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 48 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.40886114501953125.1	x^16 - 5x^15 + 6x^14 + 10x^13 - 28x^12 + 10x^11 + 18x^10 - 5x^9 - 5x^8 - 25x^7 + 32x^6 - 5x^5 + 2x^4 - 10x^3 + 4x^2 + 1	\( 3^{8}\cdot 5^{14}\cdot 1021 \)	16T1379	Trivial
16.0.58723833251953125.1	x^16 - 8x^15 + 35x^14 - 105x^13 + 238x^12 - 427x^11 + 624x^10 - 755x^9 + 764x^8 - 649x^7 + 463x^6 - 276x^5 + 137x^4 - 56x^3 + 18x^2 - 4x + 1	\( 3^{8}\cdot 5^{12}\cdot 61\cdot 601 \)	16T1379	Trivial
16.0.3117056000000000000.1	x^16 - 6x^15 + 23x^14 - 68x^13 + 148x^12 - 248x^11 + 346x^10 - 384x^9 + 293x^8 - 132x^7 + 29x^6 + 4x^5 - 7x^4 - 4x^3 + 7x^2 - 2x + 1	\( 2^{24}\cdot 5^{12}\cdot 761 \)	16T1379	Trivial
16.10.82837504000000000000.1	x^16 - 10x^14 + 27x^12 - 30x^10 - 40x^9 + 64x^8 + 100x^7 - 110x^6 - 80x^5 + 78x^4 + 20x^3 - 20x^2 + 1	\( -\,2^{32}\cdot 5^{12}\cdot 79 \)	16T1379	Trivial (GRH)
16.6.82837504000000000000.1	x^16 - 4x^15 + 10x^14 - 20x^13 + 27x^12 - 28x^11 + 40x^9 - 76x^8 + 96x^7 - 82x^6 + 16x^5 + 43x^4 - 24x^3 - 8x^2 + 4x + 1	\( -\,2^{32}\cdot 5^{12}\cdot 79 \)	16T1379	Trivial (GRH)
16.8.252706816000000000000.1	x^16 - 4x^15 - 2x^14 + 36x^13 - 83x^12 + 80x^11 + 22x^10 - 172x^9 + 245x^8 - 172x^7 + 22x^6 + 80x^5 - 83x^4 + 36x^3 - 2x^2 - 4x + 1	\( 2^{32}\cdot 5^{12}\cdot 241 \)	16T1379	Trivial (GRH)
16.8.252706816000000000000.2	x^16 - 8x^15 + 24x^14 - 24x^13 - 53x^12 + 252x^11 - 522x^10 + 696x^9 - 669x^8 + 584x^7 - 522x^6 + 288x^5 + 42x^4 - 136x^3 + 44x^2 + 8x - 4	\( 2^{32}\cdot 5^{12}\cdot 241 \)	16T1379	Trivial (GRH)
16.12.687865856000000000000.1	x^16 - 10x^14 - 4x^13 + 26x^12 + 40x^11 - 14x^10 - 108x^9 + 21x^8 + 136x^7 - 82x^6 - 72x^5 + 82x^4 + 4x^3 - 24x^2 + 4x + 1	\( 2^{36}\cdot 5^{12}\cdot 41 \)	16T1379	Trivial (GRH)
16.4.687865856000000000000.1	x^16 - 4x^15 + 2x^14 + 4x^13 - 14x^12 + 20x^11 - 22x^10 + 20x^9 - 18x^8 + 20x^7 - 22x^6 + 20x^5 - 14x^4 + 4x^3 + 2x^2 - 4x + 1	\( 2^{36}\cdot 5^{12}\cdot 41 \)	16T1379	Trivial
16.0.797966336000000000000.1	x^16 - 4x^14 - 8x^13 - 8x^12 + 24x^11 + 102x^10 + 100x^9 - 258x^8 - 672x^7 - 122x^6 + 1032x^5 + 1301x^4 + 776x^3 + 358x^2 + 148x + 31	\( 2^{32}\cdot 5^{12}\cdot 761 \)	16T1379	$[2]$
