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 254)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.145220537353515625.1	x^16 - 6x^15 + 18x^14 - 45x^13 + 105x^12 - 208x^11 + 345x^10 - 496x^9 + 621x^8 - 645x^7 + 535x^6 - 359x^5 + 208x^4 - 106x^3 + 42x^2 - 10x + 1	\( 5^{12}\cdot 29^{6} \)	$C_4\wr C_2$ (as 16T28)	Trivial
16.4.1048576000000000000.1	x^16 + 2x^12 - 41x^8 + 18x^4 + 1	\( 2^{32}\cdot 5^{12} \)	$C_4\wr C_2$ (as 16T28)	Trivial
16.4.2069703095939497984.1	x^16 - 4x^15 + 6x^14 - 4x^13 - 5x^12 + 12x^11 + 12x^10 - 68x^9 + 126x^8 - 132x^7 + 70x^6 - 24x^5 + 28x^4 - 36x^3 + 24x^2 - 8x + 1	\( 2^{44}\cdot 7^{6} \)	$C_4\wr C_2$ (as 16T28)	Trivial
16.4.2386420683693101056.1	x^16 - 2x^15 + x^13 - 2x^12 + 5x^10 + 3x^9 + 4x^8 - 23x^7 + 25x^6 - 31x^5 + 30x^4 - 18x^3 + 10x^2 - 5x + 1	\( 2^{12}\cdot 17^{12} \)	$C_4\wr C_2$ (as 16T28)	Trivial
16.4.2837698174072265625.1	x^16 - 2x^15 - x^14 + 4x^13 - 5x^12 + 11x^11 + 14x^10 - 65x^9 - 3x^8 + 111x^7 - 14x^6 - 48x^5 - 53x^4 + 15x^3 + 46x^2 - 11x + 1	\( 3^{8}\cdot 5^{12}\cdot 11^{6} \)	$C_4\wr C_2$ (as 16T28)	Trivial (GRH)
16.4.2837698174072265625.2	x^16 - 3x^15 + 3x^14 - 9x^13 + 7x^12 - 15x^11 + 27x^10 - 3x^9 - 15x^8 - 3x^7 + 27x^6 - 15x^5 + 7x^4 - 9x^3 + 3x^2 - 3x + 1	\( 3^{8}\cdot 5^{12}\cdot 11^{6} \)	$C_4\wr C_2$ (as 16T28)	Trivial (GRH)
16.4.4611686018427387904.2	x^16 - 4x^12 - 62x^8 - 60x^4 + 1	\( 2^{62} \)	$C_4\wr C_2$ (as 16T28)	Trivial
16.4.12381557655576425121.1	x^16 - 3x^15 + x^14 - 3x^13 + 19x^12 - 27x^11 + 7x^10 + 33x^9 - 47x^8 + 33x^7 + 7x^6 - 27x^5 + 19x^4 - 3x^3 + x^2 - 3x + 1	\( 3^{12}\cdot 13^{12} \)	$C_4\wr C_2$ (as 16T28)	Trivial (GRH)
16.4.16777216000000000000.2	x^16 - 2x^12 - 41x^8 - 18x^4 + 1	\( 2^{36}\cdot 5^{12} \)	$C_4\wr C_2$ (as 16T28)	Trivial (GRH)
16.4.26214400000000000000.1	x^16 - 8x^15 + 30x^14 - 60x^13 + 20x^12 + 256x^11 - 888x^10 + 1740x^9 - 2350x^8 + 2240x^7 - 1488x^6 + 704x^5 - 240x^4 + 40x^3 + 8x - 4	\( 2^{32}\cdot 5^{14} \)	$C_4\wr C_2$ (as 16T28)	Trivial (GRH)
16.4.33115249535031967744.3	x^16 - 4x^14 - 8x^13 - 10x^12 + 16x^11 + 32x^10 - 62x^8 - 48x^7 + 124x^6 + 328x^5 + 370x^4 + 240x^3 + 88x^2 + 16x + 1	\( 2^{48}\cdot 7^{6} \)	$C_4\wr C_2$ (as 16T28)	Trivial
16.4.73786976294838206464.9	x^16 - 8x^14 + 20x^12 - 8x^10 - 34x^8 + 8x^6 + 20x^4 + 8x^2 + 1	\( 2^{66} \)	$C_4\wr C_2$ (as 16T28)	Trivial (GRH)
