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 68)

Label	Polynomial	Discriminant	Galois group	Class group
18.2.84422344936728549312.1	x^18 + 3x^16 - 4x^15 + 12x^14 + 6x^13 + 47x^12 - 6x^11 + 24x^10 - 88x^9 - 21x^8 - 120x^7 - 40x^6 - 60x^5 - 27x^4 - 10x^3 - 9x^2 - 1	\( 2^{6}\cdot 3^{18}\cdot 23^{7} \)	18T734	Trivial
18.2.1055123978877614717064.1	x^18 - 2x^17 + 5x^16 - 9x^15 + 3x^14 - 2x^13 + 5x^11 + 32x^10 - 81x^9 + 66x^8 - 17x^7 + 27x^6 - 30x^5 + x^4 - 7x^3 + 7x^2 - 2x + 2	\( 2^{3}\cdot 3^{6}\cdot 7^{6}\cdot 17\cdot 67^{6} \)	18T734	Trivial
18.2.1342179767248730485677.1	x^18 - 2x^17 + 2x^16 - x^15 + 4x^14 + 14x^13 - 29x^12 + 39x^11 - 38x^10 + 57x^9 - 24x^8 - 34x^7 + 78x^6 - 51x^5 - 13x^4 + 46x^3 - 29x^2 + 6x + 1	\( 3^{6}\cdot 7^{6}\cdot 67^{6}\cdot 173 \)	18T734	Trivial
18.0.1408356802897182756864.1	x^18 + 3x^16 - 6x^14 - 16x^12 + 6x^10 + 42x^8 + 47x^6 + 57x^4 + 36x^2 + 9	\( -\,2^{12}\cdot 3^{18}\cdot 31^{6} \)	18T734	Trivial (GRH)
18.0.2279403313291670831424.1	x^18 - 3x^17 + 6x^16 - 20x^15 + 57x^14 - 102x^13 + 159x^12 - 312x^11 + 567x^10 - 735x^9 + 855x^8 - 1155x^7 + 1382x^6 - 1122x^5 + 567x^4 - 172x^3 + 33x^2 - 6x + 1	\( -\,2^{6}\cdot 3^{21}\cdot 23^{7} \)	18T734	$[2]$ (GRH)
18.2.4225070408691548270592.1	x^18 - 3x^12 + 9x^10 + 6x^8 - 23x^6 - 36x^4 - 15x^2 - 3	\( 2^{12}\cdot 3^{19}\cdot 31^{6} \)	18T734	Trivial (GRH)
18.4.5064288990059881824256.1	x^18 - 8x^16 + 25x^14 - 41x^12 + 39x^10 - 14x^8 - 10x^6 + 15x^4 - 7x^2 + 1	\( -\,2^{24}\cdot 7^{6}\cdot 37^{6} \)	18T734	Trivial (GRH)
18.4.28488347429695597360728.1	x^18 - 4x^17 + 16x^16 - 38x^15 + 79x^14 - 110x^13 + 113x^12 - 22x^11 - 148x^10 + 381x^9 - 560x^8 + 629x^7 - 547x^6 + 365x^5 - 181x^4 + 34x^3 - 3x^2 - 20x + 4	\( -\,2^{3}\cdot 3^{9}\cdot 7^{6}\cdot 17\cdot 67^{6} \)	18T734	Trivial (GRH)
18.0.1830076447935430656000000.1	x^18 - 3x^17 + 8x^16 - 10x^15 - 3x^14 + 25x^13 - 28x^12 + 6x^11 + 27x^10 - 45x^9 + 24x^8 + 18x^7 - x^6 - 5x^5 + 20x^4 + 18x^3 + 40x^2 + 28x + 8	\( -\,2^{30}\cdot 3^{6}\cdot 5^{6}\cdot 13^{6}\cdot 31 \)	18T734	Trivial
