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 50 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.59436404287430625.1	x^16 - 2x^15 - x^14 + 2x^12 + 5x^11 - 2x^10 + 3x^9 + x^8 - 3x^7 - 2x^6 - 5x^5 + 2x^4 - x^2 + 2x + 1	\( 3^{14}\cdot 5^{4}\cdot 7^{6}\cdot 13^{2} \)	16T1177	Trivial
16.0.59436404287430625.2	x^16 - 7x^15 + 25x^14 - 64x^13 + 130x^12 - 214x^11 + 289x^10 - 319x^9 + 286x^8 - 210x^7 + 129x^6 - 72x^5 + 42x^4 - 24x^3 + 15x^2 - 9x + 3	\( 3^{14}\cdot 5^{4}\cdot 7^{6}\cdot 13^{2} \)	16T1177	Trivial
16.0.146031297540653056.1	x^16 + 6x^14 + 21x^12 + 40x^10 + 50x^8 + 30x^6 + 8x^4 + 4x^2 + 1	\( 2^{32}\cdot 7^{6}\cdot 17^{2} \)	16T1177	Trivial
16.4.146031297540653056.1	x^16 - 6x^14 + 21x^12 - 40x^10 + 50x^8 - 30x^6 + 8x^4 - 4x^2 + 1	\( 2^{32}\cdot 7^{6}\cdot 17^{2} \)	16T1177	Trivial
16.0.267302963318358016.1	x^16 - 4x^15 + 6x^14 - 8x^13 + 15x^12 - 12x^11 + 2x^10 - 12x^9 - x^8 + 12x^7 + 2x^6 + 12x^5 + 15x^4 + 8x^3 + 6x^2 + 4x + 1	\( 2^{32}\cdot 7^{6}\cdot 23^{2} \)	16T1177	Trivial
16.4.267302963318358016.1	x^16 - 4x^15 + 6x^14 - 11x^12 + 16x^11 - 8x^10 - 8x^9 + 4x^8 + 56x^7 - 134x^6 + 144x^5 - 86x^4 + 24x^3 + 2x^2 - 4x + 1	\( 2^{32}\cdot 7^{6}\cdot 23^{2} \)	16T1177	Trivial
16.0.10891836672635305984.1	x^16 - 6x^15 + 19x^14 - 42x^13 + 69x^12 - 80x^11 + 66x^10 - 68x^9 + 109x^8 - 134x^7 + 99x^6 - 42x^5 + 45x^4 - 60x^3 + 44x^2 - 16x + 4	\( 2^{28}\cdot 17^{6}\cdot 41^{2} \)	16T1177	Trivial
16.0.10891836672635305984.2	x^16 - 6x^15 + 19x^14 - 38x^13 + 58x^12 - 86x^11 + 151x^10 - 258x^9 + 378x^8 - 442x^7 + 389x^6 - 246x^5 + 99x^4 - 20x^3 + 6x^2 - 8x + 4	\( 2^{28}\cdot 17^{6}\cdot 41^{2} \)	16T1177	Trivial
16.0.93846982311209926656.1	x^16 - 6x^15 + 13x^14 - 6x^13 - 11x^12 - 24x^11 + 115x^10 - 96x^9 - 77x^8 + 138x^7 + 10x^6 - 96x^5 + 40x^4 + 24x^3 - 32x^2 + 16	\( 2^{16}\cdot 3^{14}\cdot 11^{6}\cdot 13^{2} \)	16T1177	$[2]$
16.4.93846982311209926656.1	x^16 - 4x^15 + 22x^13 - 22x^12 - 48x^11 + 106x^10 - 40x^9 - 93x^8 + 158x^7 - 98x^6 + 60x^5 - 61x^4 + 28x^3 - 27x^2 - 10x + 1	\( 2^{16}\cdot 3^{14}\cdot 11^{6}\cdot 13^{2} \)	16T1177	Trivial
