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 46 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.40144896000000000000.1	x^16 - 6x^15 + 18x^14 - 26x^13 + 2x^12 + 40x^11 + 52x^10 - 438x^9 + 855x^8 - 428x^7 - 1188x^6 + 2530x^5 - 1258x^4 - 1226x^3 + 1758x^2 - 776x + 121	\( 2^{24}\cdot 3^{4}\cdot 5^{12}\cdot 11^{2} \)	16T781	Trivial (GRH)
16.0.40144896000000000000.2	x^16 - 6x^15 + 14x^14 - 12x^13 + 9x^12 - 134x^11 + 646x^10 - 1658x^9 + 2891x^8 - 4090x^7 + 5720x^6 - 8400x^5 + 11145x^4 - 11450x^3 + 8250x^2 - 3700x + 775	\( 2^{24}\cdot 3^{4}\cdot 5^{12}\cdot 11^{2} \)	16T781	Trivial (GRH)
16.4.84566416000000000000.1	x^16 - 2x^15 + 4x^13 - 32x^12 + 64x^11 - 6x^10 - 4x^9 - 145x^8 + 102x^7 + 128x^6 - 156x^5 + 57x^4 - 6x^3 - 3x^2 - 2x + 1	\( 2^{16}\cdot 5^{12}\cdot 11^{4}\cdot 19^{2} \)	16T781	Trivial (GRH)
16.0.126877696000000000000.3	x^16 + 12x^14 + 63x^12 + 194x^10 + 415x^8 + 664x^6 + 703x^4 + 352x^2 + 121	\( 2^{32}\cdot 5^{12}\cdot 11^{2} \)	16T781	Trivial (GRH)
16.0.126877696000000000000.4	x^16 - 12x^14 + 63x^12 - 194x^10 + 415x^8 - 664x^6 + 703x^4 - 352x^2 + 121	\( 2^{32}\cdot 5^{12}\cdot 11^{2} \)	16T781	Trivial (GRH)
16.4.176464656000000000000.1	x^16 - 6x^15 + 13x^14 - 14x^13 - 3x^12 + 16x^11 + 13x^10 - 26x^9 - 61x^8 + 130x^7 + 74x^6 - 508x^5 + 788x^4 - 680x^3 + 360x^2 - 112x + 16	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 41^{2} \)	16T781	Trivial (GRH)
16.0.181063936000000000000.4	x^16 + 11x^14 + 55x^12 + 149x^10 + 219x^8 + 144x^6 - 24x^2 + 16	\( 2^{20}\cdot 5^{12}\cdot 29^{4} \)	16T781	Trivial
16.0.181063936000000000000.5	x^16 - 11x^14 + 55x^12 - 149x^10 + 219x^8 - 144x^6 + 24x^2 + 16	\( 2^{20}\cdot 5^{12}\cdot 29^{4} \)	16T781	Trivial
16.4.252301456000000000000.1	x^16 - 4x^15 + 6x^14 - 10x^13 + 15x^12 - 26x^11 + 95x^10 - 120x^9 + 136x^8 - 340x^7 + 335x^6 - 246x^5 + 335x^4 - 240x^3 + 81x^2 - 14x + 1	\( 2^{16}\cdot 5^{12}\cdot 11^{2}\cdot 19^{4} \)	16T781	Trivial
16.8.1158738620062500000000.1	x^16 - x^14 - 21x^12 + 8x^10 + 89x^8 + 16x^6 - 74x^4 - 18x^2 + 1	\( 2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 41^{4} \)	16T781	Trivial (GRH)
16.4.4836472252562500000000.1	x^16 - 2x^15 - 7x^14 + 16x^13 + 3x^12 - 26x^11 - 2x^10 - 22x^9 + 45x^8 - 96x^7 + 92x^6 - 84x^5 + 56x^4 - 66x^3 + 72x^2 - 80x + 71	\( 2^{8}\cdot 5^{12}\cdot 11^{8}\cdot 19^{2} \)	16T781	Trivial (GRH)
16.0.5470673296000000000000.1	x^16 - 26x^14 + 286x^12 - 1706x^10 + 5976x^8 - 12500x^6 + 15435x^4 - 10450x^2 + 3025	\( 2^{16}\cdot 5^{12}\cdot 11^{2}\cdot 41^{4} \)	16T781	Trivial (GRH)