18.4.1830076447935430656000000.1	x^18 - 5x^17 + 13x^16 - 27x^15 + 52x^14 - 76x^13 + 69x^12 + 9x^11 - 82x^10 + 170x^9 - 349x^8 + 335x^7 + 139x^6 - 379x^5 + 148x^4 + 4x^3 + 24x^2 + 40x - 32	\( -\,2^{30}\cdot 3^{6}\cdot 5^{6}\cdot 13^{6}\cdot 31 \)	18T734	Trivial
18.2.2199043473728864256000000.1	x^18 - 9x^17 + 32x^16 - 51x^15 + x^14 + 172x^13 - 400x^12 + 384x^11 + 288x^10 - 1536x^9 + 2492x^8 - 2436x^7 + 1632x^6 - 796x^5 + 336x^4 - 196x^3 + 132x^2 - 56x + 8	\( 2^{28}\cdot 3^{6}\cdot 5^{6}\cdot 13^{6}\cdot 149 \)	18T734	Trivial
18.4.2420423689204924416000000.1	x^18 - 4x^17 + 6x^16 - 8x^15 - 17x^14 + 72x^13 - 130x^12 + 244x^11 - 249x^10 + 264x^9 - 278x^8 + 244x^7 - 269x^6 + 248x^5 - 140x^4 + 136x^3 - 26x^2 + 36x - 2	\( -\,2^{30}\cdot 3^{6}\cdot 5^{6}\cdot 13^{6}\cdot 41 \)	18T734	Trivial
18.2.2553251818490560512000000.1	x^18 - 7x^17 + 24x^16 - 47x^15 + 34x^14 + 93x^13 - 342x^12 + 507x^11 - 325x^10 - 184x^9 + 696x^8 - 908x^7 + 572x^6 + 176x^5 - 704x^4 + 544x^3 - 192x^2 + 64x - 64	\( 2^{28}\cdot 3^{6}\cdot 5^{6}\cdot 13^{6}\cdot 173 \)	18T734	Trivial (GRH)
18.6.2794179896948010589618176.1	x^18 - 3x^16 - 12x^15 + 3x^14 + 30x^13 + 5x^12 - 54x^11 - 93x^10 + 294x^9 - 72x^8 - 318x^7 + 478x^6 - 378x^5 + 99x^4 + 78x^3 - 72x^2 + 24x - 1	\( 2^{18}\cdot 3^{18}\cdot 31^{7} \)	18T734	Trivial (GRH)
18.6.8382539690844031768854528.1	x^18 - 3x^17 - 9x^16 + 10x^15 + 57x^14 + 6x^13 - 182x^12 - 192x^11 + 276x^10 + 623x^9 + 141x^8 - 366x^7 - 665x^6 - 381x^5 + 399x^4 + 376x^3 - 6x^2 - 15x - 1	\( 2^{18}\cdot 3^{19}\cdot 31^{7} \)	18T734	Trivial (GRH)
18.6.10899803098504187420700672.2	x^18 - x^16 - 18x^14 + 16x^12 + 98x^10 - 42x^8 - 294x^6 - 245x^4 + 1372x^2 - 343	\( 2^{12}\cdot 3^{6}\cdot 7^{9}\cdot 67^{6} \)	18T734	Trivial (GRH)
18.6.12746681249561193422474469.1	x^18 - 9x^17 + 27x^16 - 12x^15 - 90x^14 + 126x^13 + 124x^12 - 276x^11 - 135x^10 + 345x^9 + 177x^8 - 276x^7 - 212x^6 + 126x^5 + 150x^4 - 12x^3 - 45x^2 - 9x + 2	\( 3^{6}\cdot 7^{6}\cdot 67^{6}\cdot 173\cdot 9497 \)	18T734	Trivial (GRH)
18.0.13380662562832253498425344.2	x^18 + 7x^16 + 3x^14 - 24x^12 + 90x^10 + 207x^8 - 189x^6 + 27x^4 + 972x^2 + 729	\( -\,2^{24}\cdot 3^{12}\cdot 107^{6} \)	18T734	$[2]$ (GRH)
