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 24 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.4.2315693668589360644096.1	x^18 + 2x^16 - 2x^15 - 3x^14 + 6x^13 - 11x^12 + 24x^11 - 39x^10 + 68x^9 - 102x^8 + 120x^7 - 134x^6 + 114x^5 - 45x^4 - 8x^3 + 15x^2 - 6x + 1	\( -\,2^{18}\cdot 37^{6}\cdot 151^{3} \)	18T486	Trivial
18.4.3295805625871197274112.1	x^18 - 2x^17 - x^16 + 12x^14 - 12x^13 - 10x^12 + 4x^11 + 42x^10 - 34x^9 - 20x^8 + 16x^7 + 18x^6 - 24x^5 + 8x^4 + 6x^3 - 9x^2 + 2x + 1	\( -\,2^{20}\cdot 37^{6}\cdot 107^{3} \)	18T486	Trivial
18.2.43369397037232870916096.1	x^18 - 4x^17 + 11x^16 - 30x^15 + 69x^14 - 128x^13 + 228x^12 - 398x^11 + 582x^10 - 676x^9 + 735x^8 - 860x^7 + 899x^6 - 678x^5 + 355x^4 - 150x^3 + 60x^2 - 16x + 1	\( 2^{18}\cdot 37^{6}\cdot 401^{3} \)	18T486	Trivial
18.2.335405228452106761142272.1	x^18 - 4x^17 + 3x^16 - 8x^15 + 45x^14 - 94x^13 + 62x^12 + 68x^11 - 156x^10 + 70x^9 + 101x^8 - 164x^7 + 123x^6 - 106x^5 + 115x^4 - 72x^3 + 18x^2 - 2x + 1	\( 2^{18}\cdot 13^{3}\cdot 37^{6}\cdot 61^{3} \)	18T486	$[2]$
18.0.514687157793406972592128.1	x^18 + 3x^16 + 6x^14 + 22x^12 + 82x^10 + 285x^8 + 524x^6 + 381x^4 + 202x^2 + 1303	\( -\,2^{18}\cdot 31^{6}\cdot 1303^{3} \)	18T486	$[4]$
18.0.719728602127529789882368.1	x^18 + 4x^16 + 14x^14 + 44x^12 + 211x^10 + 353x^8 + 700x^6 + 2652x^4 + 1685x^2 + 2647	\( -\,2^{18}\cdot 23^{6}\cdot 2647^{3} \)	18T486	$[2]$
18.6.1673586788240844494212561.1	x^18 - 2x^17 - 17x^16 + 8x^15 + 142x^14 + 133x^13 - 476x^12 - 1285x^11 - 286x^10 + 3773x^9 + 4819x^8 - 3473x^7 - 9463x^6 - 1813x^5 + 6262x^4 + 3766x^3 - 527x^2 - 792x - 121	\( 23^{6}\cdot 59^{5}\cdot 251^{3} \)	18T486	Trivial (GRH)
18.8.28192666322626401521369088.1	x^18 - 6x^17 + 7x^16 + 38x^15 - 138x^14 + 88x^13 + 313x^12 - 680x^11 + 373x^10 + 394x^9 - 515x^8 - 186x^7 + 447x^6 + 54x^5 - 248x^4 - 42x^3 + 72x^2 + 28x + 1	\( -\,2^{27}\cdot 3^{6}\cdot 257^{6} \)	18T486	Trivial
18.0.30582621154749211119190016.1	x^18 + 4x^16 - 8x^15 + 5x^14 - 74x^13 + 23x^12 - 184x^11 + 395x^10 - 206x^9 + 1318x^8 - 518x^7 + 1856x^6 - 1632x^5 + 1643x^4 - 1516x^3 + 1185x^2 - 634x + 191	\( -\,2^{18}\cdot 101^{6}\cdot 479^{3} \)	18T486	$[4]$
18.6.59213367012524597901566561.1	x^18 - 3x^17 + 2x^16 - 4x^15 - 47x^14 - 44x^13 + 138x^12 + 686x^11 + 262x^10 + 593x^9 - 169x^8 - 640x^7 + 2443x^6 + 2473x^5 - 2549x^4 - 12680x^3 + 7834x^2 - 7500x + 5723	\( 23^{6}\cdot 43^{3}\cdot 347^{5} \)	18T486	Trivial (GRH)
18.10.81886042102565127232000000.1	x^18 - 7x^17 + 5x^16 + 58x^15 - 110x^14 - 93x^13 + 384x^12 - 375x^11 - 357x^10 + 1271x^9 + 424x^8 - 56x^7 - 744x^6 - 1719x^5 - 236x^4 + 825x^3 + 446x^2 - 13	\( 2^{12}\cdot 5^{6}\cdot 13^{3}\cdot 37^{6}\cdot 61^{3} \)	18T486	Trivial (GRH)
