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 75)

Label	Polynomial	Discriminant	Galois group	Class group
15.5.8565893077528823.1	x^15 - 6x^13 + 9x^11 - 18x^10 + x^9 + 32x^8 - 17x^7 - 19x^6 + 24x^5 + 3x^4 - 15x^3 + 3x^2 + 4x - 1	\( -\,23^{5}\cdot 191^{4} \)	15T32	Trivial
15.5.10496055636998343.1	x^15 - 4x^14 + 6x^13 - x^12 - 11x^11 + 18x^10 - 10x^9 - 9x^8 + 19x^7 - 12x^6 - 3x^5 + 9x^4 - 5x^3 - x^2 + 3x - 1	\( -\,3^{5}\cdot 157\cdot 2377\cdot 115742009 \)	15T104	Trivial
15.5.35351257235385344.1	x^15 - 3x^13 - 5x^12 + 8x^11 + x^10 + 14x^9 - 13x^8 - 17x^7 + 4x^6 + x^5 + 22x^4 - 2x^3 - 8x^2 - 3x - 1	\( -\,2^{10}\cdot 11^{13} \)	$S_3 \times C_5$ (as 15T4)	Trivial
15.5.77595502265817783.1	x^15 - 3x^13 - 2x^12 + x^11 + 12x^10 + 3x^9 - 15x^8 - 10x^7 - 4x^6 + 20x^5 + 7x^4 - 3x^3 - 7x^2 - 4x + 1	\( -\,3\cdot 13^{3}\cdot 11772948303113 \)	15T104	Trivial
15.5.154972454814106259.1	x^15 - x^14 - 2x^13 + x^12 + x^11 - x^10 + 2x^9 - 15x^8 + 8x^7 + 28x^6 - 34x^5 - 7x^4 + 27x^3 - 7x^2 - 3x + 1	\( -\,11^{13}\cdot 67^{2} \)	15T44	Trivial
15.5.388863829589238784.1	x^15 - 3x^14 + 2x^13 - x^12 + 5x^11 - 22x^9 + 33x^8 - 22x^7 + 22x^6 - 22x^5 - 9x^4 + 38x^3 - 29x^2 + 9x - 1	\( -\,2^{10}\cdot 11^{14} \)	$S_3 \times C_5$ (as 15T4)	Trivial
15.5.982108001708984375.1	x^15 - 4x^13 - 11x^12 + 9x^11 + 30x^10 + 5x^9 + 7x^8 - 32x^7 - 7x^6 - 78x^5 - 120x^4 + 36x^3 + 154x^2 + 134x + 43	\( -\,5^{16}\cdot 23^{5} \)	15T32	Trivial
15.5.1094025140357425839.1	x^15 - 4x^14 + 9x^13 - 7x^12 - 10x^11 + 31x^10 - 21x^9 - 32x^8 + 45x^7 + 13x^6 - 35x^5 - 2x^4 + 12x^3 - 3x^2 - 5x - 1	\( -\,3^{2}\cdot 121558348928602871 \)	15T104	Trivial
15.5.2375619759167837184.1	x^15 - 5x^14 + 7x^13 - 2x^12 + 11x^11 - 42x^10 + 54x^9 - 28x^8 + 39x^7 - 96x^6 + 36x^5 + 3x^4 + 7x^3 + 54x^2 + 19x + 1	\( -\,2^{10}\cdot 3^{9}\cdot 4903^{3} \)	15T93	Trivial
15.5.9527712342331717571.1	x^15 - 2x^14 - 8x^13 + 17x^12 + 27x^11 - 63x^10 - 46x^9 + 131x^8 + 31x^7 - 154x^6 + 7x^5 + 95x^4 - 10x^3 - 31x^2 + 2x + 4	\( -\,23^{4}\cdot 32411^{3} \)	15T91	Trivial
15.5.20200001513509571303.1	x^15 - x^14 - 4x^13 + 7x^12 + 24x^11 - 26x^10 - 57x^9 + 76x^8 + 79x^7 - 88x^6 - 97x^5 + 35x^4 + 42x^3 - 15x^2 + 1	\( -\,11^{12}\cdot 23^{5} \)	$S_3 \times C_5$ (as 15T4)	Trivial
15.5.24552700042724609375.1	x^15 - 15x^13 - 20x^12 + 70x^11 + 199x^10 + 50x^9 - 440x^8 - 740x^7 - 400x^6 + 200x^5 + 425x^4 + 275x^3 + 90x^2 + 15x + 1	\( -\,5^{18}\cdot 23^{5} \)	$((C_5^2 : C_3):C_2):C_2$ (as 15T18)	Trivial