18.0.15112889376499040256000000.1	x^18 + 5x^16 + 11x^14 + 11x^12 + 52x^10 + 244x^8 + 404x^6 + 376x^4 + 156x^2 + 4	\( -\,2^{38}\cdot 3^{6}\cdot 5^{6}\cdot 13^{6} \)	18T734	Trivial (GRH)
18.0.43599212394016749682802688.1	x^18 - 6x^17 + 8x^16 - 2x^15 + 51x^14 - 74x^13 - 188x^12 + 76x^11 + 682x^10 + 30x^9 - 373x^8 - 3434x^7 + 5336x^6 - 3832x^5 + 7421x^4 - 11846x^3 + 9861x^2 - 6026x + 2818	\( -\,2^{14}\cdot 3^{6}\cdot 7^{9}\cdot 67^{6} \)	18T734	$[2]$ (GRH)
18.10.243147802712890724112956129280.1	x^18 - 6x^17 + 15x^16 - 20x^15 - 9x^14 + 54x^13 - 143x^12 + 600x^11 - 552x^10 - 572x^9 + 360x^8 - 528x^7 + 3292x^6 - 3504x^5 + 624x^4 + 1024x^3 - 768x^2 + 128	\( 2^{26}\cdot 3^{24}\cdot 5\cdot 37^{6} \)	18T734	Trivial (GRH)
18.6.632184287053515882693685936128.1	x^18 - 15x^16 - 8x^15 - 21x^14 - 12x^13 + 627x^12 + 648x^11 - 972x^10 + 2612x^9 + 7152x^8 - 14160x^7 - 52476x^6 - 54864x^5 - 16956x^4 + 13640x^3 + 16044x^2 + 4704x - 1372	\( 2^{26}\cdot 3^{24}\cdot 13\cdot 37^{6} \)	18T734	Trivial (GRH)
18.8.778072968681250317161459613696.2	x^18 - 6x^16 - 8x^15 - 3x^14 + 120x^13 - 234x^12 - 312x^11 + 2817x^10 - 2172x^9 - 8964x^8 + 9792x^7 + 7753x^6 + 1404x^5 + 1044x^4 - 39608x^3 + 12072x^2 + 25200x - 11600	\( -\,2^{30}\cdot 3^{24}\cdot 37^{6} \)	18T734	Trivial (GRH)
18.12.923961650308984751629233291264.1	x^18 - 3x^17 - 15x^16 + 42x^15 + 63x^14 + 39x^13 - 962x^12 - 843x^11 + 7701x^10 - 1216x^9 - 23187x^8 + 10881x^7 + 32397x^6 - 5766x^5 - 24150x^4 - 8056x^3 + 2130x^2 + 1530x + 214	\( -\,2^{26}\cdot 3^{24}\cdot 19\cdot 37^{6} \)	18T734	Trivial (GRH)
18.10.972591210851562896451824517120.1	x^18 - 6x^17 - 15x^16 + 94x^15 + 135x^14 - 402x^13 - 1081x^12 - 336x^11 + 3906x^10 + 6812x^9 - 1482x^8 - 13188x^7 - 12196x^6 - 2520x^5 + 2244x^4 + 1128x^3 - 72x^2 - 96x - 4	\( 2^{28}\cdot 3^{24}\cdot 5\cdot 37^{6} \)	18T734	Trivial (GRH)
18.10.972591210851562896451824517120.2	x^18 - 24x^16 - 36x^15 + 153x^14 + 588x^13 + 366x^12 - 2100x^11 - 5109x^10 - 2316x^9 + 7032x^8 + 11268x^7 + 2623x^6 - 7620x^5 - 7026x^4 - 812x^3 + 1524x^2 + 612x + 52	\( 2^{28}\cdot 3^{24}\cdot 5\cdot 37^{6} \)	18T734	Trivial (GRH)
