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 all 30 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.49617562500000000.1	x^16 - 5x^15 + 13x^14 - 27x^13 + 46x^12 - 57x^11 + 63x^10 - 57x^9 + 25x^8 - 11x^7 - 3x^6 + 28x^5 + 8x^4 + 13x^3 - 3x^2 - 4x + 1	\( 2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 11^{2} \)	16T797	Trivial
16.0.394070062500000000.4	x^16 - 5x^15 + 15x^14 - 32x^13 + 46x^12 - 45x^11 + 64x^10 - 214x^9 + 611x^8 - 1228x^7 + 1822x^6 - 2061x^5 + 1792x^4 - 1182x^3 + 569x^2 - 183x + 31	\( 2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 31^{2} \)	16T797	Trivial
16.0.5012631230712890625.1	x^16 - x^15 + 6x^14 - 18x^13 + 22x^12 - 100x^11 + 118x^10 - 258x^9 + 472x^8 - 348x^7 + 1000x^6 - 260x^5 + 1090x^4 - 126x^3 + 576x^2 - 44x + 121	\( 3^{8}\cdot 5^{12}\cdot 29^{2}\cdot 61^{2} \)	16T797	Trivial
16.0.10019302138916015625.1	x^16 - x^15 - 15x^14 + 8x^13 + 98x^12 + 27x^11 - 304x^10 - 478x^9 + 135x^8 + 1876x^7 + 2092x^6 - 2537x^5 - 6198x^4 - 1338x^3 + 5643x^2 + 5701x + 1831	\( 3^{8}\cdot 5^{12}\cdot 41^{2}\cdot 61^{2} \)	16T797	Trivial
16.0.378535936000000000000.1	x^16 + 10x^14 - 8x^13 + 42x^12 - 80x^11 + 164x^10 - 272x^9 + 464x^8 - 672x^7 + 884x^6 - 996x^5 + 779x^4 - 376x^3 + 106x^2 - 16x + 1	\( 2^{32}\cdot 5^{12}\cdot 19^{2} \)	16T797	Trivial
16.0.378535936000000000000.2	x^16 + 2x^14 - 12x^13 + 32x^12 - 48x^11 + 44x^10 - 56x^9 + 140x^8 - 304x^7 + 552x^6 - 836x^5 + 997x^4 - 888x^3 + 542x^2 - 196x + 31	\( 2^{32}\cdot 5^{12}\cdot 19^{2} \)	16T797	Trivial
16.12.3251736576000000000000.1	x^16 - 2x^15 - 14x^14 + 14x^13 + 74x^12 + 12x^11 - 146x^10 - 214x^9 - 149x^8 + 260x^7 + 770x^6 + 370x^5 - 470x^4 - 450x^3 + 100x + 25	\( 2^{24}\cdot 3^{8}\cdot 5^{12}\cdot 11^{2} \)	16T797	Trivial (GRH)
16.4.3251736576000000000000.1	x^16 - 2x^15 + 2x^14 - 14x^13 + 18x^12 - 36x^11 + 54x^10 - 102x^9 - 77x^8 - 4x^7 + 66x^6 + 522x^5 - 1142x^4 + 1062x^3 - 392x^2 - 16x + 1	\( 2^{24}\cdot 3^{8}\cdot 5^{12}\cdot 11^{2} \)	16T797	Trivial (GRH)
16.8.3251736576000000000000.1	x^16 - 2x^15 - 8x^14 - 8x^13 + 32x^12 + 110x^11 + 58x^10 - 174x^9 - 195x^8 + 54x^7 - 82x^6 - 350x^5 + 12x^4 + 288x^3 + 62x^2 - 38x + 1	\( 2^{24}\cdot 3^{8}\cdot 5^{12}\cdot 11^{2} \)	16T797	Trivial (GRH)
16.8.3251736576000000000000.2	x^16 - 2x^15 - 4x^14 + 34x^13 - 41x^12 - 88x^11 + 294x^10 - 134x^9 - 434x^8 + 480x^7 - 60x^6 - 80x^5 + 170x^4 - 300x^3 + 50x^2 + 150x + 25	\( 2^{24}\cdot 3^{8}\cdot 5^{12}\cdot 11^{2} \)	16T797	Trivial (GRH)
