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 17 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.0.30265280228738545047.1	x^18 - x^17 - 3x^16 - x^15 + 12x^14 + 2x^13 - 15x^12 - 17x^11 + 19x^10 + 22x^9 - x^8 - 25x^7 - 12x^6 + 17x^5 + 13x^4 - 8x^3 - 5x^2 + 2x + 1	\( -\,3^{9}\cdot 29^{6}\cdot 2585029 \)	18T903	Trivial
18.4.22980339374478576171875.1	x^18 - 5x^16 - 6x^15 + 9x^14 + 25x^13 + 5x^12 - 36x^11 - 36x^10 + 10x^9 + 39x^8 + 22x^7 - 10x^6 - 21x^5 - 11x^4 + 4x^3 + 9x^2 + 5x + 1	\( -\,5^{9}\cdot 23^{6}\cdot 431\cdot 184409 \)	18T903	Trivial
18.2.48510363931036681640625.1	x^18 - 6x^16 - 6x^15 + 15x^14 + 30x^13 - 4x^12 - 60x^11 - 48x^10 + 37x^9 + 87x^8 + 36x^7 - 43x^6 - 57x^5 - 18x^4 + 13x^3 + 15x^2 + 6x + 1	\( 3^{18}\cdot 5^{9}\cdot 2749\cdot 23321 \)	18T903	Trivial
18.6.5138988305270978725019648.1	x^18 - 17x^16 - 6x^15 + 122x^14 + 85x^13 - 460x^12 - 488x^11 + 890x^10 + 1405x^9 - 551x^8 - 1950x^7 - 757x^6 + 795x^5 + 975x^4 + 469x^3 + 122x^2 + 17x + 1	\( 2^{18}\cdot 13^{9}\cdot 29\cdot 63745501 \)	18T903	Trivial
18.8.4462547975980091466677734375.1	x^18 + x^16 - 6x^15 - 8x^14 - 5x^13 + 9x^12 + 32x^11 + 26x^10 - 2x^9 - 38x^8 - 42x^7 - 8x^6 + 22x^5 + 21x^4 - 8x^2 - x + 1	\( -\,5^{9}\cdot 109\cdot 157^{6}\cdot 1399679 \)	18T903	Trivial (GRH)
18.10.8105659363067336949418164224.1	x^18 - 6x^16 - 6x^15 + 9x^14 + 30x^13 + 19x^12 - 36x^11 - 73x^10 - 32x^9 + 56x^8 + 86x^7 + 28x^6 - 38x^5 - 43x^4 - 10x^3 + 9x^2 + 6x + 1	\( 2^{33}\cdot 37^{6}\cdot 647\cdot 568439 \)	18T903	Trivial (GRH)
18.4.31529670483033070306483765248.1	x^18 + 6x^16 - 8x^15 + 9x^14 - 48x^13 - 46x^12 - 180x^11 - 186x^10 - 92x^9 - 360x^8 + 216x^7 - 559x^6 + 1908x^5 + 2340x^4 + 3568x^3 + 1728x^2 + 384x - 64	\( -\,2^{39}\cdot 3^{18}\cdot 23^{6} \)	18T903	Trivial (GRH)
18.12.144370314942980255288000000000.1	x^18 - 11x^16 - 6x^15 + 40x^14 + 55x^13 - 26x^12 - 160x^11 - 172x^10 + 103x^9 + 391x^8 + 234x^7 - 187x^6 - 311x^5 - 117x^4 + 35x^3 + 40x^2 + 11x + 1	\( -\,2^{12}\cdot 5^{9}\cdot 17^{2}\cdot 37^{6}\cdot 691\cdot 35221 \)	18T903	Trivial (GRH)
18.0.202243698273060960219338637312.1	x^18 - 18x^16 - 8x^15 + 135x^14 + 120x^13 - 496x^12 - 720x^11 + 687x^10 + 2032x^9 + 918x^8 - 2088x^7 - 3527x^6 - 1512x^5 + 588x^4 + 3072x^3 + 4464x^2 + 1152x + 3392	\( -\,2^{31}\cdot 3^{18}\cdot 79^{6} \)	18T903	Trivial (GRH)
18.14.1302090701650633611622253330432.1	x^18 - 18x^16 - 6x^15 + 129x^14 + 90x^13 - 453x^12 - 516x^11 + 719x^10 + 1384x^9 - 84x^8 - 1618x^7 - 1076x^6 + 342x^5 + 809x^4 + 462x^3 + 129x^2 + 18x + 1	\( 2^{33}\cdot 23^{2}\cdot 37^{6}\cdot 111682561 \)	18T903	Trivial (GRH)