18.4.1118479892479297330919598194688.1	x^18 - 9x^17 + 42x^16 - 132x^15 + 189x^14 + 273x^13 - 2723x^12 + 9435x^11 - 20541x^10 + 31161x^9 - 24705x^8 - 10569x^7 + 75102x^6 - 133578x^5 + 150453x^4 - 115013x^3 + 59250x^2 - 18636x + 2614	\( -\,2^{26}\cdot 3^{24}\cdot 23\cdot 37^{6} \)	18T734	Trivial (GRH)
18.8.1118479892479297330919598194688.1	x^18 - 9x^17 + 48x^16 - 152x^15 + 282x^14 - 186x^13 - 930x^12 + 2868x^11 - 1899x^10 - 2591x^9 + 5772x^8 - 4530x^7 - 5712x^6 + 9042x^5 + 8034x^4 - 10546x^3 - 2064x^2 + 2472x - 268	\( -\,2^{26}\cdot 3^{24}\cdot 23\cdot 37^{6} \)	18T734	Trivial (GRH)
18.8.1118479892479297330919598194688.2	x^18 - 3x^17 - 6x^16 + 26x^15 - 81x^14 + 135x^13 + 97x^12 - 591x^11 + 1101x^10 - 1893x^9 + 3429x^8 - 2733x^7 - 3034x^6 + 9504x^5 - 13209x^4 + 11669x^3 - 6252x^2 + 2178x - 454	\( -\,2^{26}\cdot 3^{24}\cdot 23\cdot 37^{6} \)	18T734	Trivial (GRH)
18.6.1410257255734766199855145549824.1	x^18 - 6x^17 + 27x^16 - 92x^15 + 228x^14 - 432x^13 + 316x^12 + 804x^11 - 4230x^10 + 7876x^9 - 4962x^8 - 5316x^7 + 12696x^6 - 11832x^5 + 1776x^4 + 2444x^3 - 1143x^2 + 138x - 5	\( 2^{26}\cdot 3^{24}\cdot 29\cdot 37^{6} \)	18T734	Trivial (GRH)
18.8.2091071103330860227371422711808.1	x^18 - 6x^17 + 18x^16 - 8x^15 - 129x^14 + 234x^13 + 184x^12 - 648x^11 - 201x^10 + 1230x^9 + 1434x^8 - 2088x^7 + 1233x^6 + 3150x^5 - 13140x^4 - 13704x^3 + 2328x^2 + 3264x - 368	\( -\,2^{26}\cdot 3^{24}\cdot 37^{6}\cdot 43 \)	18T734	Trivial (GRH)
18.2.2528737148214063530774743744512.1	x^18 - 12x^16 - 4x^15 - 42x^14 - 108x^13 + 474x^12 + 96x^11 - 4152x^10 - 14208x^9 - 24000x^8 - 21024x^7 - 15584x^6 - 14592x^5 + 3840x^4 - 3072x^3 + 9216x^2 + 4096	\( 2^{28}\cdot 3^{24}\cdot 13\cdot 37^{6} \)	18T734	Trivial (GRH)
18.8.2869144072012110544532882325504.1	x^18 - 27x^16 - 48x^15 + 33x^14 + 204x^13 + 621x^12 + 240x^11 - 1662x^10 - 1680x^9 + 2010x^8 + 3540x^7 - 448x^6 - 2952x^5 - 888x^4 + 768x^3 + 360x^2 + 24x - 4	\( -\,2^{26}\cdot 3^{24}\cdot 37^{6}\cdot 59 \)	18T734	Trivial (GRH)
18.12.3112291874725001268645838454784.2	x^18 - 12x^16 + 15x^14 + 230x^12 - 489x^10 - 1128x^8 + 2029x^6 - 510x^4 - 192x^2 + 4	\( -\,2^{32}\cdot 3^{24}\cdot 37^{6} \)	18T734	Trivial (GRH)
