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
16.4.4489289603531640625.1	x^16 - 4x^15 + 19x^13 - 20x^12 - 12x^11 + 45x^9 + 2x^8 - 72x^7 + 17x^6 + 65x^5 - 31x^4 - 34x^3 + 15x^2 + 9x + 1	\( 5^{8}\cdot 29^{6}\cdot 139^{2} \)	16T1429	Trivial
16.0.8292394719615385600.1	x^16 + 4x^14 - 4x^13 + 6x^12 - 8x^11 + 12x^10 - 4x^9 - 4x^8 - 20x^7 - 28x^6 + 4x^5 + 16x^4 + 32x^3 + 16x^2 + 2	\( 2^{36}\cdot 5^{2}\cdot 13^{6} \)	16T1429	Trivial
16.0.8990543797188296704.1	x^16 - 6x^15 + 20x^14 - 30x^13 + 5x^12 + 82x^11 - 116x^10 + 20x^9 + 168x^8 - 76x^7 + 2x^6 + 4x^5 + 196x^4 + 210x^3 - 218x^2 + 102x + 289	\( 2^{24}\cdot 17^{6}\cdot 149^{2} \)	16T1429	Trivial
16.4.15227477017600000000.1	x^16 + 5x^14 + 5x^12 - 13x^10 - 32x^8 - 20x^6 + x^4 + 3x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 29^{6} \)	16T1429	Trivial
16.0.163266119413359765625.1	x^16 - 5x^15 + 14x^14 - 29x^13 + 42x^12 - 51x^11 + 90x^10 - 173x^9 + 243x^8 - 254x^7 + 230x^6 - 206x^5 + 173x^4 - 119x^3 + 59x^2 - 18x + 4	\( 5^{8}\cdot 29^{2}\cdot 89^{6} \)	16T1429	Trivial
16.8.176042996446164680704.1	x^16 - 4x^15 + 6x^14 - 29x^12 + 76x^11 - 86x^10 + 24x^9 + 88x^8 - 184x^7 + 152x^6 - 36x^5 - 2x^4 - 8x^3 + 4x - 1	\( 2^{24}\cdot 41^{6}\cdot 47^{2} \)	16T1429	Trivial
16.4.348725955724781640625.1	x^16 - 4x^15 + 2x^14 + 9x^13 - 10x^12 + 7x^11 - 62x^10 + 143x^9 - 90x^8 - 81x^7 + 132x^6 - 26x^5 - 40x^4 + 17x^3 + 3x^2 - 3x + 1	\( 5^{8}\cdot 29^{2}\cdot 101^{6} \)	16T1429	Trivial
16.8.411627264599250390625.1	x^16 - 6x^15 + 5x^14 + 36x^13 - 79x^12 - 6x^11 + 76x^10 + 154x^9 - 286x^8 - 46x^7 + 191x^6 + 66x^5 - 117x^4 - 8x^3 + 21x^2 - 1	\( 5^{8}\cdot 11^{6}\cdot 29^{6} \)	16T1429	Trivial
16.8.424686794052336615424.1	x^16 - 2x^15 - 7x^14 + 22x^13 - 3x^12 - 38x^11 + 18x^10 - 12x^9 - 35x^8 + 66x^7 + 56x^6 - 20x^5 + 8x^4 + 16x^3 - 16x^2 - 12x - 1	\( 2^{24}\cdot 41^{6}\cdot 73^{2} \)	16T1429	Trivial
16.8.631252410525156376576.1	x^16 - 4x^15 + 30x^13 - 62x^12 + 12x^11 + 91x^10 - 110x^9 + 55x^8 - 32x^7 - 30x^6 + 168x^5 - 136x^4 - 64x^3 + 96x^2 - 16	\( 2^{24}\cdot 41^{6}\cdot 89^{2} \)	16T1429	Trivial
16.4.845468605385858351104.1	x^16 - 4x^15 + 12x^14 - 28x^13 + 48x^12 - 60x^11 + 44x^10 - 58x^9 + 29x^8 + 48x^7 - 118x^6 + 174x^5 - 33x^4 - 62x^3 + 61x^2 + 34x + 1	\( 2^{24}\cdot 41^{6}\cdot 103^{2} \)	16T1429	Trivial
16.12.1017606619113208152064.1	x^16 - 2x^15 - 13x^14 + 20x^13 + 73x^12 - 56x^11 - 265x^10 + 26x^9 + 617x^8 + 88x^7 - 744x^6 - 200x^5 + 400x^4 + 240x^3 - 136x^2 - 64x + 16	\( 2^{24}\cdot 41^{6}\cdot 113^{2} \)	16T1429	Trivial
