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 )

Label	Polynomial	Discriminant	Galois group	Class group
18.0.36374607805480156224815104.1	x^18 + 18x^16 + 125x^14 + 434x^12 + 818x^10 + 861x^8 + 509x^6 + 162x^4 + 24x^2 + 1	\( -\,2^{18}\cdot 11779563529^{2} \)	18T913	$[15]$
18.0.63744201554816021271484375.1	x^18 - 9x^17 + 66x^16 - 318x^15 + 1216x^14 - 3630x^13 + 8805x^12 - 17428x^11 + 28338x^10 - 37881x^9 + 41417x^8 - 36489x^7 + 25499x^6 - 13718x^5 + 5500x^4 - 1784x^3 + 688x^2 - 288x + 64	\( -\,5^{9}\cdot 7^{12}\cdot 11^{9} \)	$S_3 \times C_3$ (as 18T3)	$[12]$
18.0.74037208411275264000000000.1	x^18 + 18x^16 - 24x^15 + 147x^14 - 342x^13 + 996x^12 - 2514x^11 + 5586x^10 - 11958x^9 + 22581x^8 - 40962x^7 + 66838x^6 - 97902x^5 + 124314x^4 - 128200x^3 + 101529x^2 - 54078x + 15931	\( -\,2^{27}\cdot 3^{24}\cdot 5^{9} \)	$S_3 \times C_6$ (as 18T6)	$[14]$ (GRH)
18.0.75613185918270483380568064.1	x^18 + 17x^16 + 120x^14 + 455x^12 + 1001x^10 + 1287x^8 + 924x^6 + 330x^4 + 45x^2 + 1	\( -\,2^{18}\cdot 19^{16} \)	$C_{18}$ (as 18T1)	$[19]$
18.0.104192253035948620552339456.1	x^18 + 17x^16 + 114x^14 + 389x^12 + 728x^10 + 758x^8 + 433x^6 + 131x^4 + 19x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 169457^{2} \)	18T768	$[16]$ (GRH)
18.0.110609092182866440454328583.1	x^18 - x^17 + 5x^16 - 10x^15 + 31x^14 - 76x^13 + 210x^12 + 366x^11 + 550x^10 + 704x^9 + 1130x^8 + 1136x^7 + 2680x^6 + 734x^5 + 201x^4 + 55x^3 + 15x^2 + 4x + 1	\( -\,7^{15}\cdot 13^{12} \)	$C_6 \times C_3$ (as 18T2)	$[13]$
18.0.134467867946269093836238848.1	x^18 - 35x^12 + 907x^6 + 27	\( -\,2^{12}\cdot 3^{21}\cdot 11^{12} \)	$C_3^2 : C_2$ (as 18T4)	$[2, 6]$
18.0.161536237646646866899894272.1	x^18 + 12x^16 + 54x^14 + 173x^12 + 681x^10 + 2232x^8 + 4894x^6 + 7221x^4 + 5484x^2 + 1297	\( -\,2^{18}\cdot 3^{24}\cdot 1297^{3} \)	18T472	$[20]$
18.0.208728361158759000000000000.1	x^18 - 6x^17 + 6x^16 + 21x^15 - 18x^14 - 84x^13 + 41x^12 + 270x^11 - 184x^10 - 305x^9 + 96x^8 + 240x^7 + 316x^6 - 396x^5 + 32x^4 - 116x^3 + 136x^2 + 16x + 16	\( -\,2^{12}\cdot 3^{9}\cdot 5^{12}\cdot 13^{9} \)	$S_3^2$ (as 18T9)	$[12]$ (GRH)
18.0.220341376966031977018118679.1	x^18 - 4x^17 + 7x^16 - 13x^15 + 73x^14 - 196x^13 + 456x^12 - 1442x^11 + 5024x^10 - 11878x^9 + 20482x^8 - 24026x^7 + 20896x^6 - 9772x^5 + 3997x^4 + 1484x^3 + 1519x^2 + 343x + 49	\( -\,3^{9}\cdot 7^{15}\cdot 11^{9} \)	$S_3 \times C_3$ (as 18T3)	$[2, 6]$
