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 22 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.59536000000000000.1	x^16 - x^14 - 4x^13 - 3x^12 + 8x^11 + 23x^10 + 10x^9 - 28x^8 - 44x^7 - 23x^6 + 16x^5 + 31x^4 + 22x^3 + 12x^2 + 4x + 1	\( 2^{16}\cdot 5^{12}\cdot 61^{2} \)	$C_2^4.C_2^3$ (as 16T208)	Trivial
16.0.126736000000000000.1	x^16 - 2x^15 - x^14 + 6x^13 - 11x^12 + 2x^11 + 21x^10 - 12x^9 - 12x^8 - 14x^7 + 9x^6 + 26x^5 + 29x^4 + 22x^3 + 11x^2 + 4x + 1	\( 2^{16}\cdot 5^{12}\cdot 89^{2} \)	$C_2^4.C_2^3$ (as 16T208)	Trivial
16.0.3936256000000000000.1	x^16 - 6x^15 + 21x^14 - 58x^13 + 117x^12 - 190x^11 + 278x^10 - 328x^9 + 347x^8 - 298x^7 + 240x^6 - 140x^5 + 80x^4 - 36x^3 + 16x^2 - 4x + 1	\( 2^{24}\cdot 5^{12}\cdot 31^{2} \)	$C_2^4.C_2^3$ (as 16T208)	Trivial
16.0.6885376000000000000.1	x^16 - 2x^15 + 7x^14 - 16x^13 + 33x^12 - 40x^11 + 61x^10 - 48x^9 + 18x^8 + 44x^7 - 61x^6 + 32x^5 + 23x^4 - 42x^3 + 28x^2 - 8x + 1	\( 2^{24}\cdot 5^{12}\cdot 41^{2} \)	$C_2^4.C_2^3$ (as 16T208)	Trivial
16.0.20647936000000000000.1	x^16 - 2x^15 - 5x^14 + 20x^13 - 7x^12 - 28x^11 + 49x^10 - 60x^9 + 84x^8 - 36x^7 - 7x^6 - 4x^5 + 17x^4 + 6x^3 + 8x^2 + 4x + 1	\( 2^{24}\cdot 5^{12}\cdot 71^{2} \)	$C_2^4.C_2^3$ (as 16T208)	Trivial
16.0.32444416000000000000.1	x^16 - 2x^15 + 9x^14 - 24x^13 + 51x^12 - 76x^11 + 95x^10 - 120x^9 + 162x^8 - 200x^7 + 205x^6 - 152x^5 + 101x^4 - 42x^3 + 26x^2 - 4x + 1	\( 2^{24}\cdot 5^{12}\cdot 89^{2} \)	$C_2^4.C_2^3$ (as 16T208)	Trivial
16.0.167487679775634765625.1	x^16 - x^15 + 6x^14 - 10x^13 + 13x^12 - 30x^11 + 9x^10 - 46x^9 + 98x^8 - 159x^7 + 349x^6 - 240x^5 + 243x^4 - 55x^3 + 31x^2 + x + 1	\( 5^{12}\cdot 13^{8}\cdot 29^{2} \)	$C_2^4.C_2^3$ (as 16T208)	Trivial
16.0.237899776000000000000.1	x^16 - 2x^15 + x^14 + 2x^13 + 4x^12 + 12x^11 - 33x^10 + 16x^9 + 71x^8 - 13x^6 - 4x^5 + 74x^4 + 90x^3 + 55x^2 + 6x + 1	\( 2^{24}\cdot 5^{12}\cdot 241^{2} \)	$C_2^4.C_2^3$ (as 16T208)	Trivial
16.4.1007681536000000000000.1	x^16 - 8x^15 + 20x^14 - 68x^12 + 44x^11 + 110x^10 - 331x^8 + 92x^7 + 322x^6 + 48x^5 - 242x^4 - 168x^3 + 28x^2 + 152x - 4	\( 2^{32}\cdot 5^{12}\cdot 31^{2} \)	$C_2^4.C_2^3$ (as 16T208)	Trivial (GRH)
16.12.1759218604441600000000.1	x^16 - 12x^14 + 58x^12 - 184x^10 + 431x^8 - 480x^6 + 214x^4 - 28x^2 + 1	\( 2^{52}\cdot 5^{8} \)	$C_2^4.C_2^3$ (as 16T208)	Trivial (GRH)
16.4.1759218604441600000000.1	x^16 - 4x^14 - 6x^12 - 24x^10 - 45x^8 - 264x^6 + 114x^4 - 44x^2 + 1	\( 2^{52}\cdot 5^{8} \)	$C_2^4.C_2^3$ (as 16T208)	Trivial (GRH)
