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
16.0.1286133193603515625.1	x^16 - 2x^15 + 3x^14 - 5x^13 - 5x^12 - 3x^11 + 54x^10 - 35x^9 - 46x^8 + 10x^7 + 71x^6 - 31x^5 - 25x^4 + 12x^2 + x + 1	\( 5^{12}\cdot 181^{2}\cdot 401^{2} \)	16T1224	Trivial
16.0.1286133193603515625.2	x^16 - 4x^15 + 17x^14 - 35x^13 + 70x^12 - 66x^11 + 56x^10 + 40x^9 - 56x^8 + 85x^7 + 9x^6 - 18x^5 + 35x^4 + 10x^3 + 3x^2 + 3x + 1	\( 5^{12}\cdot 181^{2}\cdot 401^{2} \)	16T1224	Trivial
16.0.4885860237929611264.1	x^16 - 4x^15 + 10x^14 - 24x^13 + 47x^12 - 80x^11 + 138x^10 - 220x^9 + 319x^8 - 432x^7 + 508x^6 - 504x^5 + 422x^4 - 272x^3 + 120x^2 - 32x + 4	\( 2^{44}\cdot 17^{2}\cdot 31^{2} \)	16T1224	Trivial
16.4.4885860237929611264.1	x^16 - 4x^15 + 6x^14 - 31x^12 + 96x^11 - 166x^10 + 196x^9 - 137x^8 - 8x^7 + 152x^6 - 216x^5 + 186x^4 - 112x^3 + 48x^2 - 16x + 4	\( 2^{44}\cdot 17^{2}\cdot 31^{2} \)	16T1224	Trivial
16.0.4885860237929611264.2	x^16 - 4x^15 + 14x^14 - 24x^13 + 35x^12 - 16x^11 + 2x^10 + 44x^9 - 36x^8 + 44x^7 + 2x^6 - 16x^5 + 35x^4 - 24x^3 + 14x^2 - 4x + 1	\( 2^{44}\cdot 17^{2}\cdot 31^{2} \)	16T1224	Trivial
16.4.4885860237929611264.2	x^16 - 4x^15 + 6x^14 - 8x^13 + 15x^12 - 32x^11 + 38x^10 - 28x^9 + 31x^8 - 64x^7 + 84x^6 - 40x^5 - 26x^4 + 48x^3 - 24x^2 + 4	\( 2^{44}\cdot 17^{2}\cdot 31^{2} \)	16T1224	Trivial
16.8.31730128766824873984.1	x^16 - 4x^15 + 2x^14 + 13x^12 + 24x^11 - 82x^10 - 20x^9 + 128x^8 - 20x^7 - 82x^6 + 24x^5 + 13x^4 + 2x^2 - 4x + 1	\( 2^{44}\cdot 17^{2}\cdot 79^{2} \)	16T1224	Trivial
16.8.31730128766824873984.2	x^16 - 4x^15 - 2x^14 + 24x^13 - 13x^12 - 48x^11 + 50x^10 + 28x^9 - 68x^8 + 28x^7 + 50x^6 - 48x^5 - 13x^4 + 24x^3 - 2x^2 - 4x + 1	\( 2^{44}\cdot 17^{2}\cdot 79^{2} \)	16T1224	Trivial
16.12.178657056758056640625.1	x^16 - 2x^15 - 8x^14 + 29x^13 - 18x^12 - 106x^11 + 223x^10 + 67x^9 - 495x^8 + 211x^7 + 419x^6 - 336x^5 - 112x^4 + 149x^3 - 10x^2 - 12x + 1	\( 3^{8}\cdot 5^{12}\cdot 59^{2}\cdot 179^{2} \)	16T1224	Trivial
16.8.178657056758056640625.1	x^16 - 6x^15 + 7x^14 + 17x^13 - 34x^12 - 19x^11 + 52x^10 + 126x^9 - 498x^8 + 720x^7 - 497x^6 + 178x^5 - 133x^4 + 31x^3 + 64x^2 + 15x + 1	\( 3^{8}\cdot 5^{12}\cdot 59^{2}\cdot 179^{2} \)	16T1224	Trivial
16.0.502656400000000000000.1	x^16 + 11x^14 - 10x^13 + 52x^12 - 50x^11 + 143x^10 - 120x^9 + 205x^8 - 70x^7 + 117x^6 + 10x^5 + 52x^4 + 10x^3 + 9x^2 + 1	\( 2^{16}\cdot 5^{14}\cdot 19^{2}\cdot 59^{2} \)	16T1224	$[2]$