18.0.225016488014952555075055616.2	x^18 - x^17 + 13x^16 + 14x^15 + 56x^14 + 169x^13 + 406x^12 + 308x^11 + 2504x^10 - 1429x^9 + 9291x^8 - 10863x^7 + 21735x^6 - 23733x^5 + 43497x^4 - 20412x^3 + 48114x^2 - 13122x + 19683	\( -\,2^{12}\cdot 11^{9}\cdot 13^{12} \)	$S_3 \times C_6$ (as 18T6)	$[14]$ (GRH)
18.0.232218265089212416000000000.1	x^18 + 14x^16 + 77x^14 + 310x^12 + 994x^10 + 1876x^8 + 3289x^6 + 3290x^4 + 1400x^2 + 1000	\( -\,2^{33}\cdot 5^{9}\cdot 7^{12} \)	$S_3 \times C_6$ (as 18T6)	$[3, 6]$ (GRH)
18.0.242190571378050467501912064.1	x^18 - 2x^17 - 4x^16 + 22x^15 + 44x^14 - 74x^13 + 223x^12 + 312x^11 - 1620x^10 - 576x^9 + 5508x^8 - 2916x^7 - 3861x^6 + 7614x^5 + 2916x^4 - 486x^3 + 2916x^2 + 1458x + 729	\( -\,2^{12}\cdot 3^{9}\cdot 113^{9} \)	$C_3^2 : C_2$ (as 18T4)	$[3, 6]$
18.0.258151783382020583032356864.7	x^18 + 18x^16 + 135x^14 + 546x^12 + 1287x^10 + 1782x^8 + 1386x^6 + 540x^4 + 81x^2 + 1	\( -\,2^{18}\cdot 3^{44} \)	$C_{18}$ (as 18T1)	$[19]$
18.0.267565734285752664500207616.1	x^18 - 6x^17 + 13x^16 + 10x^15 - 136x^14 + 370x^13 - 397x^12 - 442x^11 + 2502x^10 - 4778x^9 + 5325x^8 - 3574x^7 + 2237x^6 - 5348x^5 + 11786x^4 - 13880x^3 + 9112x^2 - 2592x + 526	\( -\,2^{33}\cdot 3^{8}\cdot 7^{15} \)	$C_2\times S_3^2$ (as 18T29)	$[12]$ (GRH)
18.0.294294683659613060358918144.1	x^18 - 3x^17 + 11x^16 - 11x^15 + 24x^14 - 12x^13 + 121x^12 - 95x^11 + 727x^10 + 25x^9 + 1172x^8 + 1386x^7 + 3079x^6 + 893x^5 + 4781x^4 + 825x^3 + 1247x^2 - 1319x + 982	\( -\,2^{12}\cdot 3^{9}\cdot 7^{9}\cdot 67^{6} \)	18T228	$[2, 8]$
18.0.303843936636352000000000000.1	x^18 - 2x^17 + 8x^16 - x^15 + 58x^14 - 55x^13 + 123x^12 + 9x^11 + 70x^10 - 12x^9 + 49x^8 + 204x^7 + 37x^6 + 175x^5 + 118x^4 + 90x^3 + 264x^2 + 208x + 64	\( -\,2^{18}\cdot 5^{12}\cdot 7^{15} \)	$C_3\times S_3^2$ (as 18T46)	$[18]$ (GRH)
18.0.309733882939010758901760000.1	x^18 + 8x^16 + 35x^14 + 139x^12 + 433x^10 + 823x^8 + 857x^6 + 450x^4 + 108x^2 + 9	\( -\,2^{18}\cdot 3^{8}\cdot 5^{4}\cdot 257^{6} \)	18T487	$[12]$
18.0.316075500780176721688542927.1	x^18 - 6x^17 + 6x^16 + 20x^15 - 48x^14 - 96x^13 + 459x^12 + 66x^11 - 435x^10 + 664x^9 + 4833x^8 + 900x^7 + 287x^6 + 3024x^5 + 13032x^4 + 5976x^3 + 12069x^2 + 7938x + 20331	\( -\,3^{24}\cdot 47^{9} \)	$S_3 \times C_3$ (as 18T3)	$[15]$
18.0.352460338371438479971671591.1	x^18 + 9x^16 - 9x^15 + 162x^14 - 99x^13 + 1473x^12 - 1404x^11 + 6264x^10 - 5939x^9 + 12636x^8 - 11961x^7 + 14742x^6 - 10530x^5 + 7452x^4 - 3267x^3 + 1215x^2 - 243x + 27	\( -\,3^{44}\cdot 71^{3} \)	$C_2\times C_2^2:C_9$ (as 18T26)	$[21]$