16.8.93846982311209926656.1	x^16 - 4x^15 + 5x^14 - 6x^13 + 8x^12 + 10x^11 - 17x^10 - 18x^9 + 25x^8 - 12x^7 + 7x^6 + 32x^5 - 46x^4 + 6x^3 + 17x^2 - 8x + 1	\( 2^{16}\cdot 3^{14}\cdot 11^{6}\cdot 13^{2} \)	16T1177	Trivial
16.4.93846982311209926656.2	x^16 + 2x^14 - 6x^13 - 2x^12 - 6x^11 - 22x^10 - 35x^8 - 18x^7 + 110x^6 + 108x^5 + 139x^4 + 192x^3 + 71x^2 - 6x + 1	\( 2^{16}\cdot 3^{14}\cdot 11^{6}\cdot 13^{2} \)	16T1177	Trivial
16.0.647004903499506909184.1	x^16 + 6x^14 - 12x^13 - 2x^12 - 56x^11 + 6x^10 - 12x^9 + 257x^8 + 272x^7 + 124x^6 - 176x^5 - 180x^4 + 128x^3 + 48x^2 - 64x + 16	\( 2^{32}\cdot 17^{6}\cdot 79^{2} \)	16T1177	$[4]$
16.8.647004903499506909184.1	x^16 - 8x^14 + 30x^12 - 28x^10 - 123x^8 + 260x^6 - 128x^4 + 8x^2 + 4	\( 2^{32}\cdot 17^{6}\cdot 79^{2} \)	16T1177	Trivial
16.4.802983833359687890625.1	x^16 - 7x^15 + 23x^14 - 38x^13 + 16x^12 + 58x^11 - 115x^10 + 55x^9 + 92x^8 - 136x^7 - 15x^6 + 90x^5 - 32x^4 + 4x^3 + 29x^2 - 13x - 11	\( 5^{8}\cdot 11^{2}\cdot 13^{4}\cdot 29^{6} \)	16T1177	Trivial
16.4.802983833359687890625.2	x^16 - 3x^15 + x^13 - 14x^12 + 27x^11 + 13x^10 - 32x^9 + 66x^8 - 113x^7 - 82x^6 + 53x^5 - 29x^4 + 19x^3 - 10x^2 - 7x + 1	\( 5^{8}\cdot 11^{2}\cdot 13^{4}\cdot 29^{6} \)	16T1177	Trivial
16.4.975431683548607676416.1	x^16 - 4x^15 + 4x^14 - 4x^13 + x^12 + 60x^11 - 68x^10 + 64x^9 - 4x^8 - 84x^7 + 60x^6 + 4x^5 - 31x^4 + 28x^3 - 12x^2 + 1	\( 2^{32}\cdot 17^{6}\cdot 97^{2} \)	16T1177	Trivial
16.4.975431683548607676416.2	x^16 - 8x^15 + 26x^14 - 36x^13 - 30x^12 + 204x^11 - 348x^10 + 224x^9 + 167x^8 - 508x^7 + 540x^6 - 360x^5 + 114x^4 - 36x^3 + 22x^2 + 4x + 1	\( 2^{32}\cdot 17^{6}\cdot 97^{2} \)	16T1177	Trivial
16.0.5063349862493096771584.1	x^16 + 8x^14 + 12x^12 + 16x^10 + 96x^8 + 64x^6 + 192x^4 + 512x^2 + 256	\( 2^{32}\cdot 13^{2}\cdot 17^{8} \)	16T1177	$[2]$
16.8.5063349862493096771584.1	x^16 - 4x^14 + 3x^12 - 2x^10 + 6x^8 - 2x^6 + 3x^4 - 4x^2 + 1	\( 2^{32}\cdot 13^{2}\cdot 17^{8} \)	16T1177	Trivial (GRH)
16.0.20253399449972387086336.1	x^16 - 2x^15 - 4x^13 + 24x^12 - 52x^11 + 40x^10 + 136x^9 + 465x^8 + 598x^7 + 1176x^6 + 2100x^5 + 1958x^4 + 904x^3 + 176x^2 - 8x + 4	\( 2^{34}\cdot 13^{2}\cdot 17^{8} \)	16T1177	$[2]$
16.8.20253399449972387086336.1	x^16 - 8x^15 + 20x^14 - 24x^13 + 78x^12 - 188x^11 + 70x^10 + 318x^8 + 264x^7 - 1088x^6 + 308x^5 + 127x^4 + 240x^3 + 48x^2 - 160x - 8	\( 2^{34}\cdot 13^{2}\cdot 17^{8} \)	16T1177	Trivial