16.10.1325400064000000000000.1	x^16 - 14x^14 - 4x^13 + 64x^12 + 52x^11 - 132x^10 - 116x^9 + 87x^8 + 8x^7 - 56x^6 + 72x^5 + 88x^4 + 40x^3 + 22x^2 + 8x + 1	\( -\,2^{36}\cdot 5^{12}\cdot 79 \)	16T1379	Trivial (GRH)
16.6.1325400064000000000000.1	x^16 - 8x^15 + 24x^14 - 16x^13 - 108x^12 + 400x^11 - 688x^10 + 624x^9 - 88x^8 - 544x^7 + 760x^6 - 480x^5 + 80x^4 + 112x^3 - 96x^2 + 32x - 4	\( -\,2^{36}\cdot 5^{12}\cdot 79 \)	16T1379	Trivial (GRH)
16.8.1427111936000000000000.1	x^16 - 8x^15 + 28x^14 - 56x^13 + 57x^12 + 12x^11 - 102x^10 + 92x^9 - 8x^7 - 74x^6 + 44x^5 + 17x^4 + 4x^3 - 12x^2 + 1	\( 2^{32}\cdot 5^{12}\cdot 1361 \)	16T1379	Trivial (GRH)
16.8.1427111936000000000000.2	x^16 - 4x^15 + 2x^14 + 8x^13 - 14x^12 + 24x^11 - 58x^10 + 24x^9 + 122x^8 - 140x^7 - 22x^6 + 92x^5 - 23x^4 - 16x^3 + 4x^2 + 1	\( 2^{32}\cdot 5^{12}\cdot 1361 \)	16T1379	Trivial (GRH)
16.6.1486355184000000000000.1	x^16 - 8x^15 + 36x^14 - 112x^13 + 259x^12 - 462x^11 + 637x^10 - 666x^9 + 491x^8 - 190x^7 - 63x^6 + 154x^5 - 106x^4 + 30x^3 + 5x^2 - 6x + 1	\( -\,2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 14159 \)	16T1379	Trivial (GRH)
16.14.1585557504000000000000.1	x^16 - 4x^15 - 12x^14 + 70x^13 - 25x^12 - 262x^11 + 290x^10 + 326x^9 - 604x^8 - 50x^7 + 490x^6 - 146x^5 - 152x^4 + 76x^3 + 12x^2 - 10x + 1	\( -\,2^{24}\cdot 3^{8}\cdot 5^{12}\cdot 59 \)	16T1379	Trivial (GRH)
16.2.1585557504000000000000.1	x^16 - 4x^15 + 4x^14 + 8x^13 - 7x^12 - 78x^11 + 342x^10 - 758x^9 + 1146x^8 - 1332x^7 + 1424x^6 - 1532x^5 + 1570x^4 - 1306x^3 + 710x^2 - 308x + 61	\( -\,2^{24}\cdot 3^{8}\cdot 5^{12}\cdot 59 \)	16T1379	Trivial
16.12.1639305216000000000000.1	x^16 - 8x^15 + 18x^14 + 8x^13 - 82x^12 + 72x^11 + 104x^10 - 136x^9 - 77x^8 + 12x^7 + 116x^6 + 80x^5 - 122x^4 - 16x^3 + 42x^2 - 12x + 1	\( 2^{24}\cdot 3^{8}\cdot 5^{12}\cdot 61 \)	16T1379	Trivial (GRH)
16.4.1639305216000000000000.1	x^16 - 8x^15 + 30x^14 - 64x^13 + 68x^12 - 24x^11 - 6x^10 + 24x^9 - 155x^8 + 228x^7 - 82x^6 + 116x^5 - 188x^4 - 4x^3 - 28x^2 + 32x + 1	\( 2^{24}\cdot 3^{8}\cdot 5^{12}\cdot 61 \)	16T1379	Trivial (GRH)