18.0.411558530965263777632956416.1	x^18 - 3x^17 - 9x^16 + 6x^15 + 129x^14 - 123x^13 - 90x^12 - 909x^11 + 1545x^10 + 446x^9 - 519x^8 - 1077x^7 + 3981x^6 - 3468x^5 + 2646x^4 - 816x^3 + 1608x^2 + 792x + 484	\( -\,2^{12}\cdot 3^{25}\cdot 17^{9} \)	$S_3^2$ (as 18T11)	$[3, 6]$ (GRH)
18.0.430285483449173885556359168.1	x^18 - 2x^17 - 11x^16 + 2x^15 + 95x^14 - 26x^13 - 85x^12 - 154x^11 + 1159x^10 - 2970x^9 - 4843x^8 - 4982x^7 + 12797x^6 + 18420x^5 + 54332x^4 + 85532x^3 + 82964x^2 + 37800x + 46984	\( -\,2^{18}\cdot 7^{12}\cdot 17^{9} \)	$S_3 \times C_3$ (as 18T3)	$[12]$
18.0.439683473024149336981766144.1	x^18 + 26x^14 + 52x^12 + 169x^10 + 7436x^8 + 25181x^6 + 43940x^4 + 43940x^2 + 17576	\( -\,2^{33}\cdot 13^{15} \)	$S_3 \times C_6$ (as 18T6)	$[18]$ (GRH)
18.0.530727912779568801529540608.1	x^18 - 2x^17 + 10x^16 + 10x^15 + 7x^14 + 97x^13 + 127x^12 - 201x^11 + 915x^10 - 653x^9 + 656x^8 + 76x^7 - 34x^6 + 161x^5 + 28x^4 - 8x^3 + 27x^2 - 5x + 1	\( -\,2^{12}\cdot 3^{9}\cdot 37^{12} \)	$S_3 \times C_6$ (as 18T6)	$[12]$ (GRH)
18.0.530727912779568801529540608.2	x^18 - 3x^17 + 5x^16 + 6x^15 - 12x^14 - 28x^13 + 63x^12 + 17x^11 - 17x^10 - 126x^9 + 130x^8 - 112x^7 + 216x^6 - 144x^5 + 200x^4 - 112x^3 + 112x^2 - 32x + 64	\( -\,2^{12}\cdot 3^{9}\cdot 37^{12} \)	$S_3^2$ (as 18T11)	$[12]$ (GRH)
18.0.535422519938359574117644671.2	x^18 - 17x^15 + 193x^12 - 1057x^9 + 3187x^6 - 4125x^3 + 15625	\( -\,3^{21}\cdot 13^{15} \)	$S_3 \times C_6$ (as 18T6)	$[12]$ (GRH)
18.0.569862261508654647313096707.1	x^18 + 6x^16 - 18x^15 + 60x^14 - 75x^13 + 256x^12 - 459x^11 + 966x^10 - 871x^9 + 1740x^8 - 1116x^7 + 2869x^6 - 2424x^5 + 6450x^4 - 2606x^3 + 3006x^2 - 513x + 361	\( -\,3^{27}\cdot 73^{3}\cdot 577^{3} \)	18T285	$[2, 12]$
18.0.592297667290202112000000000.1	x^18 - 6x^17 + 18x^16 - 36x^15 + 57x^14 + 54x^13 - 262x^12 - 408x^11 + 4434x^10 - 14948x^9 + 43596x^8 - 97524x^7 + 191241x^6 - 297918x^5 + 389286x^4 - 440316x^3 + 419904x^2 - 314928x + 157464	\( -\,2^{30}\cdot 3^{24}\cdot 5^{9} \)	$S_3 \times C_6$ (as 18T6)	$[2, 6]$ (GRH)
18.0.615992567705547976896144751.1	x^18 + 22x^16 - 8x^15 + 193x^14 - 138x^13 + 1085x^12 - 921x^11 + 4781x^10 - 3596x^9 + 13950x^8 - 12017x^7 + 36528x^6 - 25667x^5 + 61742x^4 - 59237x^3 + 44674x^2 - 56832x + 39944	\( -\,13^{12}\cdot 31^{9} \)	$S_3 \times C_3$ (as 18T3)	$[2, 6]$ (GRH)
18.0.663767077778191870430588928.1	x^18 + 28x^16 + 252x^14 + 1157x^12 + 2772x^10 + 3556x^8 + 2575x^6 + 1092x^4 + 252x^2 + 27	\( -\,2^{12}\cdot 3^{9}\cdot 7^{12}\cdot 29^{6} \)	$S_3^2$ (as 18T11)	$[3, 6]$ (GRH)