16.4.502656400000000000000.1	x^16 - 4x^14 - 13x^12 - 30x^11 + 8x^10 + 20x^9 - 60x^8 - 10x^7 + 72x^6 - 150x^5 + 87x^4 + 4x^2 + 10x + 1	\( 2^{16}\cdot 5^{14}\cdot 19^{2}\cdot 59^{2} \)	16T1224	Trivial
16.0.502656400000000000000.2	x^16 - 6x^15 + 26x^14 - 94x^13 + 293x^12 - 756x^11 + 1594x^10 - 2742x^9 + 3873x^8 - 4526x^7 + 4366x^6 - 3452x^5 + 2208x^4 - 1112x^3 + 424x^2 - 112x + 16	\( 2^{16}\cdot 5^{14}\cdot 19^{2}\cdot 59^{2} \)	16T1224	$[2]$
16.4.502656400000000000000.2	x^16 - 6x^15 + 11x^14 + 6x^13 - 57x^12 + 114x^11 - 136x^10 + 88x^9 + 43x^8 - 216x^7 + 336x^6 - 282x^5 + 88x^4 + 28x^3 - 16x^2 - 2x + 1	\( 2^{16}\cdot 5^{14}\cdot 19^{2}\cdot 59^{2} \)	16T1224	Trivial
16.0.1107957565927179943936.1	x^16 + 4x^14 + 10x^12 + 20x^10 + 31x^8 + 40x^6 + 40x^4 + 32x^2 + 16	\( 2^{60}\cdot 31^{2} \)	16T1224	Trivial
16.4.1107957565927179943936.1	x^16 - 8x^14 + 16x^12 - 24x^10 + 26x^8 - 24x^6 + 16x^4 - 8x^2 + 1	\( 2^{60}\cdot 31^{2} \)	16T1224	Trivial
16.0.1848055014225549931321.1	x^16 - x^15 + 9x^14 - 19x^13 + 44x^12 - 63x^11 + 128x^10 - 165x^9 + 223x^8 - 190x^7 + 195x^6 - 116x^5 + 61x^4 - 9x^3 + 8x^2 - 4x + 1	\( 13^{2}\cdot 17^{12}\cdot 137^{2} \)	16T1224	$[2]$
16.4.1848055014225549931321.1	x^16 - 2x^15 + 2x^14 + x^13 + 7x^12 - 10x^11 - 19x^10 + 11x^9 + 2x^8 + 11x^7 - 19x^6 - 10x^5 + 7x^4 + x^3 + 2x^2 - 2x + 1	\( 13^{2}\cdot 17^{12}\cdot 137^{2} \)	16T1224	Trivial
16.8.1848055014225549931321.1	x^16 - x^15 - 8x^14 + 15x^13 - 7x^12 + 5x^11 + 43x^10 - 131x^9 + 36x^8 + 133x^7 - 77x^6 - 14x^5 - 24x^4 + 42x^3 - 9x^2 - 4x + 1	\( 13^{2}\cdot 17^{12}\cdot 137^{2} \)	16T1224	Trivial
16.4.1848055014225549931321.2	x^16 - x^15 + 9x^14 - 15x^13 + 29x^12 - 72x^11 + 17x^10 - 125x^9 - 2x^8 - 20x^7 - 17x^6 - 26x^5 - 29x^4 - 52x^3 + 70x^2 - 19x + 1	\( 13^{2}\cdot 17^{12}\cdot 137^{2} \)	16T1224	Trivial
16.0.2522048400000000000000.1	x^16 - 3x^14 + 18x^12 - 21x^10 + 35x^8 + 69x^6 + 33x^4 + 12x^2 + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{14}\cdot 31^{2} \)	16T1224	$[2]$
16.4.2522048400000000000000.1	x^16 - 3x^14 + 3x^12 - 6x^10 + 5x^8 - 6x^6 + 3x^4 - 3x^2 + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{14}\cdot 31^{2} \)	16T1224	Trivial
16.12.4431830263708719775744.1	x^16 - 16x^14 + 96x^12 - 264x^10 + 326x^8 - 160x^6 + 32x^4 - 8x^2 + 1	\( 2^{62}\cdot 31^{2} \)	16T1224	Trivial (GRH)
16.8.4431830263708719775744.1	x^16 - 8x^14 + 28x^12 - 40x^10 - 56x^8 + 256x^6 - 232x^4 + 16x^2 + 4	\( 2^{62}\cdot 31^{2} \)	16T1224	Trivial (GRH)