16.0.32480690176000000000000.1	x^16 + 10x^14 + 38x^12 + 50x^10 - 26x^8 + 110x^6 + 662x^4 + 550x^2 + 121	\( 2^{40}\cdot 5^{12}\cdot 11^{2} \)	16T781	$[2]$ (GRH)
16.8.32480690176000000000000.1	x^16 - 10x^14 + 38x^12 - 50x^10 - 26x^8 - 110x^6 + 662x^4 - 550x^2 + 121	\( 2^{40}\cdot 5^{12}\cdot 11^{2} \)	16T781	Trivial (GRH)
16.0.38023440016000000000000.1	x^16 - 32x^14 + 457x^12 - 3800x^10 + 20056x^8 - 68560x^6 + 147938x^4 - 184266x^2 + 101761	\( 2^{16}\cdot 5^{12}\cdot 29^{2}\cdot 41^{4} \)	16T781	$[2]$ (GRH)
16.0.42917363397401430196224.1	x^16 - 8x^15 + 32x^14 - 72x^13 + 62x^12 + 96x^11 - 256x^10 - 544x^9 + 4135x^8 - 11144x^7 + 18992x^6 - 21536x^5 + 16530x^4 - 7272x^3 + 3976x^2 - 1920x + 367	\( 2^{52}\cdot 3^{4}\cdot 7^{6} \)	16T781	$[2]$ (GRH)
16.8.42917363397401430196224.1	x^16 - 8x^14 - 8x^13 + 48x^12 - 40x^11 - 112x^10 + 288x^9 + 258x^8 - 864x^7 + 280x^6 + 320x^5 - 584x^4 + 432x^3 + 80x^2 - 64x + 4	\( 2^{52}\cdot 3^{4}\cdot 7^{6} \)	16T781	Trivial (GRH)
16.4.96905199616000000000000.1	x^16 + 2x^14 - 34x^12 - 74x^10 + 259x^8 + 358x^6 - 856x^4 - 76x^2 + 361	\( 2^{40}\cdot 5^{12}\cdot 19^{2} \)	16T781	Trivial (GRH)
16.4.96905199616000000000000.2	x^16 - 2x^14 - 34x^12 + 74x^10 + 259x^8 - 358x^6 - 856x^4 + 76x^2 + 361	\( 2^{40}\cdot 5^{12}\cdot 19^{2} \)	16T781	Trivial (GRH)
16.0.110912977296000000000000.1	x^16 + 4x^14 - 6x^12 + 248x^10 + 2719x^8 + 10356x^6 + 20241x^4 + 21087x^2 + 9801	\( 2^{16}\cdot 3^{4}\cdot 5^{12}\cdot 11^{2}\cdot 29^{4} \)	16T781	$[2]$ (GRH)
16.0.110912977296000000000000.2	x^16 - 4x^14 - 6x^12 - 248x^10 + 2719x^8 - 10356x^6 + 20241x^4 - 21087x^2 + 9801	\( 2^{16}\cdot 3^{4}\cdot 5^{12}\cdot 11^{2}\cdot 29^{4} \)	16T781	$[2]$ (GRH)
16.8.115439575696000000000000.1	x^16 - 2x^15 - 10x^14 + 74x^12 + 78x^11 - 232x^10 - 530x^9 - 29x^8 + 1598x^7 + 2188x^6 - 516x^5 - 2891x^4 - 1594x^3 + 139x^2 + 186x - 19	\( 2^{16}\cdot 5^{12}\cdot 29^{4}\cdot 101^{2} \)	16T781	Trivial (GRH)
16.8.234658861056000000000000.1	x^16 - 6x^15 + 2x^14 + 60x^13 - 125x^12 - 64x^11 + 576x^10 - 980x^9 - 311x^8 + 3360x^7 - 1756x^6 - 3502x^5 + 1045x^4 + 2560x^3 - 172x^2 - 368x + 41	\( 2^{24}\cdot 3^{4}\cdot 5^{12}\cdot 29^{4} \)	16T781	Trivial (GRH)
16.0.294897793270447177990144.1	x^16 - 12x^14 - 16x^13 + 66x^12 + 176x^11 + 12x^10 - 584x^9 - 775x^8 + 608x^7 + 3464x^6 + 5800x^5 + 5888x^4 + 4000x^3 + 1792x^2 + 480x + 62	\( 2^{56}\cdot 7^{2}\cdot 17^{4} \)	16T781	$[2]$ (GRH)
16.12.296637086736000000000000.1	x^16 - 12x^14 + 46x^12 - 41x^10 - 106x^8 + 182x^6 - 6x^4 - 49x^2 + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 41^{4} \)	16T781	Trivial (GRH)
