16 - 3x^15 - 4x^14 + 23x^13 - 26x^12 - 9x^11 + 65x^10 - 68x^9 - 20x^8 + 63x^7 + 3x^6 - 35x^5 - 15x^4 + 43x^3 - 17x^2 - x + 1	\( 5^{8}\cdot 29^{6}\cdot 941^{2} \)	16T1445	Trivial
16.8.3224041149785400390625.1	x^16 - 7x^15 + 16x^14 - 17x^13 + 32x^12 - 40x^11 - 85x^10 + 125x^9 + 58x^8 + 244x^7 - 404x^6 - 362x^5 + 324x^4 + 253x^3 - 82x^2 - 56x + 11	\( 5^{12}\cdot 29^{6}\cdot 149^{2} \)	16T1445	Trivial
16.8.3224041149785400390625.2	x^16 - x^15 - 2x^14 + 6x^13 - 33x^12 + 51x^11 - 2x^10 - 76x^9 + 244x^8 - 390x^7 + 174x^6 + 282x^5 - 477x^4 + 375x^3 - 155x^2 - 37x + 11	\( 5^{12}\cdot 29^{6}\cdot 149^{2} \)	16T1445	Trivial
16.0.3898234116505600000000.1	x^16 - 4x^15 + 18x^14 - 44x^13 + 124x^12 - 254x^11 + 562x^10 - 934x^9 + 1668x^8 - 2356x^7 + 3284x^6 - 3966x^5 + 4181x^4 - 3904x^3 + 2846x^2 - 1282x + 271	\( 2^{24}\cdot 5^{8}\cdot 29^{6} \)	16T1445	$[2]$
16.12.3898234116505600000000.1	x^16 - 4x^15 - 10x^14 + 58x^13 - 8x^12 - 274x^11 + 362x^10 + 332x^9 - 1235x^8 + 802x^7 + 1138x^6 - 2068x^5 + 548x^4 + 978x^3 - 832x^2 + 230x - 19	\( 2^{24}\cdot 5^{8}\cdot 29^{6} \)	16T1445	Trivial (GRH)
16.4.3898234116505600000000.1	x^16 - 6x^15 + 16x^14 - 30x^13 + 34x^12 - 54x^11 + 124x^10 - 6x^9 - 134x^8 + 52x^7 - 28x^6 + 56x^5 + 227x^4 + 182x^3 + 80x^2 + 16x - 1	\( 2^{24}\cdot 5^{8}\cdot 29^{6} \)	16T1445	$[2]$
16.8.3898234116505600000000.1	x^16 - 6x^15 + 14x^14 - 12x^13 - 8x^12 + 50x^11 - 262x^10 + 940x^9 - 1852x^8 + 1706x^7 + 300x^6 - 2258x^5 + 1777x^4 - 32x^3 - 584x^2 + 258x - 31	\( 2^{24}\cdot 5^{8}\cdot 29^{6} \)	16T1445	Trivial
16.0.3898234116505600000000.2	x^16 - 2x^15 + 8x^14 - 20x^13 + 30x^12 - 50x^11 + 42x^10 + 38x^9 - 134x^8 + 302x^7 - 446x^6 + 310x^5 + 71x^4 - 454x^3 + 798x^2 - 384x + 479	\( 2^{24}\cdot 5^{8}\cdot 29^{6} \)	16T1445	$[2]$
16.12.3898234116505600000000.2	x^16 - 6x^15 + 48x^13 - 53x^12 - 56x^11 - 12x^10 + 176x^9 + 121x^8 - 312x^7 - 34x^6 + 14x^5 + 199x^4 + 12x^3 - 166x^2 + 80x - 11	\( 2^{24}\cdot 5^{8}\cdot 29^{6} \)	16T1445	Trivial (GRH)
16.4.3898234116505600000000.2	x^16 - 2x^15 - 4x^14 + 20x^13 - 23x^12 - 46x^11 + 120x^10 + 106x^9 - 314x^8 - 316x^7 + 560x^6 + 30x^5 + 12x^4 - 28x^3 + 2x^2 + 2x + 1	\( 2^{24}\cdot 5^{8}\cdot 29^{6} \)	16T1445	$[2]$