15.5.34046877842531000000.1	x^15 - 3x^14 - 5x^13 + 25x^12 - 16x^11 - 46x^10 + 94x^9 - 29x^8 - 96x^7 + 107x^6 + 51x^5 - 191x^4 + 173x^3 - 78x^2 + 15x - 1	\( -\,2^{6}\cdot 5^{6}\cdot 32411^{3} \)	15T91	Trivial
15.5.45033016903730593947.1	x^15 - 2x^12 - 5x^9 + 13x^6 - 7x^3 + 1	\( -\,3^{15}\cdot 11^{12} \)	15T33	Trivial
15.5.45033016903730593947.2	x^15 - 10x^12 + 29x^9 - 25x^6 + 3x^3 + 1	\( -\,3^{15}\cdot 11^{12} \)	15T33	Trivial
15.5.70908197723388671875.1	x^15 - 15x^13 + 90x^11 - 2x^10 - 275x^9 + 20x^8 + 450x^7 - 70x^6 - 374x^5 + 100x^4 + 120x^3 - 50x^2 + 5x - 1	\( -\,5^{15}\cdot 19^{2}\cdot 23^{5} \)	15T68	Trivial
15.5.78524595786905053696.1	x^15 - 4x^13 - 4x^12 + 13x^11 + 4x^10 - 43x^9 + 89x^8 - 67x^7 - 64x^6 + 90x^5 - 9x^4 - 26x^3 + 13x^2 - 1	\( -\,2^{9}\cdot 31^{6}\cdot 557^{3} \)	$S_5 \times S_3$ (as 15T29)	Trivial
15.5.81054473740791453091.1	x^15 - 5x^14 + 9x^13 - 8x^12 + 14x^11 - 37x^10 + 67x^9 - 149x^8 + 274x^7 - 274x^6 + 183x^5 - 117x^4 - 51x^3 + 171x^2 - 70x - 7	\( -\,7^{3}\cdot 53\cdot 1217^{3}\cdot 2473633 \)	15T93	Trivial
15.5.91411367382133293359.1	x^15 - 2x^14 - 3x^13 + 18x^12 + 16x^11 - 40x^10 - 33x^9 + 101x^8 + 52x^7 - 96x^6 - 59x^5 + 32x^4 + 23x^3 - 12x^2 + 1	\( -\,23^{5}\cdot 61^{3}\cdot 397^{3} \)	$S_5 \times S_3$ (as 15T29)	Trivial
15.5.103907026580810546875.1	x^15 - 15x^13 + 90x^11 - 3x^10 - 275x^9 + 30x^8 + 450x^7 - 105x^6 - 373x^5 + 150x^4 + 115x^3 - 75x^2 + 10x + 1	\( -\,5^{15}\cdot 23^{7} \)	15T27	Trivial
15.5.105716774627685546875.1	x^15 - 15x^13 + 90x^11 - 2x^10 - 275x^9 + 20x^8 + 450x^7 - 70x^6 - 376x^5 + 100x^4 + 130x^3 - 50x^2 - 5x + 3	\( -\,5^{15}\cdot 11^{2}\cdot 31^{5} \)	15T68	Trivial
15.5.203788581389938989891.1	x^15 - 2x^12 - 3x^9 + 6x^6 - 1	\( -\,3^{15}\cdot 61^{3}\cdot 397^{3} \)	15T70	Trivial
15.5.203788581389938989891.2	x^15 - 5x^9 - x^6 + 3x^3 + 1	\( -\,3^{15}\cdot 61^{3}\cdot 397^{3} \)	15T70	Trivial
15.5.405150968993137160643.1	x^15 - 3x^14 - x^13 - 4x^12 + 10x^11 + 25x^10 + 36x^9 - 46x^8 - 111x^7 - 151x^6 + 138x^5 + 181x^4 - 15x^3 - 52x^2 - 24x + 3	\( -\,3^{5}\cdot 401^{7} \)	$D_5\times S_3$ (as 15T7)	Trivial
15.5.608974093750000000000.1	x^15 - 15x^13 + 90x^11 - x^10 - 275x^9 + 10x^8 + 450x^7 - 35x^6 - 376x^5 + 50x^4 + 130x^3 - 25x^2 - 5x - 1	\( -\,2^{10}\cdot 5^{15}\cdot 11^{7} \)	15T27	Trivial (GRH)