16.4.296637086736000000000000.1	x^16 + 12x^14 + 46x^12 + 41x^10 - 106x^8 - 182x^6 - 6x^4 + 49x^2 + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 41^{4} \)	16T781	$[2]$ (GRH)
16.12.296637086736000000000000.2	x^16 - 13x^14 + 61x^12 - 124x^10 + 99x^8 - 2x^6 - 26x^4 + 4x^2 + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 41^{4} \)	16T781	Trivial (GRH)
16.4.296637086736000000000000.2	x^16 + 13x^14 + 61x^12 + 124x^10 + 99x^8 + 2x^6 - 26x^4 - 4x^2 + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 41^{4} \)	16T781	$[2]$ (GRH)
16.8.744861422351789571702784.1	x^16 - 8x^15 + 20x^14 - 82x^12 + 112x^11 - 16x^10 + 304x^9 - 1364x^8 + 1368x^7 + 2384x^6 - 7816x^5 + 8622x^4 - 3880x^3 - 204x^2 + 640x - 79	\( 2^{50}\cdot 17^{4}\cdot 89^{2} \)	16T781	Trivial (GRH)
16.0.1400236755856000000000000.1	x^16 - 4x^15 + 2x^14 - 2x^13 + 81x^12 - 96x^11 + 342x^10 - 876x^9 + 1537x^8 - 2090x^7 + 3498x^6 - 4348x^5 + 3372x^4 - 3936x^3 + 3904x^2 - 1280x + 256	\( 2^{16}\cdot 5^{12}\cdot 29^{2}\cdot 101^{4} \)	16T781	$[12]$ (GRH)
16.8.2979445689407158286811136.1	x^16 - 16x^14 - 8x^13 - 64x^12 - 112x^11 + 1284x^10 + 2616x^9 + 1044x^8 + 2160x^7 + 2448x^6 - 1936x^5 + 108x^4 + 928x^3 - 820x^2 + 272x - 31	\( 2^{52}\cdot 17^{4}\cdot 89^{2} \)	16T781	$[2]$ (GRH)
16.8.2979445689407158286811136.2	x^16 - 12x^14 - 40x^13 + 8x^12 + 272x^11 + 580x^10 - 120x^9 - 2282x^8 - 1456x^7 + 3596x^6 + 3256x^5 - 2712x^4 - 3072x^3 + 604x^2 + 1224x + 289	\( 2^{52}\cdot 17^{4}\cdot 89^{2} \)	16T781	Trivial (GRH)
16.0.18425247191296000000000000.1	x^16 + 42x^14 + 735x^12 + 6972x^10 + 38719x^8 + 135438x^6 + 356920x^4 + 444048x^2 + 1628176	\( 2^{20}\cdot 5^{12}\cdot 11^{2}\cdot 29^{6} \)	16T781	$[2, 2]$ (GRH)
16.0.18425247191296000000000000.2	x^16 - 43x^14 + 850x^12 - 10098x^10 + 77159x^8 - 364002x^6 + 1032100x^4 - 1737912x^2 + 1628176	\( 2^{20}\cdot 5^{12}\cdot 11^{2}\cdot 29^{6} \)	16T781	$[2, 2]$ (GRH)
16.0.1996961573765376000000000000.1	x^16 + 49x^14 + 987x^12 + 10477x^10 + 62235x^8 + 201538x^6 + 317672x^4 + 190896x^2 + 26896	\( 2^{20}\cdot 3^{8}\cdot 5^{12}\cdot 29^{4}\cdot 41^{2} \)	16T781	$[2, 2, 296]$ (GRH)
16.0.3869303279468176000000000000.1	x^16 - 28x^14 + 788x^12 - 11316x^10 + 162415x^8 - 1399986x^6 + 12864693x^4 - 62924873x^2 + 341917081	\( 2^{16}\cdot 5^{12}\cdot 11^{2}\cdot 29^{4}\cdot 41^{4} \)	16T781	$[2, 2]$ (GRH)
