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 44 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.0.23063472457103779840000.1	x^18 + 9x^16 + 38x^14 + 91x^12 + 139x^10 + 134x^8 + 73x^6 + 14x^4 - 6x^2 + 1	\( -\,2^{14}\cdot 5^{4}\cdot 83^{8} \)	18T772	Trivial (GRH)
18.0.23063472457103779840000.2	x^18 - x^16 - x^14 + 3x^12 - x^10 - 2x^8 + 5x^6 - 4x^4 + x^2 + 1	\( -\,2^{14}\cdot 5^{4}\cdot 83^{8} \)	18T772	Trivial (GRH)
18.2.81700735597888774602752.1	x^18 - 7x^16 + 26x^14 - 62x^12 + 108x^10 - 140x^8 + 138x^6 - 102x^4 + 51x^2 - 17	\( 2^{28}\cdot 11^{8}\cdot 17^{5} \)	18T772	Trivial (GRH)
18.2.115317362285518899200000.1	x^18 - 7x^16 + 18x^14 - 14x^12 - 20x^10 + 32x^8 + 14x^6 - 60x^4 + 55x^2 - 20	\( 2^{14}\cdot 5^{5}\cdot 83^{8} \)	18T772	Trivial (GRH)
18.10.1416462745925547756167680000.1	x^18 - 15x^16 - 16x^15 - 6x^14 - 48x^13 + 171x^12 + 462x^11 - 350x^10 - 1258x^9 + 473x^8 + 1954x^7 - 641x^6 - 1748x^5 + 484x^4 + 812x^3 - 124x^2 - 152x - 4	\( 2^{12}\cdot 5^{4}\cdot 13\cdot 37^{8}\cdot 59^{4} \)	18T772	Trivial (GRH)
18.12.1743338764216058776821760000.1	x^18 - 2x^17 - 16x^16 - 5x^15 + 129x^14 + 198x^13 - 515x^12 - 850x^11 + 1039x^10 + 1049x^9 - 1411x^8 - 129x^7 + 1189x^6 - 284x^5 - 500x^4 + 26x^3 + 76x^2 + 6x - 2	\( -\,2^{16}\cdot 5^{4}\cdot 37^{8}\cdot 59^{4} \)	18T772	Trivial (GRH)
18.6.1852297436979562450373120000.1	x^18 - 8x^17 + 15x^16 + 7x^15 - 50x^14 + 96x^13 - 105x^12 + 61x^11 + 11x^10 - 39x^9 + 11x^8 + 61x^7 - 105x^6 + 96x^5 - 50x^4 + 7x^3 + 15x^2 - 8x + 1	\( 2^{12}\cdot 5^{4}\cdot 17\cdot 37^{8}\cdot 59^{4} \)	18T772	Trivial (GRH)
18.12.2070214782506569797475840000.1	x^18 - 4x^17 - 17x^16 + 59x^15 + 134x^14 - 281x^13 - 605x^12 + 425x^11 + 1551x^10 - 26x^9 - 2260x^8 - 110x^7 + 1656x^6 + 362x^5 - 377x^4 - 124x^3 + 20x^2 + 11x + 1	\( -\,2^{12}\cdot 5^{4}\cdot 19\cdot 37^{8}\cdot 59^{4} \)	18T772	Trivial (GRH)
18.14.2179173455270073471027200000.1	x^18 - 7x^17 - x^16 + 105x^15 - 182x^14 - 351x^13 + 1001x^12 + 223x^11 - 1921x^10 + 622x^9 + 1311x^8 - 999x^7 + 171x^6 + 425x^5 - 520x^4 - 5x^3 + 145x^2 - 15x - 5	\( 2^{14}\cdot 5^{5}\cdot 37^{8}\cdot 59^{4} \)	18T772	Trivial (GRH)
18.12.2506049473560584491681280000.1	x^18 - 3x^17 - 12x^16 + 58x^15 - 16x^14 - 288x^13 + 477x^12 + 240x^11 - 1166x^10 + 491x^9 + 941x^8 - 914x^7 - 52x^6 + 725x^5 - 807x^4 + 215x^3 + 260x^2 - 182x + 31	\( -\,2^{12}\cdot 5^{4}\cdot 23\cdot 37^{8}\cdot 59^{4} \)	18T772	Trivial (GRH)
18.2.3159801510141606532989440000.1	x^18 - 2x^17 + 8x^16 - 6x^15 + 98x^14 - 59x^13 + 242x^12 - 580x^11 + 102x^10 - 1720x^9 + 491x^8 - 812x^7 + 1862x^6 + 1762x^5 - 480x^4 + 1105x^3 - 2392x^2 + 548x - 316	\( 2^{12}\cdot 5^{4}\cdot 29\cdot 37^{8}\cdot 59^{4} \)	18T772	Trivial (GRH)
