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 matches 1-50 of 54)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.4186494384765625.1	x^16 - 4x^15 + 8x^14 - 6x^13 - 5x^12 + 15x^11 - 6x^10 - 17x^9 + 26x^8 - 7x^7 - 16x^6 + 17x^5 - 2x^4 - 9x^3 + 9x^2 - 4x + 1	\( 5^{12}\cdot 41^{2}\cdot 101^{2} \)	16T1720	Trivial
16.0.29761640869140625.1	x^16 - 2x^15 - 2x^14 + 3x^13 + 6x^12 - 13x^10 - 5x^9 + 17x^8 + 5x^7 - 13x^6 + 6x^4 - 3x^3 - 2x^2 + 2x + 1	\( 5^{12}\cdot 61^{2}\cdot 181^{2} \)	16T1720	Trivial
16.4.8621564062500000000.1	x^16 - 7x^14 + 18x^12 - 19x^10 + 5x^8 + x^6 - 2x^4 + 3x^2 + 1	\( 2^{8}\cdot 3^{8}\cdot 5^{14}\cdot 29^{2} \)	16T1720	Trivial
16.4.10593592223482249216.1	x^16 - 4x^14 - 2x^12 + 20x^10 - 19x^8 + 20x^4 - 16x^2 + 4	\( 2^{50}\cdot 97^{2} \)	16T1720	Trivial
16.4.64919406220731744256.1	x^16 - 16x^13 - 26x^12 - 32x^11 + 48x^9 + 67x^8 + 48x^7 - 32x^5 - 26x^4 - 16x^3 + 1	\( 2^{44}\cdot 17^{2}\cdot 113^{2} \)	16T1720	Trivial
16.0.100080016000000000000.1	x^16 - 2x^15 + 3x^14 - 6x^13 + 2x^12 + 12x^10 + 8x^9 + 25x^8 + 8x^7 + 12x^6 + 2x^4 - 6x^3 + 3x^2 - 2x + 1	\( 2^{16}\cdot 5^{12}\cdot 41^{2}\cdot 61^{2} \)	16T1720	$[2]$
16.4.100080016000000000000.1	x^16 - 4x^15 + 6x^14 - 4x^13 + 2x^12 + 12x^11 - 37x^10 + 14x^9 + 26x^8 - 12x^7 - 39x^6 + 10x^5 - 14x^4 - 16x^3 - 5x^2 + 1	\( 2^{16}\cdot 5^{12}\cdot 41^{2}\cdot 61^{2} \)	16T1720	Trivial
16.8.100080016000000000000.1	x^16 - 2x^15 - 7x^14 + 24x^13 - 3x^12 - 80x^11 + 97x^10 + 78x^9 - 225x^8 + 38x^7 + 222x^6 - 120x^5 - 123x^4 + 74x^3 + 38x^2 - 12x - 4	\( 2^{16}\cdot 5^{12}\cdot 41^{2}\cdot 61^{2} \)	16T1720	Trivial (GRH)
16.4.100080016000000000000.2	x^16 - 4x^14 - 2x^13 + 5x^12 - 4x^11 + 13x^10 - 32x^9 + 6x^8 - 74x^7 + 16x^6 + 46x^5 - 12x^4 + 8x^3 - 75x^2 + 28x + 1	\( 2^{16}\cdot 5^{12}\cdot 41^{2}\cdot 61^{2} \)	16T1720	Trivial
16.4.147130835062500000000.1	x^16 + 2x^14 - 3x^12 - 10x^10 - 24x^8 - 10x^6 + 8x^4 + 6x^2 + 1	\( 2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 599^{2} \)	16T1720	Trivial (GRH)
16.4.333194314831378776064.1	x^16 - 8x^15 + 20x^14 - 82x^12 + 128x^11 + 4x^10 - 240x^9 + 285x^8 - 8x^7 - 280x^6 + 272x^5 - 76x^4 - 48x^3 + 48x^2 - 16x + 2	\( 2^{60}\cdot 17^{2} \)	16T1720	Trivial (GRH)
16.8.333194314831378776064.1	x^16 - 8x^15 + 36x^14 - 112x^13 + 258x^12 - 456x^11 + 600x^10 - 536x^9 + 179x^8 + 344x^7 - 680x^6 + 616x^5 - 310x^4 + 64x^3 + 12x^2 - 8x + 1	\( 2^{60}\cdot 17^{2} \)	16T1720	Trivial (GRH)
16.4.365421456000000000000.3	x^16 + 4x^14 + 9x^12 + 13x^10 - 21x^8 - 59x^6 - 34x^4 - 3x^2 + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 59^{2} \)	16T1720	Trivial