18.16.3258180556352735703113612132352.1	x^18 - 33x^16 - 4x^15 + 447x^14 + 96x^13 - 3317x^12 - 1032x^11 + 15000x^10 + 6720x^9 - 41586x^8 - 26076x^7 + 63828x^6 + 50472x^5 - 44976x^4 - 38968x^3 + 13200x^2 + 9096x - 2276	\( -\,2^{26}\cdot 3^{24}\cdot 37^{6}\cdot 67 \)	18T734	Trivial (GRH)
18.4.3258180556352735703113612132352.1	x^18 - 9x^17 + 63x^16 - 300x^15 + 1125x^14 - 3339x^13 + 7554x^12 - 12915x^11 + 11061x^10 + 11960x^9 - 80865x^8 + 194967x^7 - 325767x^6 + 398124x^5 - 346464x^4 + 206832x^3 - 47088x^2 - 14940x + 22628	\( -\,2^{26}\cdot 3^{24}\cdot 37^{6}\cdot 67 \)	18T734	Trivial (GRH)
18.16.3695846601235939006516933165056.1	x^18 - 6x^17 - 15x^16 + 170x^15 - 186x^14 - 1392x^13 + 4226x^12 + 678x^11 - 20544x^10 + 29008x^9 + 12396x^8 - 66546x^7 + 50014x^6 + 16776x^5 - 41670x^4 + 19786x^3 - 2589x^2 - 114x - 1	\( -\,2^{28}\cdot 3^{24}\cdot 19\cdot 37^{6} \)	18T734	Trivial (GRH)
18.8.3695846601235939006516933165056.1	x^18 - 9x^17 + 6x^16 + 111x^15 - 162x^14 - 561x^13 + 1357x^12 + 2406x^11 - 6900x^10 - 14914x^9 - 270x^8 + 15012x^7 + 4576x^6 - 7500x^5 - 2676x^4 + 1312x^3 + 120x^2 + 72x - 8	\( -\,2^{28}\cdot 3^{24}\cdot 19\cdot 37^{6} \)	18T734	Trivial (GRH)
18.4.3890364843406251585807298068480.1	x^18 - 24x^16 - 88x^15 - 9x^14 + 624x^13 + 2518x^12 + 6444x^11 + 12867x^10 + 20560x^9 + 24660x^8 + 23640x^7 + 23445x^6 + 21024x^5 + 12210x^4 + 7812x^3 + 8784x^2 + 4464x + 92	\( -\,2^{30}\cdot 3^{24}\cdot 5\cdot 37^{6} \)	18T734	Trivial (GRH)
18.10.3890364843406251585807298068480.1	x^18 - 24x^16 - 12x^15 + 159x^14 + 210x^13 - 1032x^11 - 3177x^10 + 1158x^9 + 10554x^8 + 2136x^7 - 16839x^6 - 8142x^5 + 18624x^4 + 18692x^3 + 1824x^2 - 2058x + 2	\( 2^{30}\cdot 3^{24}\cdot 5\cdot 37^{6} \)	18T734	Trivial (GRH)
18.12.4473919569917189323678392778752.1	x^18 - 3x^16 - 153x^14 + 1215x^12 - 1428x^10 - 10128x^8 + 27908x^6 - 19008x^4 - 396x^2 + 92	\( -\,2^{28}\cdot 3^{24}\cdot 23\cdot 37^{6} \)	18T734	Trivial (GRH)
18.8.4473919569917189323678392778752.1	x^18 + 6x^16 - 117x^14 - 264x^12 + 3351x^10 - 6x^8 - 10399x^6 - 4008x^4 + 1920x^2 + 368	\( -\,2^{28}\cdot 3^{24}\cdot 23\cdot 37^{6} \)	18T734	Trivial (GRH)