18.12.3377718855668613880092160000.1	x^18 - 5x^17 + 5x^16 + 18x^15 - 117x^14 + 307x^13 + 96x^12 - 1793x^11 + 1699x^10 + 3408x^9 - 5617x^8 - 2121x^7 + 7013x^6 - 734x^5 - 3700x^4 + 1176x^3 + 600x^2 - 256x + 16	\( -\,2^{12}\cdot 5^{4}\cdot 31\cdot 37^{8}\cdot 59^{4} \)	18T772	Trivial (GRH)
18.10.5665850983702191024670720000.1	x^18 - 6x^17 + 7x^16 + 28x^15 - 102x^14 + 16x^13 + 343x^12 + 84x^11 - 830x^10 - 848x^9 + 1643x^8 + 596x^7 - 747x^6 - 930x^5 + 1332x^4 - 484x^3 - 100x^2 + 68x - 4	\( 2^{14}\cdot 5^{4}\cdot 13\cdot 37^{8}\cdot 59^{4} \)	18T772	Trivial (GRH)
18.6.6646479038573724086632960000.1	x^18 - 2x^17 - 12x^16 + 22x^15 + 82x^14 - 220x^13 - 143x^12 + 1332x^11 - 2284x^10 + 256x^9 + 5028x^8 - 6464x^7 + 555x^6 + 2838x^5 - 72x^4 - 882x^3 - 158x^2 + 84x + 19	\( 2^{12}\cdot 5^{4}\cdot 37^{8}\cdot 59^{4}\cdot 61 \)	18T772	Trivial (GRH)
18.8.6973355056864235107287040000.1	x^18 + 10x^16 - 119x^12 - 72x^10 + 214x^8 + 31x^6 - 68x^4 - 8x^2 + 1	\( -\,2^{18}\cdot 5^{4}\cdot 37^{8}\cdot 59^{4} \)	18T772	Trivial (GRH)
18.8.6973355056864235107287040000.2	x^18 + 15x^16 + 6x^14 - 517x^12 - 1786x^10 - 1113x^8 + 1461x^6 + 528x^4 - 392x^2 + 16	\( -\,2^{18}\cdot 5^{4}\cdot 37^{8}\cdot 59^{4} \)	18T772	Trivial (GRH)
18.4.7300231075154746127941120000.1	x^18 - 9x^17 + 55x^16 - 236x^15 + 774x^14 - 2002x^13 + 4095x^12 - 6630x^11 + 8176x^10 - 6989x^9 + 2401x^8 + 3834x^7 - 8454x^6 + 9227x^5 - 6692x^4 + 3329x^3 - 1060x^2 + 180x - 10	\( -\,2^{12}\cdot 5^{4}\cdot 37^{8}\cdot 59^{4}\cdot 67 \)	18T772	Trivial (GRH)
18.14.7409189747918249801492480000.1	x^18 - 3x^17 - 18x^16 + 103x^15 - 91x^14 - 586x^13 + 1845x^12 - 939x^11 - 4771x^10 + 9488x^9 - 3075x^8 - 8691x^7 + 8169x^6 + 1846x^5 - 4039x^4 + 31x^3 + 684x^2 + 39x - 1	\( 2^{14}\cdot 5^{4}\cdot 17\cdot 37^{8}\cdot 59^{4} \)	18T772	Trivial (GRH)
18.4.8607735148316790210557440000.1	x^18 - 9x^17 + 40x^16 - 116x^15 + 192x^14 - 28x^13 - 841x^12 + 2784x^11 - 4870x^10 + 4693x^9 + 1405x^8 - 13632x^7 + 28184x^6 - 36661x^5 + 34749x^4 - 23987x^3 + 11818x^2 - 3722x + 551	\( -\,2^{12}\cdot 5^{4}\cdot 37^{8}\cdot 59^{4}\cdot 79 \)	18T772	Trivial (GRH)
18.8.10351073912532848987379200000.1	x^18 - 4x^17 - 3x^16 - x^15 - 12x^14 + 10x^13 - 3x^12 + 3x^11 + 23x^10 - 9x^9 + 23x^8 + 3x^7 - 3x^6 + 10x^5 - 12x^4 - x^3 - 3x^2 - 4x + 1	\( -\,2^{12}\cdot 5^{5}\cdot 19\cdot 37^{8}\cdot 59^{4} \)	18T772	Trivial (GRH)
18.10.12639206040566426131957760000.1	x^18 - x^17 - 18x^16 + 5x^15 - 29x^14 + 124x^13 + 307x^12 - 561x^11 - 553x^10 + 404x^9 + 745x^8 + 795x^7 - 1059x^6 - 424x^5 + 757x^4 - 399x^3 + 136x^2 - 23x + 1	\( 2^{14}\cdot 5^{4}\cdot 29\cdot 37^{8}\cdot 59^{4} \)	18T772	Trivial (GRH)