16.8.365421456000000000000.4	x^16 - 4x^14 + 9x^12 - 13x^10 - 21x^8 + 59x^6 - 34x^4 + 3x^2 + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 59^{2} \)	16T1720	Trivial (GRH)
16.8.365421456000000000000.5	x^16 - 7x^14 + 10x^12 + 18x^10 - 41x^8 + 7x^6 + 15x^4 - 3x^2 + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 59^{2} \)	16T1720	Trivial (GRH)
16.12.741813314062500000000.1	x^16 - 9x^14 + 27x^12 - 22x^10 - 35x^8 + 72x^6 - 38x^4 + 4x^2 + 1	\( 2^{8}\cdot 3^{8}\cdot 5^{14}\cdot 269^{2} \)	16T1720	Trivial (GRH)
16.0.1039792207867206959104.1	x^16 - 4x^15 + 14x^14 - 20x^13 + 35x^12 - 16x^11 + 60x^10 - 40x^9 + 194x^8 - 72x^7 + 292x^6 + 72x^5 + 266x^4 + 80x^3 + 184x^2 + 8	\( 2^{50}\cdot 31^{4} \)	16T1720	Trivial
16.4.1039792207867206959104.1	x^16 - 4x^15 + 14x^14 - 20x^13 + 29x^12 - 48x^11 + 60x^10 - 40x^9 - 46x^8 - 8x^7 - 60x^6 + 200x^5 - 154x^4 - 80x^3 - 88x^2 + 64x - 8	\( 2^{50}\cdot 31^{4} \)	16T1720	Trivial
16.0.1039792207867206959104.2	x^16 - 4x^15 + 6x^14 - 8x^13 + 23x^12 + 32x^11 + 50x^10 + 44x^9 + 45x^8 + 8x^7 + 60x^6 + 24x^5 + 2x^4 + 12x^2 - 8x + 2	\( 2^{50}\cdot 31^{4} \)	16T1720	Trivial
16.4.1039792207867206959104.2	x^16 - 4x^15 + 2x^14 + 16x^13 - 43x^12 + 40x^11 + 46x^10 - 164x^9 + 87x^8 + 312x^7 - 756x^6 + 888x^5 - 738x^4 + 480x^3 - 220x^2 + 56x - 2	\( 2^{50}\cdot 31^{4} \)	16T1720	Trivial
16.4.1332777259325515104256.1	x^16 - 8x^15 + 24x^14 - 24x^13 - 16x^12 + 8x^11 + 96x^10 + 24x^9 - 356x^8 + 8x^7 + 712x^6 - 152x^5 - 656x^4 + 152x^3 + 256x^2 - 56x - 47	\( 2^{62}\cdot 17^{2} \)	16T1720	Trivial (GRH)
16.8.1332777259325515104256.2	x^16 - 8x^15 + 24x^14 - 16x^13 - 92x^12 + 272x^11 - 264x^10 - 96x^9 + 470x^8 - 400x^7 - 8x^6 + 256x^5 - 164x^4 + 40x^2 - 16x + 2	\( 2^{62}\cdot 17^{2} \)	16T1720	Trivial (GRH)
16.12.8183508897293437763584.3	x^16 - 4x^14 - 10x^12 + 72x^10 - 109x^8 + 8x^6 + 94x^4 - 52x^2 + 1	\( 2^{56}\cdot 337^{2} \)	16T1720	Trivial (GRH)
16.4.8183508897293437763584.3	x^16 + 4x^14 - 22x^12 - 88x^10 - 77x^8 + 8x^6 + 34x^4 + 12x^2 + 1	\( 2^{56}\cdot 337^{2} \)	16T1720	Trivial
16.8.8183508897293437763584.3	x^16 + 4x^14 - 10x^12 - 16x^10 + 31x^8 + 8x^6 - 22x^4 + 4x^2 + 1	\( 2^{56}\cdot 337^{2} \)	16T1720	Trivial (GRH)
16.4.8183508897293437763584.4	x^16 + 4x^14 - 10x^12 - 72x^10 - 109x^8 - 8x^6 + 94x^4 + 52x^2 + 1	\( 2^{56}\cdot 337^{2} \)	16T1720	Trivial (GRH)
16.8.8183508897293437763584.4	x^16 + 4x^14 - 14x^12 - 24x^10 + 31x^8 + 32x^6 - 18x^4 - 12x^2 + 1	\( 2^{56}\cdot 337^{2} \)	16T1720	Trivial (GRH)
16.4.18761708397791474089984.1	x^16 - 4x^15 + 2x^14 + 8x^13 + 13x^12 - 128x^11 + 206x^10 + 4x^9 - 205x^8 + 16x^7 + 300x^6 + 296x^5 - 234x^4 - 608x^3 - 312x^2 - 32x + 4	\( 2^{44}\cdot 17^{4}\cdot 113^{2} \)	16T1720	Trivial (GRH)