16.0.121333322988525390625.1	x^16 - 7x^15 + 27x^14 - 85x^13 + 220x^12 - 461x^11 + 880x^10 - 1548x^9 + 2241x^8 - 2500x^7 + 2160x^6 - 1477x^5 + 798x^4 - 327x^3 + 93x^2 - 15x + 1	\( 5^{12}\cdot 89^{6} \)	$C_4\wr C_2$ (as 16T28)	Trivial
16.0.259160193017822265625.1	x^16 - 7x^15 + 27x^14 - 57x^13 + 83x^12 - 97x^11 + 225x^10 - 445x^9 + 641x^8 - 445x^7 + 225x^6 - 97x^5 + 83x^4 - 57x^3 + 27x^2 - 7x + 1	\( 5^{12}\cdot 101^{6} \)	$C_4\wr C_2$ (as 16T28)	$[2]$
16.4.419430400000000000000.4	x^16 + 20x^12 - 210x^8 + 100x^4 + 25	\( 2^{36}\cdot 5^{14} \)	$C_4\wr C_2$ (as 16T28)	Trivial (GRH)
16.4.766217865410400390625.1	x^16 - 7x^15 + 23x^14 - 51x^13 + 95x^12 - 187x^11 + 372x^10 - 549x^9 + 425x^8 + 176x^7 - 924x^6 + 1174x^5 - 856x^4 + 403x^3 - 191x^2 + 196x - 29	\( 5^{12}\cdot 11^{12} \)	$C_4\wr C_2$ (as 16T28)	Trivial (GRH)
16.4.2092483243792415845449.1	x^16 - 2x^15 + 29x^13 - 57x^12 + 66x^11 + 37x^10 - 106x^9 + 195x^8 - 41x^7 - 2x^6 + 105x^5 + 60x^4 + 55x^3 + 39x^2 + 11x + 1	\( 3^{12}\cdot 13^{14} \)	$C_4\wr C_2$ (as 16T28)	Trivial (GRH)
16.0.5528355987585453765625.2	x^16 - x^15 - 5x^14 - 5x^13 + 35x^12 + 13x^11 - 51x^10 - 31x^9 + 63x^8 + 31x^7 - 51x^6 - 13x^5 + 35x^4 + 5x^3 - 5x^2 + x + 1	\( 5^{6}\cdot 29^{12} \)	$C_4\wr C_2$ (as 16T28)	$[3]$
16.0.10236206731207275390625.2	x^16 - 4x^15 + 14x^14 + 11x^13 - 44x^12 + 108x^11 + 281x^10 - 317x^9 - 1098x^8 - 623x^7 + 1121x^6 + 2427x^5 + 946x^4 - 2006x^3 - 1846x^2 + 409x + 751	\( 5^{14}\cdot 109^{6} \)	$C_4\wr C_2$ (as 16T28)	Trivial (GRH)
16.4.19155446635260009765625.1	x^16 - 2x^15 + x^14 - 3x^13 + x^12 - 31x^11 - x^10 + 26x^9 + 107x^8 + 106x^7 + 294x^6 + 299x^5 - 59x^4 - 128x^3 - 404x^2 - 192x - 1264	\( 5^{14}\cdot 11^{12} \)	$C_4\wr C_2$ (as 16T28)	Trivial (GRH)
16.4.27409976440665105664441.1	x^16 - 4x^15 + 5x^14 + 14x^13 - 52x^12 + 14x^11 + 155x^10 - 74x^9 - 385x^8 - 326x^7 - 501x^6 - 1048x^5 - 1104x^4 - 568x^3 - 133x^2 - 8x + 1	\( 17^{12}\cdot 19^{6} \)	$C_4\wr C_2$ (as 16T28)	Trivial
16.0.66787881998297119140625.2	x^16 - 6x^15 - 4x^14 + 91x^13 - 52x^12 - 846x^11 + 1689x^10 + 2103x^9 - 8872x^8 + 1389x^7 + 21941x^6 - 17167x^5 - 27252x^4 + 38408x^3 + 5334x^2 - 30977x + 14851	\( 5^{14}\cdot 149^{6} \)	$C_4\wr C_2$ (as 16T28)	Trivial (GRH)