18.16.3426722037220245220088000000000.1	x^18 - 17x^16 - 6x^15 + 110x^14 + 85x^13 - 316x^12 - 440x^11 + 256x^10 + 973x^9 + 591x^8 - 682x^7 - 1177x^6 - 371x^5 + 341x^4 + 325x^3 + 110x^2 + 17x + 1	\( -\,2^{12}\cdot 5^{9}\cdot 37^{6}\cdot 166946971879 \)	18T903	Trivial (GRH)
18.18.73799780913240116924657262657536.1	x^18 - 24x^16 - 6x^15 + 234x^14 + 120x^13 - 1169x^12 - 936x^11 + 3032x^10 + 3532x^9 - 3268x^8 - 6304x^7 - 851x^6 + 3736x^5 + 3152x^4 + 1178x^3 + 234x^2 + 24x + 1	\( 2^{33}\cdot 37^{6}\cdot 22073\cdot 151702769 \)	18T903	Trivial (GRH)
18.0.9373517170938828381535914021617664.1	x^18 - 6x^16 - 8x^15 - 18x^14 + 72x^13 + 318x^12 - 828x^11 + 870x^10 + 728x^9 - 11268x^8 + 24432x^7 + 3393x^6 - 108036x^5 + 239880x^4 - 286464x^3 + 212544x^2 - 94464x + 20992	\( -\,2^{30}\cdot 3^{18}\cdot 41^{3}\cdot 83^{6} \)	18T903	$[2]$ (GRH)
18.10.3036991852889853849525071814775013376.1	x^18 - 30x^16 - 20x^15 + 279x^14 + 372x^13 - 950x^12 - 1404x^11 + 285x^10 - 1176x^9 - 72x^8 + 7848x^7 + 8708x^6 - 3024x^5 + 6576x^4 - 6656x^3 - 9792x^2 + 2304x + 512	\( 2^{31}\cdot 3^{18}\cdot 7^{9}\cdot 67^{6} \)	18T903	Trivial (GRH)
18.14.1004220442431955142780653174367877800000000000.1	x^18 - 3x^17 - 404x^16 + 1712x^15 + 43204x^14 - 224074x^13 + 1293253x^12 - 14888454x^11 - 347682222x^10 + 4245099965x^9 - 84891381x^8 - 180605815836x^7 + 987979666336x^6 - 1394245968721x^5 - 7110505980691x^4 + 29751632848805x^3 - 22916864268836x^2 - 17608077562964x - 2211171219071	\( 2^{12}\cdot 5^{11}\cdot 19^{2}\cdot 37^{6}\cdot 61\cdot 151^{4}\cdot 643^{4} \)	18T903	Trivial (GRH)
18.6.259352126175392118892826453584331145475962636576227328.1	x^18 - 486x^16 - 324x^15 + 115371x^14 + 153828x^13 - 15726660x^12 - 32209920x^11 + 1293156639x^10 + 3633226952x^9 - 65079800730x^8 - 226272859884x^7 + 1895443582761x^6 + 7061043691332x^5 - 30871641520764x^4 - 88999185241248x^3 + 378744819233904x^2 + 583573253129280x - 1858061286256064	\( 2^{43}\cdot 3^{24}\cdot 11^{10}\cdot 47^{4}\cdot 953^{4} \)	18T903	Trivial (GRH)
18.18.60354597469050827144261400747621547431798707274236593031872512.1	x^18 - 3852x^16 - 30736x^15 + 6027618x^14 + 96122064x^13 - 4525454337x^12 - 117303932784x^11 + 1264320413073x^10 + 67489049880064x^9 + 319889009391855x^8 - 16024771525133136x^7 - 266494192085567835x^6 - 226336313226170496x^5 + 36294104440432333908x^4 + 474010864334666524928x^3 + 2901079188765510844557x^2 + 9136064088352588936944x + 11952636410206805283781	\( 2^{24}\cdot 3^{24}\cdot 7^{4}\cdot 23\cdot 107^{6}\cdot 3520987^{4} \)	18T903	$[3]$ (GRH)