16.0.58264304400000000000000.1	x^16 - 4x^15 + 19x^14 - 44x^13 + 131x^12 - 202x^11 + 426x^10 - 552x^9 + 1022x^8 - 1098x^7 + 1896x^6 - 1938x^5 + 2096x^4 - 2066x^3 + 1279x^2 - 426x + 61	\( 2^{16}\cdot 3^{8}\cdot 5^{14}\cdot 149^{2} \)	16T1720	$[2]$ (GRH)
16.12.58264304400000000000000.1	x^16 - 8x^15 + 18x^14 + 14x^13 - 115x^12 + 144x^11 + 33x^10 - 198x^9 + 226x^8 - 420x^7 + 455x^6 + 110x^5 - 380x^4 + 50x^3 + 80x^2 - 10x - 5	\( 2^{16}\cdot 3^{8}\cdot 5^{14}\cdot 149^{2} \)	16T1720	Trivial (GRH)
16.4.58264304400000000000000.1	x^16 - 2x^15 - 2x^14 + 26x^13 - 105x^12 + 256x^11 - 457x^10 + 598x^9 - 519x^8 + 110x^7 + 505x^6 - 970x^5 + 1140x^4 - 750x^3 + 325x^2 - 150x + 25	\( 2^{16}\cdot 3^{8}\cdot 5^{14}\cdot 149^{2} \)	16T1720	Trivial (GRH)
16.8.58264304400000000000000.1	x^16 - 2x^15 - 4x^14 + 32x^13 - 94x^12 + 154x^11 - 121x^10 - 94x^9 + 427x^8 - 754x^7 + 759x^6 - 376x^5 - 94x^4 + 782x^3 - 1174x^2 + 708x - 149	\( 2^{16}\cdot 3^{8}\cdot 5^{14}\cdot 149^{2} \)	16T1720	Trivial (GRH)
16.0.58264304400000000000000.2	x^16 - 2x^15 + 17x^14 - 6x^13 + 76x^12 + 88x^11 + 220x^10 + 402x^9 + 809x^8 + 656x^7 + 1880x^6 + 996x^5 + 1776x^4 + 1192x^3 + 1368x^2 + 256x + 16	\( 2^{16}\cdot 3^{8}\cdot 5^{14}\cdot 149^{2} \)	16T1720	$[2]$ (GRH)
16.12.58264304400000000000000.2	x^16 - 6x^15 - x^14 + 54x^13 - 34x^12 - 238x^11 + 276x^10 + 492x^9 - 863x^8 - 382x^7 + 1266x^6 - 62x^5 - 914x^4 + 206x^3 + 299x^2 - 64x - 29	\( 2^{16}\cdot 3^{8}\cdot 5^{14}\cdot 149^{2} \)	16T1720	Trivial (GRH)
16.4.58264304400000000000000.2	x^16 - 6x^15 + 19x^14 - 56x^13 + 116x^12 - 208x^11 + 366x^10 - 418x^9 + 747x^8 - 972x^7 + 1216x^6 - 962x^5 + 766x^4 - 714x^3 + 339x^2 - 54x + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{14}\cdot 149^{2} \)	16T1720	Trivial (GRH)
16.8.58264304400000000000000.2	x^16 - 6x^15 + 11x^14 + 26x^13 - 167x^12 + 254x^11 + 219x^10 - 1322x^9 + 1773x^8 - 36x^7 - 3124x^6 + 4708x^5 - 3077x^4 - 2x^3 + 1544x^2 - 982x + 181	\( 2^{16}\cdot 3^{8}\cdot 5^{14}\cdot 149^{2} \)	16T1720	Trivial (GRH)
16.4.58264304400000000000000.3	x^16 - 6x^15 + 18x^14 - 12x^13 - 29x^12 + 94x^11 - 5x^10 - 36x^9 + 69x^8 - 262x^7 + 150x^6 + 452x^5 - 424x^4 - 224x^3 + 322x^2 + 12x - 89	\( 2^{16}\cdot 3^{8}\cdot 5^{14}\cdot 149^{2} \)	16T1720	Trivial (GRH)
16.8.58264304400000000000000.3	x^16 - 2x^15 - 2x^14 + 16x^13 - 10x^12 - 134x^11 - 22x^10 + 548x^9 + 351x^8 - 850x^7 - 780x^6 + 380x^5 + 555x^4 + 80x^3 - 75x^2 - 20x - 5	\( 2^{16}\cdot 3^{8}\cdot 5^{14}\cdot 149^{2} \)	16T1720	Trivial (GRH)
16.4.58264304400000000000000.4	x^16 - 8x^15 + 42x^14 - 154x^13 + 411x^12 - 828x^11 + 1195x^10 - 1102x^9 + 209x^8 + 1244x^7 - 2445x^6 + 2674x^5 - 1584x^4 + 228x^3 + 293x^2 - 176x + 31	\( 2^{16}\cdot 3^{8}\cdot 5^{14}\cdot 149^{2} \)	16T1720	Trivial (GRH)