16.8.17142224957643668854696574976.1	x^16 - 8x^15 + 24x^14 + 80x^13 - 1056x^12 + 3872x^11 - 3040x^10 - 27544x^9 + 120834x^8 - 213624x^7 + 78280x^6 + 355344x^5 - 662896x^4 + 585152x^3 - 422432x^2 + 210216x - 9281	\( 2^{58}\cdot 3^{4}\cdot 7^{6}\cdot 79^{2} \)	16T781	Trivial (GRH)
16.8.17142224957643668854696574976.2	x^16 - 8x^15 + 16x^14 - 24x^13 - 252x^12 + 648x^11 + 1576x^10 + 352x^9 + 64x^8 - 14368x^7 - 30320x^6 + 11248x^5 + 24088x^4 - 14832x^3 + 98064x^2 + 188176x + 71138	\( 2^{58}\cdot 3^{4}\cdot 7^{6}\cdot 79^{2} \)	16T781	Trivial (GRH)
16.16.77004006676572437563964391424.1	x^16 - 8x^15 - 48x^14 + 448x^13 + 900x^12 - 10104x^11 - 8888x^10 + 117840x^9 + 56250x^8 - 747688x^7 - 264112x^6 + 2427744x^5 + 749036x^4 - 3218552x^3 - 441080x^2 + 1107856x - 44927	\( 2^{56}\cdot 7^{4}\cdot 17^{4}\cdot 73^{2} \)	16T781	Trivial (GRH)
16.16.77004006676572437563964391424.2	x^16 - 72x^14 - 96x^13 + 1792x^12 + 4488x^11 - 16144x^10 - 62168x^9 + 29860x^8 + 327552x^7 + 219304x^6 - 583440x^5 - 721408x^4 + 278896x^3 + 600216x^2 + 27744x - 114206	\( 2^{56}\cdot 7^{4}\cdot 17^{4}\cdot 73^{2} \)	16T781	Trivial (GRH)
16.0.143132753548578816000000000000.1	x^16 - 4x^15 + 2x^14 + 54x^13 + 331x^12 - 1300x^11 - 10562x^10 - 15320x^9 + 27997x^8 + 244660x^7 + 934638x^6 + 2249700x^5 + 4135411x^4 + 6674934x^3 + 8231782x^2 + 6005216x + 1852321	\( 2^{24}\cdot 3^{4}\cdot 5^{12}\cdot 11^{2}\cdot 29^{4}\cdot 71^{2} \)	16T781	$[2, 4]$ (GRH)
16.0.153105535150776576000000000000.1	x^16 + 33x^14 + 253x^12 - 569x^10 + 13565x^8 + 387086x^6 + 1663848x^4 - 562912x^2 + 2062096	\( 2^{20}\cdot 3^{8}\cdot 5^{12}\cdot 29^{4}\cdot 359^{2} \)	16T781	$[2]$ (GRH)
16.0.196489104971479056000000000000.1	x^16 + 50x^14 + 958x^12 + 8975x^10 + 44479x^8 + 120000x^6 + 171072x^4 + 112320x^2 + 20736	\( 2^{16}\cdot 3^{4}\cdot 5^{12}\cdot 11^{8}\cdot 29^{4} \)	16T781	$[2, 4, 100]$ (GRH)
16.0.215924870769789347131555840000.1	x^16 + 32x^14 + 496x^12 + 3648x^10 + 12301x^8 - 107160x^6 + 776600x^4 - 1903500x^2 + 1380625	\( 2^{28}\cdot 5^{4}\cdot 17^{12}\cdot 47^{2} \)	16T781	$[2, 2]$ (GRH)
16.8.6513925684721600930241986953216.1	x^16 - 6x^15 - 9x^14 + 118x^13 - 765x^12 + 1842x^11 + 2973x^10 - 33624x^9 + 93214x^8 - 97134x^7 - 91951x^6 + 457456x^5 - 744437x^4 + 738828x^3 - 401358x^2 + 76790x + 1801	\( 2^{20}\cdot 13^{6}\cdot 17^{12}\cdot 47^{2} \)	16T781	$[2]$ (GRH)
16.8.6744519278804597787590135906304.1	x^16 - 8x^15 + 24x^14 + 32x^13 - 1824x^12 + 16720x^11 - 103232x^10 + 425872x^9 - 1039068x^8 + 1362160x^7 + 2223088x^6 - 10653152x^5 + 14305216x^4 - 25222144x^3 + 4498080x^2 + 40496544x + 11812348	\( 2^{58}\cdot 3^{4}\cdot 7^{6}\cdot 1567^{2} \)	16T781	$[2]$ (GRH)