16.8.3898234116505600000000.2	x^16 - 14x^14 - 2x^13 + 65x^12 - 34x^11 - 222x^10 + 206x^9 + 586x^8 - 550x^7 - 662x^6 + 910x^5 - 244x^4 - 96x^3 + 68x^2 - 14x + 1	\( 2^{24}\cdot 5^{8}\cdot 29^{6} \)	16T1445	Trivial (GRH)
16.0.3898234116505600000000.3	x^16 - 6x^15 + 20x^14 - 60x^13 + 162x^12 - 372x^11 + 728x^10 - 1280x^9 + 2038x^8 - 2838x^7 + 3458x^6 - 3424x^5 + 2663x^4 - 1410x^3 + 702x^2 - 270x + 79	\( 2^{24}\cdot 5^{8}\cdot 29^{6} \)	16T1445	$[2]$
16.4.3898234116505600000000.3	x^16 - 6x^15 + 6x^14 + 40x^13 - 122x^12 + 44x^11 + 328x^10 - 544x^9 - 12x^8 + 760x^7 - 536x^6 - 32x^5 - 136x^4 + 96x^3 + 544x^2 - 608x + 176	\( 2^{24}\cdot 5^{8}\cdot 29^{6} \)	16T1445	$[2]$
16.0.3898234116505600000000.4	x^16 - 6x^15 + 14x^14 - 16x^13 + 27x^12 - 10x^11 - 120x^10 + 362x^9 - 439x^8 + 254x^7 + 270x^6 - 832x^5 + 1187x^4 - 1182x^3 + 1048x^2 - 540x + 121	\( 2^{24}\cdot 5^{8}\cdot 29^{6} \)	16T1445	$[2]$
16.4.3898234116505600000000.4	x^16 - 6x^14 - 2x^13 + 15x^12 + 38x^11 - 100x^10 - 198x^9 - 205x^8 + 262x^7 + 96x^6 - 50x^5 - 493x^4 - 12x^3 - 272x^2 - 232x - 41	\( 2^{24}\cdot 5^{8}\cdot 29^{6} \)	16T1445	Trivial
16.0.3898234116505600000000.5	x^16 - 4x^15 + 14x^14 - 38x^13 + 108x^12 - 262x^11 + 450x^10 - 578x^9 + 632x^8 - 702x^7 + 1020x^6 - 1080x^5 + 1093x^4 - 740x^3 + 428x^2 - 182x + 49	\( 2^{24}\cdot 5^{8}\cdot 29^{6} \)	16T1445	$[2]$
16.4.3898234116505600000000.5	x^16 - 4x^15 - 2x^14 + 36x^13 - 94x^12 + 192x^11 - 362x^10 + 480x^9 - 444x^8 + 404x^7 - 262x^6 - 84x^5 + 118x^4 - 112x^3 + 50x^2 + 48x + 19	\( 2^{24}\cdot 5^{8}\cdot 29^{6} \)	16T1445	Trivial
16.0.3898234116505600000000.6	x^16 - 2x^15 + 6x^14 - 18x^13 + 38x^12 - 70x^11 + 144x^10 - 276x^9 + 454x^8 - 668x^7 + 792x^6 - 484x^5 - 209x^4 + 588x^3 - 280x^2 - 114x + 109	\( 2^{24}\cdot 5^{8}\cdot 29^{6} \)	16T1445	$[2]$
16.4.3898234116505600000000.6	x^16 - 2x^15 - 4x^14 - 4x^13 + 31x^12 + 6x^11 - 28x^10 - 86x^9 + 194x^8 - 132x^7 - 186x^6 + 402x^5 - 272x^4 - 36x^3 + 188x^2 - 114x + 31	\( 2^{24}\cdot 5^{8}\cdot 29^{6} \)	16T1445	Trivial
16.4.4338269771151234765625.1	x^16 - 7x^14 - 12x^13 + 24x^12 + 50x^11 - 40x^10 - 109x^9 + 140x^8 + 213x^7 - 207x^6 - 138x^5 + 425x^4 - 197x^3 + 45x^2 + 34x - 11	\( 5^{8}\cdot 29^{8}\cdot 149^{2} \)	16T1445	Trivial
16.4.6921229593673738140625.1	x^16 - x^15 + 4x^14 - 4x^13 - 15x^12 + 11x^11 - 54x^10 + 51x^9 + 62x^8 + 111x^7 + 82x^6 + 57x^5 - 95x^4 - 92x^3 - 28x^2 + 1	\( 5^{6}\cdot 29^{8}\cdot 941^{2} \)	16T1445	Trivial