16.8.58264304400000000000000.4	x^16 - 4x^15 - x^14 + 6x^13 + 6x^12 + 78x^11 - 74x^10 - 62x^9 - 418x^8 - 548x^7 + 481x^6 + 612x^5 - 204x^4 - 186x^3 + 29x^2 + 14x + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{14}\cdot 149^{2} \)	16T1720	Trivial (GRH)
16.0.168234506896000000000000.1	x^16 - 2x^15 + 13x^14 - 26x^13 + 107x^12 - 160x^11 + 502x^10 - 692x^9 + 1590x^8 - 2262x^7 + 3062x^6 - 4830x^5 + 5312x^4 - 4616x^3 + 5263x^2 - 3702x + 1501	\( 2^{16}\cdot 5^{12}\cdot 41^{4}\cdot 61^{2} \)	16T1720	$[2, 2]$ (GRH)
16.8.168234506896000000000000.1	x^16 - 4x^15 - 11x^14 + 44x^13 + 46x^12 - 152x^11 + 46x^10 + 264x^9 - 1194x^8 - 1856x^7 + 2295x^6 + 6326x^5 + 2167x^4 - 5168x^3 - 5500x^2 - 1764x - 179	\( 2^{16}\cdot 5^{12}\cdot 41^{4}\cdot 61^{2} \)	16T1720	Trivial (GRH)
16.0.1858139754496000000000000.1	x^16 - 2x^15 + 2x^14 + 2x^13 + 27x^12 - 60x^11 - 47x^10 + 186x^9 + 40x^8 - 456x^7 + 783x^6 - 670x^5 + 417x^4 - 162x^3 + 47x^2 - 8x + 1	\( 2^{24}\cdot 5^{12}\cdot 19^{4}\cdot 59^{2} \)	16T1720	$[2]$ (GRH)
16.0.1858139754496000000000000.2	x^16 + 12x^14 + 65x^12 + 202x^10 + 424x^8 + 618x^6 + 665x^4 + 608x^2 + 361	\( 2^{24}\cdot 5^{12}\cdot 19^{4}\cdot 59^{2} \)	16T1720	$[2]$ (GRH)
16.12.3930528293136000000000000.1	x^16 - 6x^15 - 7x^14 + 94x^13 - 88x^12 - 340x^11 + 637x^10 + 42x^9 - 665x^8 + 42x^7 + 637x^6 - 340x^5 - 88x^4 + 94x^3 - 7x^2 - 6x + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 29^{2}\cdot 211^{2} \)	16T1720	Trivial (GRH)
16.16.202486647379893148425650176.1	x^16 - 40x^14 - 16x^13 + 562x^12 + 328x^11 - 3536x^10 - 2112x^9 + 10754x^8 + 5808x^7 - 15272x^6 - 7872x^5 + 9012x^4 + 4704x^3 - 1408x^2 - 768x - 32	\( 2^{48}\cdot 449^{2}\cdot 1889^{2} \)	16T1720	Trivial (GRH)
16.0.636828239527936000000000000.1	x^16 + 40x^14 + 618x^12 + 4700x^10 + 18739x^8 + 39020x^6 + 41542x^4 + 20740x^2 + 3721	\( 2^{36}\cdot 5^{12}\cdot 61^{2}\cdot 101^{2} \)	16T1720	$[2, 142]$ (GRH)
16.16.636828239527936000000000000.1	x^16 - 4x^15 - 32x^14 + 184x^13 + 30x^12 - 1640x^11 + 2104x^10 + 3988x^9 - 9054x^8 - 492x^7 + 9844x^6 - 2008x^5 - 4342x^4 + 376x^3 + 884x^2 + 156x + 1	\( 2^{36}\cdot 5^{12}\cdot 61^{2}\cdot 101^{2} \)	16T1720	Trivial (GRH)
16.0.809946589519572593702600704.1	x^16 + 16x^14 - 8x^13 + 182x^12 + 192x^11 + 1852x^10 + 3672x^9 + 11460x^8 + 20688x^7 + 34928x^6 + 48816x^5 + 47084x^4 + 42912x^3 + 28712x^2 + 19312x + 23428	\( 2^{50}\cdot 449^{2}\cdot 1889^{2} \)	16T1720	$[2, 2, 64]$ (GRH)
16.4.1006215243042816000000000000.1	x^16 + 34x^14 + 405x^12 + 1896x^10 + 2034x^8 - 4574x^6 - 3280x^4 + 1624x^2 + 841	\( 2^{24}\cdot 3^{8}\cdot 5^{12}\cdot 29^{2}\cdot 211^{2} \)	16T1720	$[2]$ (GRH)