16.16.83564717538041455968256.1	x^16 - 4x^15 - 18x^14 + 52x^13 + 115x^12 - 252x^11 - 316x^10 + 612x^9 + 372x^8 - 780x^7 - 106x^6 + 472x^5 - 92x^4 - 92x^3 + 36x^2 - 1	\( 2^{44}\cdot 41^{6} \)	$C_4\wr C_2$ (as 16T28)	Trivial (GRH)
16.0.95038694188787201488441.2	x^16 - x^15 + 6x^14 + 13x^13 + 60x^12 + 33x^11 + 31x^10 + 28x^9 + 330x^8 + 704x^7 + 811x^6 + 579x^5 + 307x^4 + 208x^3 + 162x^2 + 90x + 27	\( 13^{14}\cdot 17^{6} \)	$C_4\wr C_2$ (as 16T28)	Trivial (GRH)
16.0.190218712922369384765625.1	x^16 - 3x^15 + 6x^14 + 8x^13 - 39x^12 + 121x^11 - 136x^10 + 14x^9 + 612x^8 - 1676x^7 + 3084x^6 - 3974x^5 + 4061x^4 - 3097x^3 + 1931x^2 - 763x + 271	\( 3^{8}\cdot 5^{14}\cdot 41^{6} \)	$C_4\wr C_2$ (as 16T28)	$[2, 4]$ (GRH)
16.16.190218712922369384765625.1	x^16 - 7x^15 + x^14 + 82x^13 - 104x^12 - 361x^11 + 624x^10 + 731x^9 - 1553x^8 - 614x^7 + 1799x^6 + 14x^5 - 844x^4 + 187x^3 + 61x^2 - 17x + 1	\( 3^{8}\cdot 5^{14}\cdot 41^{6} \)	$C_4\wr C_2$ (as 16T28)	Trivial (GRH)
16.0.516387172268851080441049.2	x^16 - 27x^13 + 5x^12 + 117x^11 + 912x^10 + 2190x^9 + 4886x^8 + 6387x^7 + 8052x^6 + 5253x^5 + 4144x^4 + 291x^3 + 1152x^2 - 135x + 81	\( 13^{12}\cdot 53^{6} \)	$C_4\wr C_2$ (as 16T28)	$[4]$ (GRH)
16.4.540360087662636962890625.1	x^16 - 2x^15 - 2x^14 - 18x^13 - 32x^12 + 68x^11 + 249x^10 + 491x^9 + 808x^8 + 358x^7 - 634x^6 + 290x^5 + 1963x^4 + 1211x^3 - 198x^2 - 353x - 109	\( 5^{12}\cdot 19^{12} \)	$C_4\wr C_2$ (as 16T28)	$[2]$ (GRH)
16.0.542560248381963759517696.3	x^16 + 32x^14 + 372x^12 + 1952x^10 + 4850x^8 + 5536x^6 + 2924x^4 + 672x^2 + 49	\( 2^{62}\cdot 7^{6} \)	$C_4\wr C_2$ (as 16T28)	$[10]$ (GRH)
16.0.1200326067404665657109641.8	x^16 - 7x^15 + 25x^14 - 70x^13 + 139x^12 - 148x^11 - 29x^10 + 617x^9 - 1111x^8 + 1511x^7 + 286x^6 - 4041x^5 + 3937x^4 - 191x^3 - 1969x^2 + 478x + 1381	\( 13^{12}\cdot 61^{6} \)	$C_4\wr C_2$ (as 16T28)	$[2]$ (GRH)
16.4.3498450596935634189769921.3	x^16 - x^15 - 15x^14 - x^13 + 103x^12 + 45x^11 - 366x^10 - 171x^9 + 636x^8 - 144x^7 + 1116x^6 - 1368x^5 + 252x^4 - 1134x^3 + 108x^2 - 243x + 81	\( 3^{12}\cdot 37^{12} \)	$C_4\wr C_2$ (as 16T28)	$[2]$ (GRH)
16.4.3682966681949923308501289.1	x^16 - 3x^15 + 6x^14 + 18x^13 - 144x^12 + 557x^11 - 1629x^10 + 3431x^9 - 5882x^8 + 8267x^7 - 8248x^6 + 5717x^5 - 2400x^4 + 37x^3 + 603x^2 - 552x + 13	\( 17^{12}\cdot 43^{6} \)	$C_4\wr C_2$ (as 16T28)	Trivial (GRH)