18.0.737445455454227457309147136.1	x^18 + 17x^16 + 115x^14 + 400x^12 + 776x^10 + 851x^8 + 511x^6 + 157x^4 + 22x^2 + 1	\( -\,2^{30}\cdot 37^{6}\cdot 16361^{2} \)	18T836	$[28]$ (GRH)
18.0.802697202857257993500622848.1	x^18 + 28x^16 + 336x^14 + 2226x^12 + 9212x^10 + 27440x^8 + 65464x^6 + 123480x^4 + 148176x^2 + 74088	\( -\,2^{33}\cdot 3^{9}\cdot 7^{15} \)	$S_3 \times C_6$ (as 18T6)	$[2, 14]$ (GRH)
18.0.802697202857257993500622848.2	x^18 - 8x^17 + 50x^16 - 214x^15 + 777x^14 - 2306x^13 + 5951x^12 - 13076x^11 + 25573x^10 - 42600x^9 + 65630x^8 - 85698x^7 + 110878x^6 - 123990x^5 + 146017x^4 - 124430x^3 + 112877x^2 - 54474x + 17851	\( -\,2^{33}\cdot 3^{9}\cdot 7^{15} \)	$S_3 \times C_6$ (as 18T6)	$[2, 14]$ (GRH)
18.0.823903027170640554647911051.1	x^18 + 17x^16 - 7x^15 + 174x^14 - 142x^13 + 1276x^12 - 1068x^11 + 6618x^10 - 6859x^9 + 25026x^8 - 25559x^7 + 58530x^6 - 44688x^5 + 47915x^4 - 20759x^3 + 14724x^2 - 2412x + 216	\( -\,7^{12}\cdot 53^{6}\cdot 139^{3} \)	$C_6\times S_4$ (as 18T61)	$[2, 2, 10]$ (GRH)
18.0.977480813971145474830595007.3	x^18 - 3x^17 + 36x^15 - 72x^14 - 108x^13 + 498x^12 - 390x^11 - 1764x^10 + 1160x^9 + 4896x^8 + 828x^7 - 3579x^6 - 4479x^5 + 756x^4 + 2892x^3 + 1056x^2 - 1728x + 512	\( -\,3^{30}\cdot 7^{15} \)	$S_3 \times C_6$ (as 18T6)	$[21]$ (GRH)
18.0.1024770265180753855691096064.1	x^18 + 30x^16 + 333x^14 + 1712x^12 + 4164x^10 + 4500x^8 + 2316x^6 + 561x^4 + 54x^2 + 1	\( -\,2^{18}\cdot 3^{24}\cdot 7^{12} \)	$C_6 \times C_3$ (as 18T2)	$[2, 14]$
18.0.1056431860294718188453625856.1	x^18 - 4x^17 + 6x^16 + 2x^15 + 3x^14 - 96x^13 + 400x^12 - 598x^11 + 361x^10 + 1116x^9 - 1796x^8 + 1670x^7 + 1665x^6 - 1256x^5 + 1240x^4 + 1374x^3 + 1474x^2 - 2208x + 534	\( -\,2^{20}\cdot 3^{9}\cdot 13^{15} \)	$C_2\times S_3^2$ (as 18T29)	$[12]$ (GRH)
18.0.1258021719181200122144096256.2	x^18 + x^16 - 36x^14 + 81x^12 + 37x^10 - 176x^8 - 84x^6 + 192x^4 + 208x^2 + 64	\( -\,2^{18}\cdot 3^{6}\cdot 37^{12} \)	$S_3^2$ (as 18T11)	$[2, 6]$ (GRH)
18.0.1272623169716040941204406272.1	x^18 + 22x^16 + 195x^14 + 905x^12 + 2407x^10 + 3777x^8 + 3444x^6 + 1699x^4 + 374x^2 + 17	\( -\,2^{18}\cdot 17^{3}\cdot 994046201^{2} \)	18T968	$[32]$
18.0.1300691549639793389396484375.1	x^18 - 9x^16 - 24x^15 + 57x^14 + 171x^13 + 78x^12 - 1398x^11 - 354x^10 + 2370x^9 + 7326x^8 - 11433x^7 + 823x^6 + 783x^5 + 55563x^4 + 3137x^3 + 48636x^2 - 42972x + 9784	\( -\,3^{24}\cdot 5^{9}\cdot 11^{9} \)	$S_3 \times C_6$ (as 18T6)	$[28]$ (GRH)