16.12.9701462016000000000000.1	x^16 - 10x^14 - 3x^12 + 260x^10 - 846x^8 + 770x^6 + 548x^4 - 1140x^2 + 361	\( 2^{24}\cdot 3^{8}\cdot 5^{12}\cdot 19^{2} \)	16T797	Trivial (GRH)
16.4.9701462016000000000000.1	x^16 + 10x^14 - 3x^12 - 260x^10 - 846x^8 - 770x^6 + 548x^4 + 1140x^2 + 361	\( 2^{24}\cdot 3^{8}\cdot 5^{12}\cdot 19^{2} \)	16T797	Trivial (GRH)
16.12.23165723849659414216704.1	x^16 - 8x^15 + 24x^14 - 16x^13 - 112x^12 + 336x^11 - 232x^10 - 304x^9 + 484x^8 - 504x^7 + 1040x^6 - 832x^5 - 224x^4 + 464x^3 - 120x^2 + 1	\( 2^{56}\cdot 3^{8}\cdot 7^{2} \)	16T797	Trivial (GRH)
16.4.23165723849659414216704.1	x^16 - 8x^15 + 24x^14 - 16x^13 - 112x^12 + 432x^11 - 888x^10 + 1440x^9 - 2060x^8 + 2328x^7 - 1840x^6 + 1280x^5 - 944x^4 + 80x^3 + 344x^2 + 80x - 47	\( 2^{56}\cdot 3^{8}\cdot 7^{2} \)	16T797	Trivial (GRH)
16.12.32480690176000000000000.1	x^16 - 16x^14 - 12x^13 + 58x^12 + 144x^11 + 44x^10 - 504x^9 - 506x^8 + 464x^7 + 968x^6 + 160x^5 - 788x^4 - 208x^3 + 224x^2 + 16x - 4	\( 2^{40}\cdot 5^{12}\cdot 11^{2} \)	16T797	Trivial (GRH)
16.8.32480690176000000000000.2	x^16 - 4x^13 - 14x^12 - 44x^10 - 8x^9 + 206x^8 + 176x^7 - 72x^6 - 32x^5 + 172x^4 + 144x^3 + 16x^2 - 16x - 4	\( 2^{40}\cdot 5^{12}\cdot 11^{2} \)	16T797	Trivial (GRH)
16.4.32480690176000000000000.3	x^16 + 8x^14 - 12x^13 - 2x^12 - 72x^11 - 160x^10 - 180x^9 + 106x^8 + 832x^7 + 920x^6 + 44x^5 - 350x^4 + 280x^3 + 632x^2 + 308x + 41	\( 2^{40}\cdot 5^{12}\cdot 11^{2} \)	16T797	Trivial (GRH)
16.8.32480690176000000000000.3	x^16 - 8x^14 - 4x^13 + 6x^12 + 24x^11 - 8x^10 - 44x^9 + 50x^8 + 32x^7 + 8x^6 - 124x^5 - 22x^4 + 184x^3 - 112x^2 + 12x + 1	\( 2^{40}\cdot 5^{12}\cdot 11^{2} \)	16T797	Trivial (GRH)
16.0.144765030400000000000000.1	x^16 - 6x^15 + 29x^14 - 126x^13 + 456x^12 - 1068x^11 + 1381x^10 + 452x^9 - 5993x^8 + 12728x^7 - 11859x^6 - 2852x^5 + 23536x^4 - 32314x^3 + 23529x^2 - 9214x + 1601	\( 2^{24}\cdot 5^{14}\cdot 29^{2}\cdot 41^{2} \)	16T797	$[2]$ (GRH)
16.0.1693912662016000000000000.1	x^16 - 8x^14 - 32x^13 - 3x^12 + 192x^11 + 514x^10 + 144x^9 - 1360x^8 - 4224x^7 - 4088x^6 + 2564x^5 + 15492x^4 + 22072x^3 + 26872x^2 + 7184x + 2911	\( 2^{32}\cdot 5^{12}\cdot 31^{2}\cdot 41^{2} \)	16T797	$[2]$ (GRH)
16.0.12796960816656000000000000.1	x^16 - 8x^15 + 62x^14 - 294x^13 + 1232x^12 - 3774x^11 + 10008x^10 - 19892x^9 + 34425x^8 - 44976x^7 + 56189x^6 - 53874x^5 + 61418x^4 - 48694x^3 + 51225x^2 - 22708x + 13921	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 61^{2}\cdot 181^{2} \)	16T797	$[2, 2, 40]$ (GRH)