16.6.3641388982686006250000.1	x^16 - 6x^15 + 15x^14 - 25x^13 + 26x^12 - 12x^11 - 11x^10 + 78x^9 - 251x^8 + 522x^7 - 791x^6 + 732x^5 - 394x^4 + 120x^3 - 9x + 1	\( -\,2^{4}\cdot 5^{8}\cdot 17^{12} \)	16T1379	Trivial (GRH)
16.10.4810420224000000000000.1	x^16 - 2x^15 - 10x^14 + 18x^13 + 43x^12 - 64x^11 - 144x^10 + 166x^9 + 356x^8 - 172x^7 - 542x^6 - 144x^5 + 200x^4 + 88x^3 - 24x^2 - 10x + 1	\( -\,2^{24}\cdot 3^{8}\cdot 5^{12}\cdot 179 \)	16T1379	Trivial (GRH)
16.14.4810420224000000000000.1	x^16 - 6x^15 - 2x^14 + 76x^13 - 118x^12 - 194x^11 + 618x^10 - 346x^9 - 266x^8 + 350x^7 - 216x^6 + 62x^5 + 123x^4 - 70x^3 - 20x^2 + 8x + 1	\( -\,2^{24}\cdot 3^{8}\cdot 5^{12}\cdot 179 \)	16T1379	Trivial (GRH)
16.2.4810420224000000000000.1	x^16 - 6x^15 + 14x^14 - 8x^13 - 22x^12 + 38x^11 + 82x^10 - 422x^9 + 786x^8 - 458x^7 - 1096x^6 + 3482x^5 - 4945x^4 + 4266x^3 - 2080x^2 + 428x + 61	\( -\,2^{24}\cdot 3^{8}\cdot 5^{12}\cdot 179 \)	16T1379	Trivial
16.6.4810420224000000000000.1	x^16 - 2x^15 - 2x^14 + 8x^13 - 14x^12 - 10x^11 - 8x^10 + 30x^9 - 133x^8 - 30x^7 + 72x^6 - 290x^5 - 114x^4 - 128x^3 - 42x^2 + 2x + 1	\( -\,2^{24}\cdot 3^{8}\cdot 5^{12}\cdot 179 \)	16T1379	Trivial (GRH)
16.12.4864167936000000000000.1	x^16 - 2x^15 - 2x^14 + 12x^13 - 2x^12 - 72x^11 - 126x^10 + 436x^9 + 598x^8 - 1122x^7 - 834x^6 + 960x^5 + 423x^4 - 154x^3 - 58x^2 + 2x + 1	\( 2^{24}\cdot 3^{8}\cdot 5^{12}\cdot 181 \)	16T1379	Trivial (GRH)
16.4.4864167936000000000000.1	x^16 - 2x^15 - 10x^14 + 14x^13 - 7x^12 - 6x^11 + 4x^10 - 54x^9 - 95x^8 + 162x^7 + 18x^6 - 316x^5 + 67x^4 + 164x^3 - 128x^2 - 52x + 61	\( 2^{24}\cdot 3^{8}\cdot 5^{12}\cdot 181 \)	16T1379	Trivial (GRH)
16.8.9220859309737679781888.1	x^16 - 8x^15 + 28x^14 - 56x^13 + 62x^12 - 8x^11 - 92x^10 + 152x^9 - 99x^8 - 32x^7 + 112x^6 - 80x^5 + 4x^4 + 32x^3 - 16x^2 + 1	\( 2^{48}\cdot 3^{8}\cdot 4993 \)	16T1379	Trivial (GRH)
16.12.12767461376000000000000.1	x^16 - 4x^15 - 2x^14 + 40x^13 - 80x^12 - 12x^11 + 270x^10 - 304x^9 - 209x^8 + 560x^7 - 110x^6 - 316x^5 + 158x^4 + 36x^3 - 28x^2 + 1	\( 2^{36}\cdot 5^{12}\cdot 761 \)	16T1379	Trivial (GRH)