18.10.14927338168600003276536320000.1	x^18 - 9x^17 + 38x^16 - 100x^15 + 98x^14 + 350x^13 - 1531x^12 + 2738x^11 - 1678x^10 - 3743x^9 + 10841x^8 - 13278x^7 + 8010x^6 + 273x^5 - 4413x^4 + 3465x^3 - 1304x^2 + 242x - 17	\( 2^{12}\cdot 5^{4}\cdot 37^{8}\cdot 59^{4}\cdot 137 \)	18T772	Trivial (GRH)
18.10.15799007550708032664947200000.1	x^18 - 6x^17 + 9x^16 - 4x^15 + 38x^14 - 88x^13 - 77x^12 + 256x^11 + 374x^10 - 460x^9 - 1625x^8 + 528x^7 + 2809x^6 + 826x^5 - 2702x^4 - 1256x^3 + 940x^2 + 396x + 4	\( 2^{12}\cdot 5^{5}\cdot 29\cdot 37^{8}\cdot 59^{4} \)	18T772	Trivial (GRH)
18.8.25714246772186866958120960000.1	x^18 - 3x^17 + 6x^16 - 24x^15 - 7x^14 + 68x^13 + 28x^12 + 588x^11 - 156x^10 - 2140x^9 - 3995x^8 + 885x^7 + 17305x^6 + 6043x^5 - 22196x^4 - 8113x^3 + 9865x^2 + 540x - 395	\( -\,2^{14}\cdot 5^{4}\cdot 37^{8}\cdot 59^{5} \)	18T772	Trivial (GRH)
18.8.27893420227456940429148160000.1	x^18 + 19x^16 + 98x^14 - 53x^12 - 1362x^10 - 1393x^8 + 3009x^6 + 212x^4 - 204x^2 + 4	\( -\,2^{20}\cdot 5^{4}\cdot 37^{8}\cdot 59^{4} \)	18T772	Trivial (GRH)
18.6.34866775284321175536435200000.1	x^18 - 6x^17 + 11x^16 + 4x^15 - 10x^14 - 282x^13 + 765x^12 + 888x^11 - 3994x^10 - 1418x^9 + 10029x^8 + 1848x^7 - 13919x^6 - 4156x^5 + 9834x^4 + 5544x^3 - 2152x^2 - 1832x - 244	\( 2^{18}\cdot 5^{5}\cdot 37^{8}\cdot 59^{4} \)	18T772	Trivial (GRH)
18.2.37550821948279787648000000000.1	x^18 + 27x^16 + 252x^14 + 1128x^12 + 2650x^10 + 3194x^8 + 1652x^6 + 104x^4 - 91x^2 - 5	\( 2^{16}\cdot 5^{9}\cdot 17^{4}\cdot 37^{8} \)	18T772	Trivial (GRH)
18.10.102856987088747467832483840000.1	x^18 - 3x^17 - 8x^16 + 18x^15 + 7x^14 + 42x^13 + 217x^12 - 546x^11 - 1909x^10 + 2108x^9 + 6748x^8 - 4473x^7 - 9343x^6 + 2278x^5 + 7198x^4 - 1926x^3 - 540x^2 + 170x - 10	\( 2^{16}\cdot 5^{4}\cdot 37^{8}\cdot 59^{5} \)	18T772	Trivial (GRH)
18.16.111573680909827761716592640000.1	x^18 - 21x^16 + 178x^14 - 793x^12 + 2006x^10 - 2873x^8 + 2141x^6 - 616x^4 - 40x^2 + 16	\( -\,2^{22}\cdot 5^{4}\cdot 37^{8}\cdot 59^{4} \)	18T772	Trivial (GRH)
18.8.111573680909827761716592640000.1	x^18 + 15x^16 - 10x^14 - 333x^12 + 294x^10 + 835x^8 - 503x^6 - 452x^4 + 232x^2 + 16	\( -\,2^{22}\cdot 5^{4}\cdot 37^{8}\cdot 59^{4} \)	18T772	Trivial (GRH)
18.16.139467101137284702145740800000.1	x^18 - 9x^16 - 26x^14 + 495x^12 - 1922x^10 + 3399x^8 - 3079x^6 + 1420x^4 - 300x^2 + 20	\( -\,2^{20}\cdot 5^{5}\cdot 37^{8}\cdot 59^{4} \)	18T772	Trivial (GRH)
18.4.557868404549138808582963200000.1	x^18 - 2x^16 - 100x^14 - 47x^12 + 2612x^10 + 7970x^8 + 6627x^6 + 2100x^4 + 240x^2 + 5	\( -\,2^{22}\cdot 5^{5}\cdot 37^{8}\cdot 59^{4} \)	18T772	Trivial (GRH)