18.0.139599627342812498772361216.1	x^18 - 2x^17 + 12x^16 - 14x^15 + 78x^14 - 52x^13 + 278x^12 - 66x^11 + 548x^10 + 200x^9 + 1278x^8 + 2462x^7 + 2100x^6 + 3778x^5 + 4606x^4 + 1046x^3 + 8996x^2 + 676x + 4394	\( -\,2^{20}\cdot 37^{6}\cdot 139^{5} \)	18T486	$[2]$
18.0.139599627342812498772361216.2	x^18 - 4x^17 + 15x^16 - 30x^15 + 78x^14 - 210x^13 + 682x^12 - 1868x^11 + 4422x^10 - 8408x^9 + 12840x^8 - 13976x^7 + 10342x^6 - 3308x^5 + 5786x^4 - 10468x^3 + 14361x^2 - 224x + 1103	\( -\,2^{20}\cdot 37^{6}\cdot 139^{5} \)	18T486	$[2]$
18.6.155803399243213903936618496.1	x^18 - 2x^16 + 6x^14 - 41x^12 - 29x^10 + 290x^8 - 219x^6 - 206x^4 + 305x^2 - 101	\( 2^{20}\cdot 101^{3}\cdot 229^{6} \)	18T486	$[2]$ (GRH)
18.10.177641050264505839272329216.1	x^18 - 14x^16 + 71x^14 - 205x^12 + 615x^10 - 2024x^8 + 4528x^6 - 5615x^4 + 3183x^2 - 401	\( 2^{30}\cdot 37^{6}\cdot 401^{3} \)	18T486	Trivial (GRH)
18.0.200481182738676633040846848.1	x^18 + 12x^16 + 69x^14 + 256x^12 + 634x^10 + 980x^8 + 873x^6 + 418x^4 + 96x^2 + 8	\( -\,2^{33}\cdot 3^{4}\cdot 257^{6} \)	18T486	$[2, 2]$
18.8.200481182738676633040846848.1	x^18 - 16x^16 + 91x^14 - 190x^12 - 65x^10 + 628x^8 - 323x^6 - 142x^4 + 72x^2 + 8	\( -\,2^{33}\cdot 3^{4}\cdot 257^{6} \)	18T486	Trivial
18.6.585210034841778067134742528.1	x^18 + 8x^16 - 5x^14 - 247x^12 - 765x^10 + 664x^8 + 6022x^6 + 5504x^4 - 2249x^2 - 157	\( 2^{20}\cdot 157^{3}\cdot 229^{6} \)	18T486	$[2]$ (GRH)
18.12.1804330644648089697367621632.1	x^18 - 4x^16 - 29x^14 + 126x^12 + 79x^10 - 536x^8 - 603x^6 + 2518x^4 - 1560x^2 + 72	\( -\,2^{33}\cdot 3^{6}\cdot 257^{6} \)	18T486	Trivial (GRH)
18.6.2945640892745755719979237376.1	x^18 - 6x^17 + 13x^16 - 28x^15 + 79x^14 - 266x^13 + 530x^12 - 584x^11 + 406x^10 - 82x^9 + 491x^8 - 142x^7 - 253x^6 - 810x^5 - 659x^4 + 126x^3 - 74x^2 - 2x + 1	\( 2^{18}\cdot 37^{6}\cdot 16361^{3} \)	18T486	$[2]$
18.6.6907264426536010794205708288.1	x^18 - 10x^16 - 12x^15 + 48x^14 - 110x^13 + 60x^12 + 100x^11 + 1142x^10 - 1990x^9 - 2136x^8 + 5220x^7 - 1690x^6 - 4688x^5 + 4120x^4 + 6426x^3 - 9234x^2 + 3416x - 386	\( 2^{20}\cdot 37^{6}\cdot 13693^{3} \)	18T486	$[2]$
18.12.5380263717332074346510281437184.1	x^18 - 3x^17 - 24x^16 + 60x^15 + 263x^14 - 333x^13 - 2144x^12 - 329x^11 + 13788x^10 + 8395x^9 - 52480x^8 - 32157x^7 + 85756x^6 + 94307x^5 - 30091x^4 - 179278x^3 + 13966x^2 + 46767x + 6363	\( -\,2^{12}\cdot 7^{9}\cdot 101^{6}\cdot 313^{3} \)	18T486	$[2]$ (GRH)
18.18.6105276260627973911312771683975168.1	x^18 - 66x^16 + 1805x^14 - 26561x^12 + 228224x^10 - 1160291x^8 + 3364823x^6 - 5025445x^4 + 2935806x^2 - 43237	\( 2^{18}\cdot 257^{6}\cdot 43237^{3} \)	18T486	$[2]$ (GRH)
18.18.78009456339906965738219631334916096.1	x^18 - 48x^16 + 950x^14 - 10109x^12 + 63279x^10 - 239621x^8 + 543059x^6 - 697871x^4 + 446364x^2 - 101081	\( 2^{18}\cdot 257^{6}\cdot 101081^{3} \)	18T486	$[2]$ (GRH)