16.4.12767461376000000000000.1	x^16 + 4x^14 - 8x^13 - 12x^12 - 64x^11 - 156x^10 - 216x^9 - 266x^8 - 64x^7 + 108x^6 + 520x^5 + 1492x^4 + 2048x^3 + 1324x^2 + 344x + 1	\( 2^{36}\cdot 5^{12}\cdot 761 \)	16T1379	Trivial (GRH)
16.10.21206401024000000000000.1	x^16 - 12x^14 - 8x^13 + 38x^12 + 72x^11 - 20x^10 - 180x^9 - 119x^8 + 128x^7 + 240x^6 + 36x^5 - 120x^4 - 80x^3 + 12x^2 + 12x + 1	\( -\,2^{40}\cdot 5^{12}\cdot 79 \)	16T1379	Trivial (GRH)
16.10.22220184100693723840512.1	x^16 - 16x^14 - 8x^13 + 48x^12 + 96x^11 + 40x^10 - 232x^9 - 10x^8 - 64x^6 + 112x^5 + 68x^4 - 16x^2 - 16x - 2	\( -\,2^{56}\cdot 3^{8}\cdot 47 \)	16T1379	Trivial (GRH)
16.6.22220184100693723840512.1	x^16 - 8x^14 - 8x^13 + 12x^12 - 16x^11 - 80x^10 + 128x^9 + 628x^8 + 960x^7 + 1040x^6 + 968x^5 + 660x^4 + 304x^3 + 96x^2 + 16x + 1	\( -\,2^{56}\cdot 3^{8}\cdot 47 \)	16T1379	Trivial (GRH)
16.10.22220184100693723840512.2	x^16 - 8x^14 - 8x^13 + 12x^12 + 80x^11 - 80x^10 - 40x^9 - 182x^8 + 576x^7 - 280x^6 - 448x^5 + 588x^4 - 224x^3 + 16x - 2	\( -\,2^{56}\cdot 3^{8}\cdot 47 \)	16T1379	Trivial (GRH)
16.12.272788217576601673531392.1	x^16 - 16x^14 - 16x^13 + 96x^12 + 192x^11 - 176x^10 - 776x^9 - 394x^8 + 960x^7 + 1424x^6 + 416x^5 - 364x^4 - 192x^3 + 32x^2 + 16x - 2	\( 2^{56}\cdot 3^{8}\cdot 577 \)	16T1379	Trivial (GRH)
16.4.272788217576601673531392.1	x^16 - 16x^13 - 8x^12 - 16x^11 + 88x^10 + 24x^9 + 100x^8 - 320x^7 + 96x^6 + 32x^5 + 664x^4 - 464x^3 + 400x^2 - 104x + 1	\( 2^{56}\cdot 3^{8}\cdot 577 \)	16T1379	Trivial (GRH)
16.16.467277674256000000000000.1	x^16 - 8x^15 + 12x^14 + 56x^13 - 161x^12 - 126x^11 + 679x^10 + 48x^9 - 1462x^8 + 170x^7 + 1785x^6 - 140x^5 - 1198x^4 - 96x^3 + 344x^2 + 96x + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 4451281 \)	16T1379	Trivial (GRH)
16.0.545103665278720501874688.1	x^16 + 16x^14 - 16x^13 + 108x^12 - 152x^11 + 472x^10 - 600x^9 + 1122x^8 - 1136x^7 + 1280x^6 - 352x^5 - 340x^4 + 784x^3 + 32x^2 - 448x + 382	\( 2^{56}\cdot 3^{8}\cdot 1153 \)	16T1379	$[2, 8]$ (GRH)
16.16.545103665278720501874688.1	x^16 - 24x^14 - 16x^13 + 208x^12 + 248x^11 - 728x^10 - 1200x^9 + 812x^8 + 1888x^7 - 336x^6 - 1248x^5 + 120x^4 + 344x^3 - 56x^2 - 16x + 1	\( 2^{56}\cdot 3^{8}\cdot 1153 \)	16T1379	Trivial (GRH)