16.8.78845048959888031640625.1	x^16 - 4x^15 + 4x^14 + 11x^13 - 3x^12 - 124x^11 + 36x^10 + 501x^9 - 160x^8 - 2036x^7 - 674x^6 + 5799x^5 + 6352x^4 + 759x^3 - 776x^2 - 16x + 1	\( 5^{8}\cdot 13^{4}\cdot 29^{6}\cdot 109^{2} \)	16T1177	Trivial (GRH)
16.8.78845048959888031640625.2	x^16 - 17x^14 + 100x^12 - 363x^10 + 1375x^8 - 4055x^6 + 7568x^4 - 6969x^2 + 961	\( 5^{8}\cdot 13^{4}\cdot 29^{6}\cdot 109^{2} \)	16T1177	Trivial (GRH)
16.0.97161043836522234765625.1	x^16 + 10x^14 + 17x^12 - 90x^10 + 264x^8 + 9565x^6 + 51533x^4 + 99050x^2 + 63001	\( 5^{8}\cdot 11^{4}\cdot 13^{4}\cdot 29^{6} \)	16T1177	$[2, 2, 2]$
16.0.97161043836522234765625.2	x^16 - x^15 + 7x^14 + 4x^13 + 91x^12 + 83x^11 + 716x^10 + 1948x^9 + 3144x^8 + 2725x^7 + 24945x^6 + 31767x^5 + 69978x^4 + 61938x^3 + 59526x^2 + 37846x + 22201	\( 5^{8}\cdot 11^{4}\cdot 13^{4}\cdot 29^{6} \)	16T1177	$[2, 4]$
16.12.212631446319650906640625.1	x^16 - 25x^14 + 256x^12 - 1455x^10 + 5111x^8 - 10315x^6 + 8856x^4 - 205x^2 + 1	\( 5^{8}\cdot 13^{4}\cdot 29^{6}\cdot 179^{2} \)	16T1177	Trivial (GRH)
16.12.212631446319650906640625.2	x^16 - 4x^15 - 20x^14 + 90x^13 + 161x^12 - 910x^11 - 466x^10 + 5065x^9 - 1299x^8 - 14840x^7 + 11135x^6 + 19836x^5 - 23704x^4 - 5655x^3 + 16385x^2 - 6525x + 725	\( 5^{8}\cdot 13^{4}\cdot 29^{6}\cdot 179^{2} \)	16T1177	Trivial (GRH)
16.0.501864895849804931640625.1	x^16 - 7x^14 - 4x^13 + 122x^12 + 206x^11 + 26x^10 - 402x^9 + 785x^8 + 1298x^7 + 1458x^6 - 672x^5 + 422x^4 + 821x^3 + 473x^2 - 437x + 361	\( 5^{12}\cdot 11^{2}\cdot 13^{4}\cdot 29^{6} \)	16T1177	$[2, 6]$
16.0.501864895849804931640625.2	x^16 - x^15 - 11x^14 - 24x^13 + 47x^12 + 395x^11 + 470x^10 - 2195x^9 - 5787x^8 + 1222x^7 + 17989x^6 + 47881x^5 + 1479x^4 - 199811x^3 - 9038x^2 - 200317x + 657721	\( 5^{12}\cdot 11^{2}\cdot 13^{4}\cdot 29^{6} \)	16T1177	$[2, 6]$
16.4.4423901850630169600000000.1	x^16 - 9x^14 - 187x^12 - 795x^10 - 1619x^8 - 3480x^6 - 5568x^4 - 2523x^2 + 841	\( 2^{16}\cdot 5^{8}\cdot 7^{4}\cdot 11^{2}\cdot 29^{6} \)	16T1177	$[2]$