16.8.1762656256000000000000.1	x^16 - 10x^14 - 4x^13 + 37x^12 - 44x^10 + 24x^9 - 56x^8 + 96x^7 + 16x^6 - 48x^5 - 11x^4 - 32x^3 + 14x^2 + 12x + 1	\( 2^{32}\cdot 5^{12}\cdot 41^{2} \)	$C_2^4.C_2^3$ (as 16T208)	Trivial (GRH)
16.8.1762656256000000000000.2	x^16 - 4x^15 - 6x^14 + 36x^13 + 9x^12 - 116x^11 - 42x^10 + 188x^9 + 146x^8 - 120x^7 - 192x^6 + 28x^5 + 114x^4 - 80x^3 - 50x^2 + 8x + 1	\( 2^{32}\cdot 5^{12}\cdot 41^{2} \)	$C_2^4.C_2^3$ (as 16T208)	Trivial (GRH)
16.12.1891079497931380752384.1	x^16 - 16x^14 + 100x^12 - 8x^11 - 304x^10 + 72x^9 + 444x^8 - 160x^7 - 352x^6 + 160x^5 + 188x^4 - 56x^3 - 64x^2 - 8x + 1	\( 2^{58}\cdot 3^{8} \)	$C_2^4.C_2^3$ (as 16T208)	Trivial (GRH)
16.0.2031559835185791015625.1	x^16 - 6x^15 + 12x^14 - 8x^13 + 7x^12 - 16x^11 + 2x^10 - 209x^9 + 1030x^8 - 1816x^7 + 1449x^6 - 458x^5 + 232x^4 - 687x^3 + 792x^2 - 405x + 81	\( 5^{12}\cdot 13^{8}\cdot 101^{2} \)	$C_2^4.C_2^3$ (as 16T208)	Trivial
16.0.2372079616000000000000.1	x^16 - 2x^15 + 13x^14 - 48x^13 + 113x^12 - 112x^11 + 119x^10 - 84x^9 + 268x^8 - 452x^7 + 551x^6 - 400x^5 + 233x^4 - 74x^3 + 32x^2 - 8x + 1	\( 2^{24}\cdot 5^{12}\cdot 761^{2} \)	$C_2^4.C_2^3$ (as 16T208)	$[4]$
16.8.8305770496000000000000.1	x^16 - 4x^15 - 10x^14 + 60x^13 + 3x^12 - 276x^11 + 86x^10 + 500x^9 + 399x^8 - 772x^7 - 1618x^6 + 528x^5 + 1747x^4 + 452x^3 - 348x^2 - 148x + 1	\( 2^{32}\cdot 5^{12}\cdot 89^{2} \)	$C_2^4.C_2^3$ (as 16T208)	Trivial (GRH)
16.0.132892327936000000000000.1	x^16 + 10x^14 - 16x^13 + 46x^12 - 60x^11 + 426x^10 - 312x^9 + 531x^8 - 416x^7 + 2578x^6 - 3928x^5 + 4412x^4 - 2724x^3 + 1296x^2 - 324x + 81	\( 2^{36}\cdot 5^{12}\cdot 89^{2} \)	$C_2^4.C_2^3$ (as 16T208)	$[2, 4]$ (GRH)
16.16.132892327936000000000000.1	x^16 - 4x^15 - 18x^14 + 104x^13 - 34x^12 - 520x^11 + 738x^10 + 500x^9 - 1538x^8 + 500x^7 + 738x^6 - 520x^5 - 34x^4 + 104x^3 - 18x^2 - 4x + 1	\( 2^{36}\cdot 5^{12}\cdot 89^{2} \)	$C_2^4.C_2^3$ (as 16T208)	Trivial (GRH)
16.16.157461916319942625460224.1	x^16 - 24x^14 + 212x^12 - 872x^10 + 1824x^8 - 1952x^6 + 984x^4 - 176x^2 + 4	\( 2^{52}\cdot 3^{8}\cdot 73^{2} \)	$C_2^4.C_2^3$ (as 16T208)	Trivial (GRH)
16.8.614839068522262365732864.1	x^16 - 16x^14 + 36x^12 - 8x^10 + 71x^8 - 56x^6 - 156x^4 - 64x^2 + 1	\( 2^{48}\cdot 3^{8}\cdot 577^{2} \)	$C_2^4.C_2^3$ (as 16T208)	Trivial (GRH)
16.0.880414396416000000000000.1	x^16 - 4x^15 + 28x^14 - 88x^13 + 373x^12 - 1030x^11 + 3164x^10 - 7514x^9 + 17493x^8 - 35362x^7 + 64076x^6 - 104914x^5 + 139463x^4 - 152794x^3 + 120792x^2 - 43324x + 10141	\( 2^{24}\cdot 3^{8}\cdot 5^{12}\cdot 181^{2} \)	$C_2^4.C_2^3$ (as 16T208)	$[2, 24]$ (GRH)