18.0.1396922880341839978152758551.1	x^18 - 6x^17 + 33x^16 - 132x^15 + 398x^14 - 878x^13 + 1591x^12 - 2720x^11 + 5300x^10 - 9712x^9 + 11716x^8 - 6585x^7 + 6401x^6 - 25670x^5 + 32584x^4 + 6876x^3 - 33816x^2 - 3691x + 27971	\( -\,7^{12}\cdot 13^{5}\cdot 43^{7} \)	18T188	$[2, 2, 6]$
18.0.1399141503834185765244506391.1	x^18 - 3x^17 + 15x^16 - 53x^15 + 207x^14 - 648x^13 + 1867x^12 - 5094x^11 + 12642x^10 - 27983x^9 + 54783x^8 - 96642x^7 + 152588x^6 - 201378x^5 + 203559x^4 - 147022x^3 + 71619x^2 - 21321x + 3079	\( -\,3^{24}\cdot 7^{12}\cdot 71^{3} \)	$C_6\times A_4$ (as 18T25)	$[2, 10]$
18.0.1399141503834185765244506391.2	x^18 - 3x^17 + 27x^16 - 52x^15 + 249x^14 - 378x^13 + 1144x^12 - 1320x^11 + 2610x^10 - 2630x^9 + 3594x^8 - 2052x^7 + 2454x^6 - 1296x^5 + 1647x^4 - 963x^3 + 567x^2 - 162x + 27	\( -\,3^{24}\cdot 7^{12}\cdot 71^{3} \)	$C_6\times A_4$ (as 18T25)	$[2, 14]$
18.0.1511989339484099453953241088.1	x^18 + 6x^16 - 12x^14 + 28x^12 + 345x^10 + 138x^8 + 14812x^6 + 39675x^4 + 36501x^2 + 12167	\( -\,2^{12}\cdot 3^{18}\cdot 23^{11} \)	$S_3\times S_4$ (as 18T65)	$[14]$ (GRH)
18.0.1529686226742116542605950976.1	x^18 - 12x^16 - 10x^15 + 108x^14 + 42x^13 - 447x^12 + 222x^11 + 2181x^10 - 4754x^9 - 5631x^8 + 19452x^7 + 1661x^6 - 32016x^5 + 66060x^4 - 105666x^3 + 112833x^2 - 91314x + 53433	\( -\,2^{27}\cdot 3^{24}\cdot 7^{9} \)	$S_3 \times C_3$ (as 18T3)	$[12]$
18.0.1605394405714515987001245696.1	x^18 - 6x^17 + 31x^16 - 126x^15 + 449x^14 - 1344x^13 + 3523x^12 - 8124x^11 + 16814x^10 - 30804x^9 + 50122x^8 - 71112x^7 + 87448x^6 - 89688x^5 + 73686x^4 - 45720x^3 + 20178x^2 - 5832x + 918	\( -\,2^{34}\cdot 3^{9}\cdot 7^{15} \)	$C_2\times S_3^2$ (as 18T29)	$[2, 6]$ (GRH)
18.0.1612515237057830683893428407.1	x^18 - 9x^17 + 16x^16 + 76x^15 - 304x^14 + 84x^13 + 1122x^12 - 1714x^11 - 220x^10 + 2464x^9 - 1596x^8 - 1124x^7 + 1128x^6 + 1970x^5 - 851x^4 - 3175x^3 + 5544x^2 - 3412x + 968	\( -\,7^{9}\cdot 43^{12} \)	$S_3 \times C_3$ (as 18T3)	$[19]$
18.0.1732489493949409312748077056.1	x^18 + 50x^12 - 47x^6 + 64	\( -\,2^{30}\cdot 3^{6}\cdot 19^{12} \)	$C_2\times S_3^2$ (as 18T29)	$[2, 6]$ (GRH)
18.0.1992907237572181137360420864.1	x^18 - 3x^16 - 6x^14 + 30x^12 + 126x^10 + 378x^8 + 594x^6 + 702x^4 + 405x^2 + 81	\( -\,2^{32}\cdot 3^{16}\cdot 47^{6} \)	18T396	$[2, 6]$
18.0.2083629921519675807054655488.1	x^18 - 3x^17 + 21x^16 - 54x^15 + 195x^14 - 471x^13 + 1077x^12 - 2142x^11 + 3306x^10 - 5050x^9 + 6096x^8 - 8646x^7 + 9585x^6 - 9465x^5 + 9138x^4 - 1689x^3 + 19827x^2 + 11898x + 10104	\( -\,2^{12}\cdot 3^{24}\cdot 23^{9} \)	$C_3:S_3:S_4$ (as 18T155)	$[14]$

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