16.8.1177363922970214400000000.1	x^16 - 8x^15 + 28x^14 - 56x^13 + 58x^12 + 16x^11 - 152x^10 + 232x^9 - 149x^8 - 48x^7 + 168x^6 - 120x^5 + 6x^4 + 48x^3 - 24x^2 + 4	\( 2^{44}\cdot 5^{8}\cdot 171329 \)	16T1379	Trivial (GRH)
16.8.2817498546176000000000000.1	x^16 + 4x^14 - 60x^12 - 24x^10 + 584x^8 + 176x^6 - 1360x^4 - 416x^2 + 656	\( 2^{48}\cdot 5^{12}\cdot 41 \)	16T1379	Trivial (GRH)
16.8.2817498546176000000000000.2	x^16 - 8x^14 - 40x^12 + 232x^10 + 269x^8 - 1092x^6 - 1030x^4 - 132x^2 + 41	\( 2^{48}\cdot 5^{12}\cdot 41 \)	16T1379	Trivial (GRH)
16.0.3268470112256000000000000.1	x^16 + 32x^14 + 418x^12 + 2864x^10 + 10975x^8 + 23024x^6 + 23518x^4 + 8432x^2 + 761	\( 2^{44}\cdot 5^{12}\cdot 761 \)	16T1379	$[50]$ (GRH)
16.8.3268470112256000000000000.1	x^16 - 8x^15 + 20x^14 - 12x^13 - 120x^12 + 660x^11 - 1612x^10 + 2072x^9 - 1563x^8 + 1204x^7 + 512x^6 - 5296x^5 + 8818x^4 - 5740x^3 + 476x^2 + 812x - 199	\( 2^{44}\cdot 5^{12}\cdot 761 \)	16T1379	Trivial (GRH)
16.8.3268470112256000000000000.2	x^16 - 8x^14 - 22x^12 + 244x^10 + 55x^8 - 1996x^6 + 738x^4 + 3252x^2 + 761	\( 2^{44}\cdot 5^{12}\cdot 761 \)	16T1379	Trivial (GRH)
16.8.3268470112256000000000000.3	x^16 - 8x^15 + 12x^14 + 24x^13 - 102x^12 + 176x^11 - 296x^10 + 392x^9 + 498x^8 - 1976x^7 + 2736x^6 - 1232x^5 - 652x^4 + 1648x^3 - 1512x^2 + 336x - 4	\( 2^{44}\cdot 5^{12}\cdot 761 \)	16T1379	Trivial (GRH)
16.8.3268470112256000000000000.4	x^16 - 4x^14 - 68x^12 + 108x^10 + 1230x^8 - 28x^6 - 5108x^4 - 3916x^2 + 761	\( 2^{44}\cdot 5^{12}\cdot 761 \)	16T1379	Trivial (GRH)
16.12.90819108489560418567132807168.1	x^16 - 40x^14 - 88x^13 + 392x^12 + 2400x^11 + 2544x^10 - 18160x^9 - 61060x^8 - 17568x^7 + 289256x^6 + 654904x^5 - 176464x^4 - 1937600x^3 - 824504x^2 + 1011312x - 162479	\( 2^{56}\cdot 3^{8}\cdot 577^{3} \)	16T1379	Trivial (GRH)
16.4.90819108489560418567132807168.1	x^16 + 40x^14 - 176x^13 + 388x^12 - 4624x^11 + 4048x^10 - 30832x^9 + 84364x^8 + 66016x^7 + 835200x^6 + 1334528x^5 + 3150192x^4 + 3657696x^3 + 2988832x^2 + 2109376x - 1981832	\( 2^{56}\cdot 3^{8}\cdot 577^{3} \)	16T1379	$[2, 2]$ (GRH)