16.4.6280210550563314266206369.6	x^16 - 6x^15 + 19x^14 - 46x^13 + 85x^12 + 130x^11 - 1319x^10 + 4522x^9 - 9870x^8 + 15280x^7 - 17725x^6 + 15928x^5 - 11733x^4 + 7254x^3 - 3488x^2 + 968x + 13	\( 17^{12}\cdot 47^{6} \)	$C_4\wr C_2$ (as 16T28)	Trivial (GRH)
16.0.12913449667746331350360169.1	x^16 - 3x^15 + 2x^14 + x^13 + 11x^12 - 111x^11 + 255x^10 - 332x^9 + 866x^8 - 890x^7 - 391x^6 - 2768x^5 + 9867x^4 - 12492x^3 + 11003x^2 - 6345x + 2209	\( 17^{12}\cdot 53^{6} \)	$C_4\wr C_2$ (as 16T28)	$[5]$ (GRH)
16.4.16695593025891398600698809.1	x^16 + 5x^14 - 2x^13 + 6x^12 - 44x^11 - 252x^10 - 602x^9 - 626x^8 - 302x^7 - 522x^6 - 1012x^5 - 861x^4 + 1698x^3 + 1645x^2 - 1016x - 164	\( 3^{6}\cdot 73^{12} \)	$C_4\wr C_2$ (as 16T28)	Trivial (GRH)
16.4.24575316877464616506889801.1	x^16 - 4x^15 + 3x^14 + 21x^13 - 57x^12 + 15x^11 + 101x^10 - 180x^9 - 167x^8 + 122x^7 - 342x^6 + 101x^5 + 431x^4 + 212x^3 - 140x^2 - 32x + 16	\( 17^{12}\cdot 59^{6} \)	$C_4\wr C_2$ (as 16T28)	Trivial (GRH)
16.0.24731386827930948650761081.2	x^16 - 19x^13 - 40x^12 + 13x^11 + 592x^10 + 453x^9 - 2871x^8 - 4141x^7 + 8492x^6 + 13969x^5 - 12657x^4 - 28530x^3 + 21357x^2 + 5103x + 2187	\( 13^{12}\cdot 101^{6} \)	$C_4\wr C_2$ (as 16T28)	$[5]$ (GRH)
16.4.52703064995487500398531609.8	x^16 - 4x^15 + 9x^14 + 3x^13 - 43x^12 + 93x^11 - 75x^10 - 132x^9 + 121x^8 - 334x^7 - 300x^6 + 875x^5 + 311x^4 - 212x^3 - 140x^2 + 32x + 16	\( 17^{12}\cdot 67^{6} \)	$C_4\wr C_2$ (as 16T28)	$[5]$ (GRH)
16.0.86380562306022715087890625.5	x^16 - 4x^15 - 3x^14 + 13x^13 + 66x^12 - 91x^11 - 108x^10 - 146x^9 + 802x^8 + 550x^7 + 2123x^6 + 102x^5 + 3277x^4 + 2194x^3 + 7204x^2 + 3820x + 3851	\( 5^{12}\cdot 29^{12} \)	$C_4\wr C_2$ (as 16T28)	$[2, 12]$ (GRH)
16.0.86380562306022715087890625.7	x^16 - 2x^15 + 6x^14 - 49x^13 + 89x^12 - 183x^11 + 929x^10 - 1413x^9 + 685x^8 - 1722x^7 + 5533x^6 - 10619x^5 + 6070x^4 + 1512x^3 + 10887x^2 - 574x + 39311	\( 5^{12}\cdot 29^{12} \)	$C_4\wr C_2$ (as 16T28)	$[2, 4]$ (GRH)
16.4.190482731772980153578634809.1	x^16 - 6x^15 + 19x^14 - 46x^13 + 145x^12 - 718x^11 + 2589x^10 - 6942x^9 + 12826x^8 - 16704x^7 + 15111x^6 - 8832x^5 + 1347x^4 + 2038x^3 - 1836x^2 + 1008x + 137	\( 17^{12}\cdot 83^{6} \)	$C_4\wr C_2$ (as 16T28)	Trivial (GRH)