16.8.84097996886016000000000000.1	x^16 - 6x^15 - 6x^14 + 152x^13 - 552x^12 + 378x^11 + 4062x^10 - 18422x^9 + 39121x^8 - 40678x^7 - 4886x^6 + 80542x^5 - 105260x^4 + 46996x^3 + 23900x^2 - 44242x + 16921	\( 2^{24}\cdot 3^{8}\cdot 5^{12}\cdot 29^{2}\cdot 61^{2} \)	16T797	Trivial (GRH)
16.8.84097996886016000000000000.2	x^16 - 6x^15 + 18x^14 - 90x^13 + 315x^12 - 688x^11 + 1650x^10 - 4086x^9 + 7981x^8 + 3690x^7 - 39830x^6 + 34596x^5 - 27147x^4 + 9004x^3 + 62442x^2 - 16890x - 15359	\( 2^{24}\cdot 3^{8}\cdot 5^{12}\cdot 29^{2}\cdot 61^{2} \)	16T797	Trivial (GRH)
16.0.819501922779136000000000000.1	x^16 - 8x^15 + 68x^14 - 308x^13 + 1366x^12 - 4000x^11 + 11742x^10 - 22360x^9 + 46707x^8 - 46980x^7 + 78102x^6 + 19260x^5 + 57936x^4 + 167908x^3 + 141578x^2 + 99788x + 251761	\( 2^{36}\cdot 5^{12}\cdot 29^{2}\cdot 241^{2} \)	16T797	$[2, 2, 190]$ (GRH)
16.16.819501922779136000000000000.1	x^16 - 4x^15 - 38x^14 + 184x^13 + 356x^12 - 2560x^11 - 62x^10 + 14300x^9 - 10478x^8 - 32820x^7 + 36258x^6 + 25240x^5 - 30844x^4 - 9136x^3 + 5922x^2 + 2476x + 241	\( 2^{36}\cdot 5^{12}\cdot 29^{2}\cdot 241^{2} \)	16T797	Trivial (GRH)
16.8.1755550085243509039467331584.1	x^16 - 8x^14 - 80x^13 - 468x^12 + 632x^11 + 5488x^10 + 8280x^9 - 10806x^8 - 58864x^7 - 80800x^6 + 736x^5 + 171092x^4 + 286640x^3 + 245072x^2 + 114928x + 21598	\( 2^{56}\cdot 3^{8}\cdot 41^{2}\cdot 47^{2} \)	16T797	$[2]$ (GRH)
16.8.1755550085243509039467331584.2	x^16 - 8x^15 + 24x^14 - 16x^13 - 232x^12 + 840x^11 - 1312x^10 + 440x^9 + 4942x^8 - 16512x^7 + 32984x^6 - 11680x^5 - 69980x^4 + 73184x^3 - 74208x^2 + 154224x - 83234	\( 2^{56}\cdot 3^{8}\cdot 41^{2}\cdot 47^{2} \)	16T797	$[2]$ (GRH)
16.16.3307735506823056000000000000.1	x^16 - 6x^15 - 74x^14 + 472x^13 + 1777x^12 - 12730x^11 - 17357x^10 + 158732x^9 + 46897x^8 - 975158x^7 + 293460x^6 + 2722820x^5 - 1862220x^4 - 2393916x^3 + 2334136x^2 + 21526x - 312839	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 29^{2}\cdot 6121^{2} \)	16T797	Trivial (GRH)
16.8.22542913242136576000000000000.1	x^16 + 32x^14 - 40x^12 - 6528x^10 - 426x^8 + 355168x^6 - 329800x^4 - 4105472x^2 + 5248681	\( 2^{44}\cdot 5^{12}\cdot 29^{2}\cdot 79^{2} \)	16T797	$[2]$ (GRH)
16.8.22542913242136576000000000000.2	x^16 + 32x^14 - 70x^12 - 6768x^10 - 3561x^8 + 305008x^6 - 47530x^4 - 3555632x^2 + 5248681	\( 2^{44}\cdot 5^{12}\cdot 29^{2}\cdot 79^{2} \)	16T797	$[2]$ (GRH)