16.8.1017606619113208152064.1	x^16 - 4x^15 + 16x^13 - 19x^12 - 8x^11 + 4x^10 + 116x^9 - 208x^8 + 112x^7 - 76x^5 + 134x^4 - 68x^3 - 10x^2 + 8x + 1	\( 2^{24}\cdot 41^{6}\cdot 113^{2} \)	16T1429	Trivial
16.4.1150291876377197265625.1	x^16 - x^15 - 6x^14 + 26x^12 + 22x^11 - 60x^10 - 92x^9 + 92x^8 + 214x^7 - 55x^6 - 301x^5 - 119x^4 + 140x^3 + 91x^2 - 12x - 19	\( 5^{12}\cdot 29^{6}\cdot 89^{2} \)	16T1429	Trivial
16.4.1495767768355846488064.1	x^16 - 2x^15 - 9x^14 + 10x^13 + 43x^12 - 18x^11 - 106x^10 + 24x^9 + 149x^8 - 42x^7 - 168x^6 + 68x^5 + 242x^4 + 184x^3 + 166x^2 + 256x + 89	\( 2^{24}\cdot 41^{6}\cdot 137^{2} \)	16T1429	Trivial
16.12.5222794846127590998016.1	x^16 - 6x^14 + 7x^12 + 20x^10 - 50x^8 + 22x^6 + 18x^4 - 12x^2 + 1	\( 2^{40}\cdot 41^{6} \)	16T1429	Trivial (GRH)
16.4.5222794846127590998016.1	x^16 + 6x^14 + 7x^12 - 20x^10 - 50x^8 - 22x^6 + 18x^4 + 12x^2 + 1	\( 2^{40}\cdot 41^{6} \)	16T1429	Trivial
16.12.5222794846127590998016.2	x^16 - 2x^14 - 15x^12 + 36x^10 + 9x^8 - 72x^6 + 55x^4 - 14x^2 + 1	\( 2^{40}\cdot 41^{6} \)	16T1429	Trivial (GRH)
16.0.8718148893119541015625.1	x^16 - 3x^15 + 6x^14 - 2x^13 + 19x^12 - x^11 + 29x^10 + 6x^9 + 35x^8 + 6x^7 + 29x^6 - x^5 + 19x^4 - 2x^3 + 6x^2 - 3x + 1	\( 5^{10}\cdot 29^{2}\cdot 101^{6} \)	16T1429	$[2, 2]$
16.8.8718148893119541015625.1	x^16 - 2x^15 - 7x^14 + 3x^13 + 18x^12 + 23x^11 - 16x^10 - 40x^9 + 3x^8 + 40x^7 - 16x^6 - 23x^5 + 18x^4 - 3x^3 - 7x^2 + 2x + 1	\( 5^{10}\cdot 29^{2}\cdot 101^{6} \)	16T1429	Trivial (GRH)
16.0.31216831471804594140625.1	x^16 - 3x^15 + 13x^14 - 30x^13 + 57x^12 - 102x^11 + 135x^10 - 201x^9 + 222x^8 - 132x^7 + 179x^6 - 130x^5 - 78x^4 + 25x^2 + 44x + 16	\( 5^{8}\cdot 89^{6}\cdot 401^{2} \)	16T1429	$[2]$
16.0.31216831471804594140625.2	x^16 - 7x^15 + 21x^14 - 40x^13 + 80x^12 - 154x^11 + 305x^10 - 370x^9 + 540x^8 - 581x^7 + 459x^6 - 222x^5 - 43x^4 + 106x^3 - 23x^2 - 12x + 4	\( 5^{8}\cdot 89^{6}\cdot 401^{2} \)	16T1429	Trivial
16.0.41796126569820100000000.1	x^16 + 2x^14 + 13x^12 + 6x^10 + 48x^8 - 198x^6 + 537x^4 - 754x^2 + 841	\( 2^{8}\cdot 5^{8}\cdot 29^{2}\cdot 89^{6} \)	16T1429	$[2]$
16.0.681587113420645172265625.1	x^16 - 3x^15 + 14x^14 - 40x^13 + 77x^12 - 90x^11 + 168x^10 + 337x^9 + 1134x^8 + 293x^7 + 12153x^6 - 4790x^5 + 52207x^4 - 4835x^3 + 122354x^2 + 21948x + 121531	\( 5^{8}\cdot 29^{6}\cdot 41^{2}\cdot 1321^{2} \)	16T1429	$[2]$