16.4.192300484323376406494140625.1	x^16 - 3x^15 - 8x^14 - 20x^13 - 37x^12 + 118x^11 - 586x^10 + 492x^9 - 2798x^8 + 4516x^7 - 2252x^6 + 10178x^5 + 1249x^4 - 24201x^3 + 6366x^2 - 40280x + 74161	\( 5^{12}\cdot 31^{12} \)	$C_4\wr C_2$ (as 16T28)	Trivial (GRH)
16.4.505811081165674302215084889.1	x^16 - 4x^15 + 5x^14 + 31x^13 - 117x^12 + 191x^11 - 295x^10 + 255x^9 + 493x^8 - 3845x^7 + 5725x^6 + 5149x^5 - 12165x^4 - 2167x^3 + 7273x^2 + 3960x - 2281	\( 3^{6}\cdot 97^{12} \)	$C_4\wr C_2$ (as 16T28)	Trivial (GRH)
16.0.624592617158605666432592809.2	x^16 - 7x^15 + 12x^14 + 6x^13 + 35x^12 - 291x^11 + 954x^10 - 3520x^9 + 9784x^8 - 13482x^7 + 5812x^6 + 3882x^5 + 13689x^4 + 18603x^3 + 18549x^2 + 6561x + 729	\( 13^{12}\cdot 173^{6} \)	$C_4\wr C_2$ (as 16T28)	$[7]$ (GRH)
16.4.1410629873249683485564270561.1	x^16 - 19x^14 - 18x^13 + 111x^12 - 18x^11 - 892x^10 + 243x^9 + 4030x^8 - 1287x^7 - 18375x^6 - 18261x^5 + 13008x^4 + 22626x^3 - 15192x^2 - 27567x - 3285	\( 3^{12}\cdot 61^{12} \)	$C_4\wr C_2$ (as 16T28)	$[2]$ (GRH)
16.0.1436256755503642932525262129.1	x^16 - 6x^15 + 5x^14 + 31x^13 + 53x^12 - 319x^11 + 95x^10 + 3586x^9 + 2583x^8 - 8982x^7 + 13076x^6 + 83143x^5 + 51395x^4 - 76748x^3 + 19400x^2 + 84280x + 30416	\( 13^{6}\cdot 29^{14} \)	$C_4\wr C_2$ (as 16T28)	Trivial (GRH)
16.4.1814980849112797822933640641.5	x^16 - 6x^15 + 36x^14 - 148x^13 + 497x^12 - 772x^11 - 315x^10 + 7670x^9 - 26334x^8 + 58350x^7 - 93825x^6 + 115850x^5 - 114924x^4 + 88560x^3 - 51824x^2 + 17184x - 832	\( 17^{14}\cdot 47^{6} \)	$C_4\wr C_2$ (as 16T28)	$[10]$ (GRH)
16.0.2371212900396504113756570569.4	x^16 - 4x^15 + 26x^14 - 47x^13 + 225x^12 - 421x^11 + 1143x^10 - 585x^9 + 2609x^8 - 2538x^7 + 8158x^6 - 3788x^5 + 2318x^4 + 1389x^3 + 1575x^2 + 459x + 81	\( 13^{6}\cdot 53^{12} \)	$C_4\wr C_2$ (as 16T28)	$[8]$ (GRH)
16.4.3340206345557585382040261009.13	x^16 - 8x^15 + 52x^14 - 224x^13 + 742x^12 - 1904x^11 + 3962x^10 - 6742x^9 + 9300x^8 - 10256x^7 + 3590x^6 + 9964x^5 - 36601x^4 + 51574x^3 - 12852x^2 - 10598x + 11839	\( 23^{6}\cdot 41^{12} \)	$C_4\wr C_2$ (as 16T28)	$[3]$ (GRH)
16.0.3859225055707220942242515625.1	x^16 - 4x^15 + 17x^14 - 29x^13 + 72x^12 - 95x^11 + 169x^10 - 620x^9 + 539x^8 - 815x^7 + 640x^6 - 317x^5 + 4266x^4 - 3864x^3 + 5176x^2 - 1552x + 512	\( 5^{6}\cdot 89^{12} \)	$C_4\wr C_2$ (as 16T28)	$[37]$ (GRH)