18.14.557868404549138808582963200000.1	x^18 - 24x^16 + 110x^14 + 315x^12 - 2484x^10 + 1646x^8 + 8487x^6 - 12410x^4 + 4350x^2 - 125	\( 2^{22}\cdot 5^{5}\cdot 37^{8}\cdot 59^{4} \)	18T772	Trivial (GRH)
18.6.557868404549138808582963200000.1	x^18 + 26x^16 + 179x^14 + 8x^12 - 1697x^10 - 318x^8 + 2117x^6 + 460x^4 - 440x^2 - 80	\( 2^{22}\cdot 5^{5}\cdot 37^{8}\cdot 59^{4} \)	18T772	Trivial (GRH)
18.4.1645711793419959485319741440000.1	x^18 - 5x^17 + 12x^16 + 15x^15 - 128x^14 + 425x^13 - 703x^12 + 2280x^11 - 3602x^10 + 6532x^9 - 120x^8 - 12928x^7 + 17384x^6 - 16720x^5 - 608x^4 + 11712x^3 - 3104x^2 - 2432x + 832	\( -\,2^{20}\cdot 5^{4}\cdot 37^{8}\cdot 59^{5} \)	18T772	$[2]$ (GRH)
18.14.1645711793419959485319741440000.1	x^18 - 2x^17 - 8x^16 + 74x^15 - 166x^14 - 484x^13 + 3165x^12 - 968x^11 - 15634x^10 + 19926x^9 + 16772x^8 - 48930x^7 + 34261x^6 - 6680x^5 - 2478x^4 + 1320x^3 - 178x^2 + 1	\( 2^{20}\cdot 5^{4}\cdot 37^{8}\cdot 59^{5} \)	18T772	Trivial (GRH)
18.12.16512904774654508734055710720000.1	x^18 - 33x^16 + 337x^14 - 383x^12 - 12358x^10 + 60072x^8 - 48960x^6 - 45896x^4 + 2368x^2 + 592	\( -\,2^{24}\cdot 5^{4}\cdot 37^{9}\cdot 59^{4} \)	18T772	Trivial (GRH)
18.12.66051619098618034936222842880000.1	x^18 - 25x^16 + 130x^14 + 777x^12 - 7318x^10 + 10121x^8 + 22657x^6 - 30310x^4 - 29600x^2 + 3700	\( -\,2^{26}\cdot 5^{4}\cdot 37^{9}\cdot 59^{4} \)	18T772	Trivial (GRH)
18.0.330258095493090174681114214400000.1	x^18 + 57x^16 + 1258x^14 + 13679x^12 + 77662x^10 + 224027x^8 + 299513x^6 + 173770x^4 + 34780x^2 + 740	\( -\,2^{26}\cdot 5^{5}\cdot 37^{9}\cdot 59^{4} \)	18T772	$[2, 2, 204]$ (GRH)
18.18.330258095493090174681114214400000.1	x^18 - 57x^16 + 1258x^14 - 13679x^12 + 77662x^10 - 224027x^8 + 299513x^6 - 173770x^4 + 34780x^2 - 740	\( 2^{26}\cdot 5^{5}\cdot 37^{9}\cdot 59^{4} \)	18T772	Trivial (GRH)
18.6.330258095493090174681114214400000.1	x^18 + 11x^16 - 231x^14 - 3483x^12 - 5672x^10 + 73572x^8 + 213296x^6 - 316960x^4 - 1160320x^2 - 500240	\( 2^{26}\cdot 5^{5}\cdot 37^{9}\cdot 59^{4} \)	18T772	$[2]$ (GRH)
18.18.974261381704616015309286932480000.1	x^18 - 59x^16 + 1366x^14 - 16299x^12 + 109802x^10 - 427411x^8 + 945383x^6 - 1135396x^4 + 663632x^2 - 139712	\( 2^{24}\cdot 5^{4}\cdot 37^{9}\cdot 59^{5} \)	18T772	Trivial (GRH)
18.6.1321032381972360698724456857600000.1	x^18 + 7x^16 - 332x^14 - 3328x^12 + 926x^10 + 112718x^8 + 458296x^6 + 643620x^4 + 203685x^2 - 53465	\( 2^{28}\cdot 5^{5}\cdot 37^{9}\cdot 59^{4} \)	18T772	$[2]$ (GRH)
18.0.12219549533244336463201225932800000.1	x^18 + 77x^16 + 2290x^14 + 32780x^12 + 229300x^10 + 728030x^8 + 1115438x^6 + 807340x^4 + 225515x^2 + 6845	\( -\,2^{26}\cdot 5^{5}\cdot 37^{10}\cdot 59^{4} \)	18T772	$[2, 2, 2, 482]$ (GRH)