15.5.695671349660522996651.1	x^15 - x^14 - 6x^13 + 29x^12 - 66x^11 - 32x^10 + 34x^9 + 100x^8 + 122x^7 + 56x^6 + 12x^5 + 11x^4 - 9x^3 + 7x^2 - 6x + 1	\( -\,11^{13}\cdot 67^{4} \)	15T44	Trivial
15.5.1453984493779059430951.1	x^15 - 4x^14 + x^13 + 10x^12 - 18x^11 + 78x^10 - 154x^9 + 13x^8 + 122x^7 + 108x^6 - 197x^5 - 61x^4 + 98x^3 + 38x^2 - 21x - 7	\( -\,7^{6}\cdot 199^{7} \)	$D_5\times S_3$ (as 15T7)	Trivial
15.5.2058857500000000000000.1	x^15 - 10x^13 + 10x^11 - 74x^10 - 90x^9 + 50x^8 - 80x^7 - 160x^6 + 124x^5 + 140x^4 - 60x^3 - 60x^2 + 4	\( -\,2^{14}\cdot 5^{16}\cdot 7^{7} \)	$F_5 \times S_3$ (as 15T11)	Trivial
15.5.2573571875000000000000.1	x^15 - 5x^13 - 5x^12 - 20x^11 - 10x^10 + 30x^9 + 70x^8 + 95x^7 + 110x^6 + 85x^5 + 185x^4 + 45x^3 + 50x^2 - 25x - 5	\( -\,2^{12}\cdot 5^{17}\cdot 7^{7} \)	$F_5 \times S_3$ (as 15T11)	Trivial
15.5.3205575570525886607247.1	x^15 - 4x^14 + 13x^12 + 10x^11 - 70x^10 - 29x^9 + 226x^8 + 13x^7 - 454x^6 + 76x^5 + 499x^4 - 78x^3 - 183x^2 + 46x + 23	\( -\,3^{12}\cdot 11^{6}\cdot 23^{7} \)	$A_5 \times S_3$ (as 15T23)	Trivial (GRH)
15.5.5094714534748474747275.1	x^15 - 7x^12 + 15x^9 - 7x^6 - 8x^3 + 5	\( -\,3^{15}\cdot 5^{2}\cdot 61^{3}\cdot 397^{3} \)	15T83	Trivial
15.5.6628916477715643169523.1	x^15 - 2x^12 - 6x^9 + 15x^6 - 8x^3 + 1	\( -\,3^{13}\cdot 401^{6} \)	15T43	Trivial (GRH)
15.5.6628916477715643169523.2	x^15 - 9x^12 + 27x^9 - 30x^6 + 7x^3 + 3	\( -\,3^{13}\cdot 401^{6} \)	15T55	Trivial
15.5.8365026531535674375871.1	x^15 - x^14 - x^13 - x^12 - x^11 + 6x^10 - 3x^9 + 5x^8 - 8x^7 + 4x^6 - x^5 + x^4 + x^3 - 2x^2 + 3x - 1	\( -\,61\cdot 443437\cdot 309247046331703 \)	15T104	Trivial (GRH)
15.5.13659290627591033588456.1	x^15 - x^14 - 6x^13 + 5x^12 + 13x^11 - 8x^10 - 15x^9 + 11x^8 + 7x^7 - 16x^6 - x^5 + 17x^4 + 2x^3 - 7x^2 - x + 1	\( -\,2^{3}\cdot 1999922317\cdot 853738824721 \)	15T104	Trivial (GRH)
15.5.27934199478110364632064.1	x^15 + 4x^13 - 19x^12 + 15x^11 - 95x^10 + 119x^9 - 195x^8 + 703x^7 - 390x^6 + 615x^5 - 946x^4 - 186x^3 - 384x^2 - 146x + 157	\( -\,2^{10}\cdot 3^{8}\cdot 401^{6} \)	15T86	Trivial
15.5.28122063322027324931072.1	x^15 - 5x^14 + 10x^13 + 2x^12 - 43x^11 + 71x^10 - 52x^9 + 24x^8 - 12x^7 - 76x^6 + 160x^5 - 80x^4 - 96x^3 + 96x^2 - 32	\( -\,2^{10}\cdot 11^{12}\cdot 43\cdot 197\cdot 1033 \)	15T81	Trivial
15.5.36495998433430934447104.1	x^15 - 6x^13 - 12x^12 + 10x^11 + 40x^10 + 39x^9 - 6x^8 - 18x^7 - 56x^6 - 143x^5 - 182x^4 - 56x^3 + 80x^2 + 80x + 32	\( -\,2^{10}\cdot 11^{12}\cdot 11356201 \)	15T81	Trivial