16.8.4423901850630169600000000.1	x^16 - 2x^14 - 2x^12 - 141x^10 - 207x^8 + 2388x^6 - 2368x^4 - 256x^2 + 256	\( 2^{16}\cdot 5^{8}\cdot 7^{4}\cdot 11^{2}\cdot 29^{6} \)	16T1177	Trivial (GRH)
16.4.4423901850630169600000000.2	x^16 + 2x^14 - 2x^12 + 141x^10 - 207x^8 - 2388x^6 - 2368x^4 + 256x^2 + 256	\( 2^{16}\cdot 5^{8}\cdot 7^{4}\cdot 11^{2}\cdot 29^{6} \)	16T1177	$[2]$
16.8.4423901850630169600000000.2	x^16 + 9x^14 - 187x^12 + 795x^10 - 1619x^8 + 3480x^6 - 5568x^4 + 2523x^2 + 841	\( 2^{16}\cdot 5^{8}\cdot 7^{4}\cdot 11^{2}\cdot 29^{6} \)	16T1177	Trivial (GRH)
16.8.4592902298545177600000000.1	x^16 - 12x^14 - 14x^13 + 35x^12 + 176x^11 - 11x^10 - 1253x^9 + 137x^8 + 6424x^7 + 1954x^6 - 10354x^5 - 8622x^4 - 20660x^3 - 22312x^2 + 11116x + 13444	\( 2^{16}\cdot 5^{8}\cdot 19^{2}\cdot 89^{6} \)	16T1177	$[2]$ (GRH)
16.0.21386894082699289600000000.1	x^16 + 26x^14 + 238x^12 + 1384x^10 + 6123x^8 + 27768x^6 + 99502x^4 + 142578x^2 + 7921	\( 2^{16}\cdot 5^{8}\cdot 41^{2}\cdot 89^{6} \)	16T1177	$[2, 12]$
16.8.73486436776722841600000000.1	x^16 - 35x^14 + 579x^12 - 5236x^10 + 24916x^8 - 66712x^6 + 94143x^4 - 59101x^2 + 11881	\( 2^{20}\cdot 5^{8}\cdot 19^{2}\cdot 89^{6} \)	16T1177	$[2]$ (GRH)
16.8.73486436776722841600000000.2	x^16 - 4x^15 - 18x^14 + 118x^13 - 174x^12 - 70x^11 + 1153x^10 - 6768x^9 + 21967x^8 - 41222x^7 + 51445x^6 - 35784x^5 - 29017x^4 + 95320x^3 - 63472x^2 - 9920x + 15376	\( 2^{20}\cdot 5^{8}\cdot 19^{2}\cdot 89^{6} \)	16T1177	$[2]$ (GRH)
16.0.142450315118638424091787264.1	x^16 - 6x^14 + 51x^12 - 174x^10 + 849x^8 + 580x^6 + 2312x^4 + 1280x^2 + 4096	\( 2^{30}\cdot 7^{4}\cdot 17^{8}\cdot 89^{2} \)	16T1177	$[2, 6, 6]$ (GRH)
16.0.342190305323188633600000000.1	x^16 - 6x^15 + 13x^14 - 44x^13 + 178x^12 - 140x^11 + 870x^10 - 2768x^9 + 617x^8 - 13570x^7 + 31239x^6 + 78298x^5 + 345311x^4 + 479660x^3 + 806840x^2 + 525250x + 466775	\( 2^{20}\cdot 5^{8}\cdot 41^{2}\cdot 89^{6} \)	16T1177	$[2, 32]$ (GRH)
16.16.417950404226786329600000000.1	x^16 - 2x^15 - 43x^14 + 90x^13 + 652x^12 - 1428x^11 - 4106x^10 + 9380x^9 + 9606x^8 - 22916x^7 - 8627x^6 + 22714x^5 + 2729x^4 - 8540x^3 - 160x^2 + 700x - 25	\( 2^{16}\cdot 5^{8}\cdot 13^{4}\cdot 29^{6}\cdot 31^{2} \)	16T1177	Trivial (GRH)
