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 48 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.0.2463405967062215950336.2	x^18 + x^16 - 4x^14 - x^12 + 12x^10 - 3x^8 - 9x^6 + 12x^2 + 4	\( -\,2^{24}\cdot 59^{8} \)	18T548	Trivial
18.2.9083809503541921316864.2	x^18 - 5x^17 + 13x^16 - 34x^15 + 76x^14 - 128x^13 + 194x^12 - 272x^11 + 359x^10 - 471x^9 + 475x^8 - 260x^7 + 136x^5 - 138x^4 + 76x^3 - 29x^2 + 7x - 1	\( 2^{20}\cdot 59^{9} \)	18T548	Trivial
18.0.9853623868248863801344.2	x^18 + 2x^16 + x^14 - 6x^12 - 13x^10 + 2x^8 + 3x^6 + 14x^4 + 8x^2 + 4	\( -\,2^{26}\cdot 59^{8} \)	18T548	Trivial
18.2.36335238014167685267456.1	x^18 - 6x^17 + 19x^16 - 38x^15 + 55x^14 - 60x^13 + 67x^12 - 100x^11 + 74x^10 - 66x^9 + 108x^8 - 32x^7 + 4x^6 - 24x^5 - 8x^4 + 12x^3 - 4x^2 - 4	\( 2^{22}\cdot 59^{9} \)	18T548	Trivial
18.10.34315860028444827786358093.1	x^18 - 2x^17 - 13x^16 + 18x^15 + 106x^14 - 109x^13 - 513x^12 + 468x^11 + 1363x^10 - 991x^9 - 2088x^8 + 700x^7 + 2017x^6 + 280x^5 - 1025x^4 - 556x^3 + 106x^2 + 164x + 37	\( 13\cdot 1129^{8} \)	18T548	Trivial
18.10.34315860028444827786358093.2	x^18 - 16x^16 + 72x^14 - 35x^12 - 276x^10 + 249x^8 + 305x^6 - 185x^4 - 129x^2 - 13	\( 13\cdot 1129^{8} \)	18T548	Trivial
18.12.50153949272342440610831059.1	x^18 - 9x^17 + 25x^16 + 4x^15 - 158x^14 + 322x^13 - 83x^12 - 854x^11 + 1654x^10 - 537x^9 - 2077x^8 + 3098x^7 - 1044x^6 - 1765x^5 + 2026x^4 - 495x^3 - 413x^2 + 305x - 29	\( -\,19\cdot 1129^{8} \)	18T548	Trivial
18.8.50153949272342440610831059.1	x^18 - 3x^17 - 14x^16 + 43x^15 + 72x^14 - 247x^13 - 118x^12 + 667x^11 - 133x^10 - 757x^9 + 378x^8 + 490x^7 - 406x^6 - 141x^5 + 189x^4 + 4x^3 - 30x^2 + 5x + 1	\( -\,19\cdot 1129^{8} \)	18T548	Trivial
18.10.97668217004035279084249957.1	x^18 - 7x^17 + 11x^16 + 31x^15 - 127x^14 + 150x^13 - 68x^12 + 102x^11 - 391x^10 + 860x^9 - 893x^8 - 32x^7 + 529x^6 + 125x^5 - 280x^4 - 105x^3 + 88x^2 + 8x - 1	\( 37\cdot 1129^{8} \)	18T548	Trivial
18.10.97668217004035279084249957.2	x^18 - 7x^17 + 11x^16 + 12x^15 - 41x^14 + 27x^13 - 8x^12 + 4x^11 + 46x^10 - 91x^9 + 46x^8 + 4x^7 - 8x^6 + 27x^5 - 41x^4 + 12x^3 + 11x^2 - 7x + 1	\( 37\cdot 1129^{8} \)	18T548	Trivial (GRH)
18.6.161020573979625730382141821.1	x^18 - 5x^17 + 11x^16 - 29x^15 + 53x^14 - 42x^13 + 22x^12 - 36x^11 + 135x^10 - 158x^9 + 183x^8 + 102x^7 + 25x^6 - 187x^5 + 100x^4 + 107x^3 - 166x^2 + 54x - 1	\( 61\cdot 1129^{8} \)	18T548	Trivial