16.8.1962532465505305600000000.1	x^16 - 31x^14 + 407x^12 - 3067x^10 + 15173x^8 - 52216x^6 + 123818x^4 - 184167x^2 + 128881	\( 2^{16}\cdot 5^{8}\cdot 29^{6}\cdot 359^{2} \)	16T1429	Trivial (GRH)
16.8.22854104234379289600000000.1	x^16 - 4x^15 + x^14 + 30x^13 - 124x^12 + 136x^11 + 625x^10 - 2312x^9 - 1700x^8 + 21856x^7 - 39356x^6 + 6880x^5 + 60884x^4 - 80214x^3 + 41797x^2 - 9142x + 701	\( 2^{16}\cdot 5^{8}\cdot 29^{2}\cdot 101^{6} \)	16T1429	Trivial (GRH)
16.16.23754879374933017600000000.1	x^16 - 4x^15 - 27x^14 + 162x^13 - 30x^12 - 1244x^11 + 1953x^10 + 2462x^9 - 7779x^8 + 1978x^7 + 8133x^6 - 5142x^5 - 2930x^4 + 2432x^3 + 333x^2 - 320x + 11	\( 2^{16}\cdot 5^{8}\cdot 29^{6}\cdot 1249^{2} \)	16T1429	Trivial (GRH)
16.12.75385528410256000000000000.1	x^16 - 4x^15 - 10x^14 + 80x^13 - 187x^12 - 26x^11 + 1471x^10 - 2910x^9 + 264x^8 + 3118x^7 - 788x^6 - 1512x^5 + 237x^4 + 532x^3 + 172x^2 + 22x + 1	\( 2^{16}\cdot 5^{12}\cdot 29^{6}\cdot 89^{2} \)	16T1429	Trivial (GRH)
16.4.75385528410256000000000000.1	x^16 - 4x^15 + 3x^14 + 26x^13 - 23x^12 - 330x^11 - 1393x^10 - 2022x^9 - 225x^8 + 368x^7 - 1198x^6 - 1150x^5 - 153x^4 + 116x^3 - 232x^2 - 174x - 29	\( 2^{16}\cdot 5^{12}\cdot 29^{6}\cdot 89^{2} \)	16T1429	$[2]$ (GRH)
16.16.505153940312306728919105536.1	x^16 - 50x^14 + 999x^12 - 10300x^10 + 59091x^8 - 190700x^6 + 336689x^4 - 295450x^2 + 96721	\( 2^{40}\cdot 41^{6}\cdot 311^{2} \)	16T1429	Trivial (GRH)
16.0.571352605859482240000000000.1	x^16 - 4x^15 + 19x^14 - 40x^13 + 68x^12 - 508x^11 + 675x^10 + 312x^9 + 7721x^8 - 32624x^7 + 52870x^6 - 54870x^5 + 48342x^4 - 29576x^3 + 17788x^2 - 5614x + 2011	\( 2^{16}\cdot 5^{10}\cdot 29^{2}\cdot 101^{6} \)	16T1429	$[2, 20]$ (GRH)
16.8.571352605859482240000000000.1	x^16 - 14x^14 - 72x^13 - 187x^12 - 566x^11 - 486x^10 + 1400x^9 + 2460x^8 + 2686x^7 + 282x^6 - 6770x^5 - 3215x^4 + 2512x^3 - 142x^2 + 666x + 181	\( 2^{16}\cdot 5^{10}\cdot 29^{2}\cdot 101^{6} \)	16T1429	$[2]$ (GRH)
16.8.571352605859482240000000000.2	x^16 - 8x^15 + 9x^14 + 54x^13 - 140x^12 + 158x^11 - 176x^10 - 82x^9 + 1636x^8 - 4612x^7 + 3265x^6 + 3546x^5 - 4216x^4 + 3166x^3 - 3858x^2 - 2446x + 3239	\( 2^{16}\cdot 5^{10}\cdot 29^{2}\cdot 101^{6} \)	16T1429	Trivial (GRH)
16.0.2739150950879730073600000000.1	x^16 - 6x^15 + 38x^14 - 50x^13 + 2x^12 + 764x^11 - 1246x^10 + 1414x^9 + 6239x^8 - 9556x^7 + 12458x^6 + 30822x^5 - 22786x^4 + 43090x^3 + 94988x^2 + 65336x + 126481	\( 2^{24}\cdot 5^{8}\cdot 29^{2}\cdot 89^{6} \)	16T1429	$[2, 2, 40]$ (GRH)