16.16.417950404226786329600000000.2	x^16 - 2x^15 - 43x^14 + 68x^13 + 654x^12 - 802x^11 - 4250x^10 + 4084x^9 + 12122x^8 - 8198x^7 - 13669x^6 + 4082x^5 + 4596x^4 - 1140x^3 - 433x^2 + 150x - 11	\( 2^{16}\cdot 5^{8}\cdot 13^{4}\cdot 29^{6}\cdot 31^{2} \)	16T1177	Trivial (GRH)
16.0.936758026692429703922265625.1	x^16 - 2x^15 + 42x^14 - 101x^13 + 778x^12 - 789x^11 + 8451x^10 - 428x^9 + 66017x^8 + 28096x^7 + 425144x^6 + 264632x^5 + 1669808x^4 + 1021152x^3 + 3693888x^2 + 1192576x + 3748096	\( 5^{8}\cdot 13^{4}\cdot 29^{6}\cdot 109^{4} \)	16T1177	$[2, 2, 2, 32]$ (GRH)
16.0.936758026692429703922265625.2	x^16 - 2x^15 - 9x^14 + 49x^13 - 110x^12 - 637x^11 + 2407x^10 + 1967x^9 - 8307x^8 + 66040x^7 + 124859x^6 - 482089x^5 - 390428x^4 + 2084554x^3 + 242264x^2 - 2226847x + 21327179	\( 5^{8}\cdot 13^{4}\cdot 29^{6}\cdot 109^{4} \)	16T1177	$[2, 2, 64]$ (GRH)
16.0.1175782988427565465600000000.1	x^16 - 2x^15 + 27x^14 - 54x^13 + 487x^12 - 1088x^11 + 6210x^10 - 13364x^9 + 52262x^8 - 82660x^7 + 229594x^6 - 129216x^5 + 397969x^4 + 311462x^3 + 514611x^2 + 490946x + 970939	\( 2^{24}\cdot 5^{8}\cdot 19^{2}\cdot 89^{6} \)	16T1177	$[2, 2, 8]$ (GRH)
16.0.1175782988427565465600000000.2	x^16 + 12x^14 + 96x^12 + 1518x^10 + 10345x^8 + 38982x^6 + 112496x^4 + 142578x^2 + 7921	\( 2^{24}\cdot 5^{8}\cdot 19^{2}\cdot 89^{6} \)	16T1177	$[2, 2, 8]$ (GRH)
16.8.1175782988427565465600000000.3	x^16 - 12x^14 + 96x^12 - 1518x^10 + 10345x^8 - 38982x^6 + 112496x^4 - 142578x^2 + 7921	\( 2^{24}\cdot 5^{8}\cdot 19^{2}\cdot 89^{6} \)	16T1177	$[2, 2]$ (GRH)
16.0.2279205041898214785468596224.1	x^16 - 6x^14 + 81x^12 - 194x^10 + 840x^8 - 350x^6 + 3217x^4 + 1286x^2 + 1849	\( 2^{34}\cdot 7^{4}\cdot 17^{8}\cdot 89^{2} \)	16T1177	$[2, 6, 12]$ (GRH)
16.0.488022614316879794822906640625.1	x^16 + 39x^14 + 948x^12 + 13986x^10 + 138918x^8 + 844707x^6 + 3286212x^4 + 5888892x^2 + 24393721	\( 5^{8}\cdot 13^{4}\cdot 29^{6}\cdot 271181^{2} \)	16T1177	$[2, 4980]$ (GRH)
16.0.488022614316879794822906640625.2	x^16 - 4x^15 + 44x^14 - 144x^13 + 1097x^12 - 3400x^11 + 18491x^10 - 52652x^9 + 222830x^8 - 586952x^7 + 1901988x^6 - 4222836x^5 + 10063831x^4 - 16091218x^3 + 22963320x^2 - 12168844x + 25104719	\( 5^{8}\cdot 13^{4}\cdot 29^{6}\cdot 271181^{2} \)	16T1177	$[6, 1920]$ (GRH)