18.14.266607835605609815878628261.1	x^18 - 2x^17 - 17x^16 + 40x^15 + 86x^14 - 285x^13 - 59x^12 + 803x^11 - 587x^10 - 607x^9 + 1151x^8 - 533x^7 - 273x^6 + 497x^5 - 263x^4 + 36x^3 + 21x^2 - 9x + 1	\( 101\cdot 1129^{8} \)	18T548	Trivial (GRH)
18.6.266607835605609815878628261.1	x^18 - 4x^17 - 2x^16 + 41x^15 - 64x^14 - 97x^13 + 309x^12 + 53x^11 - 453x^10 - 544x^9 + 998x^8 + 844x^7 - 760x^6 - 821x^5 - 104x^4 + 251x^3 + 18x^2 - 8x + 1	\( 101\cdot 1129^{8} \)	18T548	Trivial
18.12.271887198686909020153452583.1	x^18 - 3x^17 - 11x^16 + 25x^15 + 56x^14 - 67x^13 - 108x^12 + 39x^11 - 59x^10 + 122x^9 + 472x^8 - 243x^7 - 567x^6 + 142x^5 + 242x^4 + 11x^3 - 40x^2 - 12x - 1	\( -\,103\cdot 1129^{8} \)	18T548	Trivial (GRH)
18.8.271887198686909020153452583.1	x^18 - 9x^17 + 42x^16 - 132x^15 + 265x^14 - 259x^13 - 139x^12 + 847x^11 - 1267x^10 + 835x^9 + 153x^8 - 777x^7 + 634x^6 - 170x^5 - 76x^4 + 67x^3 - 12x^2 - 3x + 1	\( -\,103\cdot 1129^{8} \)	18T548	Trivial
18.12.440826817288483556947830887.1	x^18 - 9x^17 + 21x^16 + 29x^15 - 175x^14 + 144x^13 + 328x^12 - 827x^11 + 168x^10 + 1694x^9 - 814x^8 - 1761x^7 + 229x^6 + 442x^5 - 217x^4 - 236x^3 - 76x^2 - 13x - 1	\( -\,167\cdot 1129^{8} \)	18T548	Trivial
18.4.440826817288483556947830887.1	x^18 - 6x^17 + 5x^16 - 7x^15 + 19x^14 + 4x^13 + 32x^12 + 7x^11 + 27x^10 + 3x^9 + 27x^8 + 7x^7 + 32x^6 + 4x^5 + 19x^4 - 7x^3 + 5x^2 - 6x + 1	\( -\,167\cdot 1129^{8} \)	18T548	Trivial
18.8.440826817288483556947830887.1	x^18 - x^17 - 10x^16 + 6x^15 + 28x^14 + 19x^13 + 62x^12 - 150x^11 - 377x^10 + 330x^9 + 442x^8 - 447x^7 - 151x^6 + 249x^5 + 61x^4 - 69x^3 - 40x^2 + 19x + 1	\( -\,167\cdot 1129^{8} \)	18T548	Trivial
18.12.440826817288483556947830887.2	x^18 - 7x^16 - 9x^15 + 5x^14 + 120x^13 - 47x^12 - 697x^11 + 607x^10 + 1902x^9 - 2093x^8 - 2414x^7 + 3339x^6 + 1282x^5 - 2507x^4 - 41x^3 + 695x^2 - 148x + 1	\( -\,167\cdot 1129^{8} \)	18T548	Trivial (GRH)
18.8.440826817288483556947830887.2	x^18 - 3x^17 - 11x^16 + 25x^15 - 17x^14 - 22x^13 + 51x^12 - 41x^11 + 18x^10 - x^9 + 18x^8 - 41x^7 + 51x^6 - 22x^5 - 17x^4 + 25x^3 - 11x^2 - 3x + 1	\( -\,167\cdot 1129^{8} \)	18T548	Trivial
18.6.456664906532381169772303853.1	x^18 - 8x^16 - 12x^15 + 23x^14 + 46x^13 - 87x^12 - 92x^11 + 330x^10 + 482x^9 - 1231x^8 - 701x^7 + 1868x^6 + 1750x^5 - 3467x^4 - 1689x^3 + 3827x^2 - 138x - 229	\( 173\cdot 1129^{8} \)	18T548	Trivial