16.4.6921229593673738140625.2	x^16 - 2x^15 + 12x^14 - 20x^13 + 8x^12 - 36x^11 - 19x^10 - 73x^9 - 75x^8 - 87x^7 - 12x^6 + 71x^5 + 123x^4 + 97x^3 + 48x^2 + 12x + 1	\( 5^{6}\cdot 29^{8}\cdot 941^{2} \)	16T1445	Trivial
16.0.58625838959875846045696.1	x^16 - 4x^15 + 2x^14 + 4x^13 + 5x^12 - 8x^11 - 8x^10 - 168x^9 + 952x^8 - 1328x^7 - 120x^6 + 1632x^5 - 1084x^4 - 160x^3 + 448x^2 - 192x + 32	\( 2^{40}\cdot 17^{6}\cdot 47^{2} \)	16T1445	$[2]$
16.0.58625838959875846045696.2	x^16 - 4x^15 + 6x^14 - 8x^13 + 23x^12 - 44x^11 + 56x^10 - 3x^8 - 92x^7 + 158x^6 + 296x^5 - 99x^4 - 180x^3 + 68x^2 + 32x + 14	\( 2^{40}\cdot 17^{6}\cdot 47^{2} \)	16T1445	$[2]$
16.4.114523100106217078515625.1	x^16 - x^15 + 17x^14 + x^13 + 79x^12 + 140x^11 + 51x^10 + 596x^9 + 34x^8 - 191x^7 + 740x^6 - 1376x^5 - 1713x^4 - 305x^3 + 260x^2 + 107x + 11	\( 5^{8}\cdot 29^{6}\cdot 149^{4} \)	16T1445	Trivial
16.0.128590026636328369140625.1	x^16 - 8x^15 + 29x^14 - 57x^13 + 59x^12 + 2x^11 - 79x^10 + 76x^9 - 36x^8 + 34x^7 + 41x^6 + 20x^5 + 237x^4 + 106x^3 - 135x^2 - 50x + 31	\( 5^{12}\cdot 29^{6}\cdot 941^{2} \)	16T1445	$[2]$
16.8.128590026636328369140625.1	x^16 - x^15 - 7x^14 + 14x^13 - 18x^12 - 80x^11 + 82x^10 - 33x^9 - 180x^8 + 172x^7 + 387x^6 + 1170x^5 + 1482x^4 + 274x^3 - 572x^2 - 481x - 139	\( 5^{12}\cdot 29^{6}\cdot 941^{2} \)	16T1445	Trivial (GRH)
16.0.1103341620319083198765625.1	x^16 - x^15 - 13x^14 + 17x^13 + 83x^12 - 80x^11 - 351x^10 + 156x^9 + 1248x^8 + 76x^7 - 2803x^6 - 459x^5 + 3870x^4 + 642x^3 - 2712x^2 - 302x + 749	\( 5^{6}\cdot 29^{8}\cdot 109^{4} \)	16T1445	$[2]$
16.4.1103341620319083198765625.1	x^16 - 3x^15 + 5x^14 - 7x^13 + 4x^12 + 20x^11 + 12x^10 - 223x^9 + 349x^8 - 99x^7 - 123x^6 + 390x^5 - 2087x^4 + 4813x^3 - 5440x^2 + 3116x - 721	\( 5^{6}\cdot 29^{8}\cdot 109^{4} \)	16T1445	Trivial
16.0.13483641577021465600000000.1	x^16 + 37x^14 + 427x^12 + 2397x^10 + 7503x^8 + 13536x^6 + 13518x^4 + 6409x^2 + 841	\( 2^{16}\cdot 5^{8}\cdot 29^{6}\cdot 941^{2} \)	16T1445	$[152]$ (GRH)
16.12.13483641577021465600000000.1	x^16 - 3x^14 - 91x^12 + 342x^10 + 1793x^8 - 9161x^6 + 12621x^4 - 6264x^2 + 841	\( 2^{16}\cdot 5^{8}\cdot 29^{6}\cdot 941^{2} \)	16T1445	Trivial (GRH)