18.12.4473919569917189323678392778752.2	x^18 - 18x^16 + 111x^14 - 228x^12 - 261x^10 + 1458x^8 - 823x^6 - 1452x^4 + 672x^2 + 368	\( -\,2^{28}\cdot 3^{24}\cdot 23\cdot 37^{6} \)	18T734	Trivial (GRH)
18.4.5203362978055861496017261166592.1	x^18 + 15x^16 - 52x^15 + 114x^14 - 648x^13 + 1504x^12 - 3432x^11 + 10524x^10 - 19188x^9 + 34662x^8 - 63780x^7 + 70142x^6 - 88272x^5 + 141192x^4 - 95104x^3 - 1293x^2 + 13452x - 1885	\( -\,2^{26}\cdot 3^{24}\cdot 37^{6}\cdot 107 \)	18T734	Trivial (GRH)
18.10.5641029022939064799420582199296.1	x^18 - 27x^16 - 4x^15 + 315x^14 - 36x^13 - 2289x^12 + 1872x^11 + 12288x^10 - 18376x^9 - 44292x^8 + 83904x^7 + 89472x^6 - 222624x^5 - 121920x^4 + 295808x^3 + 144432x^2 - 78912x - 9200	\( 2^{28}\cdot 3^{24}\cdot 29\cdot 37^{6} \)	18T734	Trivial (GRH)
18.14.5641029022939064799420582199296.1	x^18 - 3x^17 - 30x^16 + 167x^15 - 54x^14 - 1659x^13 + 4269x^12 + 960x^11 - 18900x^10 + 23280x^9 + 13776x^8 - 51504x^7 + 30528x^6 + 16512x^5 - 25152x^4 + 6720x^3 + 2112x^2 - 1152x + 128	\( 2^{28}\cdot 3^{24}\cdot 29\cdot 37^{6} \)	18T734	Trivial (GRH)
18.2.6662249794333205840694997942272.1	x^18 - 3x^17 + 36x^16 - 64x^15 + 450x^14 - 498x^13 + 2684x^12 - 2196x^11 + 10113x^10 - 147x^9 + 23448x^8 + 16620x^7 + 34660x^6 + 74256x^5 + 44448x^4 + 162592x^3 + 87360x^2 + 14208x + 23680	\( 2^{26}\cdot 3^{24}\cdot 37^{6}\cdot 137 \)	18T734	Trivial (GRH)
18.12.7343063641929299868211275104256.1	x^18 - 9x^17 + 188x^15 - 354x^14 - 918x^13 + 2268x^12 + 1758x^11 - 3765x^10 - 3417x^9 - 3450x^8 + 9600x^7 + 13026x^6 - 8472x^5 - 3282x^4 - 4006x^3 - 9432x^2 - 3132x - 148	\( -\,2^{26}\cdot 3^{24}\cdot 37^{6}\cdot 151 \)	18T734	Trivial (GRH)
18.14.8996468700376956792179376783360.1	x^18 - 9x^17 + 24x^16 + 12x^15 - 261x^14 + 903x^13 - 1081x^12 - 2055x^11 + 8415x^10 - 10439x^9 + 3711x^8 + 4125x^7 - 4866x^6 + 834x^5 + 1143x^4 - 331x^3 - 138x^2 + 12x + 4	\( 2^{26}\cdot 3^{24}\cdot 5\cdot 37^{7} \)	18T734	Trivial (GRH)
18.12.28788699841206261734974005706752.2	x^18 - 6x^17 - 12x^16 + 112x^15 + 45x^14 - 636x^13 - 2154x^12 + 9516x^11 - 2901x^10 - 14942x^9 - 12654x^8 + 51144x^7 + 12255x^6 - 93876x^5 + 68694x^4 - 14304x^3 - 948x^2 + 264x - 10	\( -\,2^{30}\cdot 3^{24}\cdot 37^{7} \)	18T734	Trivial (GRH)