16.8.6213284557402587890625.1	x^16 - 4x^15 - 2x^14 + 21x^13 - 18x^12 - 40x^11 + 62x^10 + 83x^9 - 80x^8 - 142x^7 + 67x^6 + 225x^5 + 107x^4 - 49x^3 - 47x^2 - 4x + 1	\( 3^{8}\cdot 5^{12}\cdot 61^{2}\cdot 1021^{2} \)	16T1224	Trivial
16.0.12246192610345480093696.1	x^16 + 12x^14 - 8x^13 + 26x^12 - 48x^11 + 12x^10 + 16x^9 + 19x^8 + 48x^7 + 76x^6 - 168x^5 + 478x^4 + 264x^3 + 88x^2 + 1088x + 1343	\( 2^{52}\cdot 17^{2}\cdot 97^{2} \)	16T1224	$[6]$
16.8.54703954685586181640625.1	x^16 - 4x^15 + 2x^14 + 25x^13 - 10x^12 + 9x^11 - 164x^10 - 35x^9 + 204x^8 - 30x^7 + 74x^6 + 147x^5 + 10x^4 - 40x^3 - 12x^2 + 3x + 1	\( 3^{8}\cdot 5^{12}\cdot 181^{2}\cdot 1021^{2} \)	16T1224	Trivial (GRH)
16.8.54703954685586181640625.2	x^16 - x^15 - 13x^14 - 35x^13 - 20x^12 + 16x^11 + 86x^10 + 70x^9 - x^8 + 85x^7 + 44x^6 - 67x^5 + 15x^4 + 45x^3 - 7x^2 - 8x + 1	\( 3^{8}\cdot 5^{12}\cdot 181^{2}\cdot 1021^{2} \)	16T1224	Trivial (GRH)
16.0.644224548496000000000000.1	x^16 - 4x^15 + 13x^14 - 82x^13 + 383x^12 - 1012x^11 + 1746x^10 - 2616x^9 + 4783x^8 - 9728x^7 + 18049x^6 - 27814x^5 + 32373x^4 - 26136x^3 + 13632x^2 - 4128x + 556	\( 2^{16}\cdot 5^{12}\cdot 19^{2}\cdot 59^{2}\cdot 179^{2} \)	16T1224	$[10]$
16.0.644224548496000000000000.2	x^16 - 2x^15 + 5x^14 + 6x^13 - 9x^12 + 58x^11 - 42x^10 + 4x^9 + 248x^8 - 136x^7 + 408x^6 + 48x^5 - 624x^4 + 256x^3 + 1280x^2 + 768x + 256	\( 2^{16}\cdot 5^{12}\cdot 19^{2}\cdot 59^{2}\cdot 179^{2} \)	16T1224	$[2]$
16.0.4681350558152105712890625.1	x^16 - 3x^15 + 17x^14 - 39x^13 + 176x^12 - 318x^11 + 990x^10 - 1322x^9 + 3599x^8 - 2561x^7 + 6675x^6 + 929x^5 + 13181x^4 - 1097x^3 + 24498x^2 + 11224x + 3721	\( 3^{8}\cdot 5^{14}\cdot 181^{2}\cdot 1889^{2} \)	16T1224	$[2, 18]$
16.16.96097711067136000000000000.1	x^16 - 48x^14 + 810x^12 - 5688x^10 + 15179x^8 - 7752x^6 + 1290x^4 - 72x^2 + 1	\( 2^{24}\cdot 3^{8}\cdot 5^{12}\cdot 31^{2}\cdot 61^{2} \)	16T1224	Trivial (GRH)
16.16.96097711067136000000000000.2	x^16 - 6x^15 - 24x^14 + 198x^13 + 52x^12 - 2176x^11 + 2062x^10 + 9118x^9 - 13699x^8 - 15392x^7 + 30582x^6 + 8394x^5 - 25808x^4 + 378x^3 + 7206x^2 - 916x + 1	\( 2^{24}\cdot 3^{8}\cdot 5^{12}\cdot 31^{2}\cdot 61^{2} \)	16T1224	Trivial (GRH)
16.0.232565062007056000000000000.1	x^16 - 2x^14 + 79x^12 - 238x^10 + 1261x^8 - 9520x^6 + 21340x^4 + 37600x^2 + 144400	\( 2^{16}\cdot 5^{12}\cdot 19^{4}\cdot 59^{2}\cdot 179^{2} \)	16T1224	$[2, 96]$ (GRH)