15.5.58894900021692368078499.1	x^15 - 12x^12 + 53x^9 - 104x^6 + 84x^3 - 17	\( -\,3^{15}\cdot 17^{2}\cdot 61^{3}\cdot 397^{3} \)	15T83	Trivial
15.5.59660248299440788525707.1	x^15 - 20x^9 - 27x^6 - 10x^3 - 1	\( -\,3^{15}\cdot 401^{6} \)	15T43	Trivial (GRH)
15.5.69696371772723539550743.1	x^15 - 5x^14 + 21x^13 - 43x^12 - 108x^11 + 528x^10 - 737x^9 + 60x^8 + 1108x^7 - 920x^6 - 290x^5 + 1067x^4 - 91x^3 - 30x^2 + 16x - 8	\( -\,23^{5}\cdot 101^{8} \)	$(C_5^2 : C_3):C_2$ (as 15T13)	Trivial (GRH)
15.5.174837402604040846224384.1	x^15 - 5x^14 + 10x^13 - 10x^12 + 5x^11 - x^10 - 24x^9 + 72x^8 - 72x^7 + 48x^5 - 24x^4 + 32x^3 - 32x^2 + 32	\( -\,2^{10}\cdot 17\cdot 61^{3}\cdot 397^{3}\cdot 647\cdot 1093 \)	15T93	Trivial
15.5.192426600214722443506688.1	x^15 - 2x^13 - 4x^12 - 3x^11 - 12x^10 - 6x^9 + 36x^8 + 72x^7 + 48x^6 - x^5 - 10x^4 - 40x^3 - 80x^2 - 80x - 32	\( -\,2^{10}\cdot 61^{3}\cdot 149\cdot 397^{3}\cdot 88801 \)	15T93	Trivial
15.5.383635938167572021484375.1	x^15 - 30x^13 - 45x^12 + 230x^11 + 871x^10 + 750x^9 - 2445x^8 - 8010x^7 - 9505x^6 - 3026x^5 + 8475x^4 + 9910x^3 + 4635x^2 - 2935x - 2521	\( -\,5^{24}\cdot 23^{5} \)	$(C_5^2 : C_3):C_2$ (as 15T13)	Trivial (GRH)
15.5.502839296875000000000000.1	x^15 - 20x^13 + 185x^11 - 4x^10 - 950x^9 + 130x^8 + 2725x^7 - 1180x^6 - 4339x^5 + 3500x^4 + 2425x^3 - 3750x^2 + 1500x - 200	\( -\,2^{12}\cdot 5^{19}\cdot 23^{5} \)	15T49	Trivial (GRH)
15.5.502839296875000000000000.2	x^15 + 5x^13 - 55x^11 - 28x^10 - 350x^9 + 320x^8 + 25x^7 + 2760x^6 + 2544x^5 + 250x^4 - 6075x^3 - 7000x^2 + 6700x + 6680	\( -\,2^{12}\cdot 5^{19}\cdot 23^{5} \)	15T49	Trivial (GRH)
15.5.536942234694967096731363.1	x^15 - 5x^12 - 17x^9 + 10x^6 + 21x^3 - 9	\( -\,3^{17}\cdot 401^{6} \)	15T55	Trivial
15.5.24061138260758138083042304.1	x^15 - 10x^13 - 9x^12 + 128x^11 + 93x^10 - 642x^9 - 542x^8 + 1428x^7 + 1012x^6 - 2264x^5 - 408x^4 + 752x^3 + 1344x^2 - 864	\( -\,2^{10}\cdot 13\cdot 401^{6}\cdot 434717 \)	15T86	Trivial (GRH)
15.5.56665935234850614192046080.1	x^15 - 15x^13 - 30x^12 + 54x^11 + 216x^10 + 238x^9 + 132x^8 + 161x^7 - 648x^6 - 2463x^5 - 3206x^4 - 1288x^3 + 720x^2 + 720x + 288	\( -\,2^{16}\cdot 3^{4}\cdot 5\cdot 53^{9}\cdot 647 \)	15T87	Trivial (GRH)
15.5.144627327488000000000000000.1	x^15 + 5x^11 - 4x^10 - 50x^7 + 80x^6 - 32x^5 - 125x^3 + 300x^2 - 240x + 64	\( -\,2^{24}\cdot 5^{15}\cdot 7^{10} \)	15T101	Trivial (GRH)