18.4.472502995776278782596776819.1	x^18 - x^17 - 7x^16 - 14x^15 - 12x^14 + x^13 + 20x^12 + 36x^11 + 43x^10 + 45x^9 + 43x^8 + 36x^7 + 20x^6 + x^5 - 12x^4 - 14x^3 - 7x^2 - x + 1	\( -\,179\cdot 1129^{8} \)	18T548	Trivial
18.8.472502995776278782596776819.1	x^18 - 3x^17 - x^16 - 5x^15 + 49x^14 + 16x^13 - 396x^12 + 690x^11 + 108x^10 - 2008x^9 + 2600x^8 - 3x^7 - 2571x^6 + 1494x^5 + 647x^4 - 816x^3 + 148x^2 + 32x + 1	\( -\,179\cdot 1129^{8} \)	18T548	Trivial
18.8.504179174264074008245722751.1	x^18 - 2x^17 - x^16 + x^15 - 45x^14 + 112x^13 + 171x^12 - 663x^11 + 101x^10 + 1672x^9 - 2017x^8 - 1362x^7 + 5309x^6 - 2884x^5 - 4749x^4 + 6515x^3 - 1223x^2 - 1444x + 509	\( -\,191\cdot 1129^{8} \)	18T548	Trivial
18.6.181792228022997449601438115909.1	x^18 - 3x^17 + 2x^16 - 12x^15 - 7x^14 + 155x^13 - 236x^12 + 184x^11 - 543x^10 + 514x^9 + 1549x^8 - 3935x^7 + 3767x^6 - 1897x^5 + 442x^4 + 267x^3 - 372x^2 + 150x + 1	\( 61\cdot 1129^{9} \)	18T548	$[2]$ (GRH)
18.14.301000246398733482126971306669.1	x^18 - 8x^17 + 21x^16 - 3x^15 - 168x^14 + 593x^13 - 515x^12 - 1582x^11 + 4978x^10 - 5121x^9 - 6529x^8 + 22709x^7 - 5157x^6 - 27755x^5 + 10512x^4 + 13228x^3 - 3024x^2 - 1292x + 289	\( 101\cdot 1129^{9} \)	18T548	$[2]$ (GRH)
18.4.497693476718697935794101071423.1	x^18 - 4x^17 - 2x^16 + 46x^15 - 178x^14 + 369x^13 - 437x^12 + 58x^11 + 889x^10 - 1869x^9 + 1778x^8 + 232x^7 - 3496x^6 + 5904x^5 - 5696x^4 + 2944x^3 - 256x^2 - 1024x + 512	\( -\,167\cdot 1129^{9} \)	18T548	$[2]$ (GRH)
18.4.533455882231418745551761028651.1	x^18 - 6x^17 + 27x^16 - 72x^15 + 15x^14 + 345x^13 - 182x^12 - 3335x^11 + 9966x^10 - 7481x^9 - 12731x^8 + 28507x^7 - 16112x^6 - 21947x^5 + 54400x^4 - 17530x^3 - 32754x^2 + 8235x + 6183	\( -\,179\cdot 1129^{9} \)	18T548	$[2]$ (GRH)
18.8.533455882231418745551761028651.1	x^18 - 3x^17 - 5x^16 - 8x^15 + 126x^14 - 81x^13 - 785x^12 - 788x^11 + 3973x^10 + 11056x^9 + 7631x^8 - 6060x^7 - 36066x^6 - 44228x^5 - 1187x^4 + 31520x^3 + 23238x^2 + 6804x + 729	\( -\,179\cdot 1129^{9} \)	18T548	$[2]$ (GRH)
18.8.569218287744139555309420985879.1	x^18 - x^17 - 16x^16 - 16x^15 + 154x^14 + 265x^13 - 742x^12 - 878x^11 - 545x^10 + 3172x^9 + 4910x^8 - 1131x^7 - 6587x^6 - 5326x^5 + 2884x^4 + 4037x^3 + 405x^2 - 246x - 341	\( -\,191\cdot 1129^{9} \)	18T548	$[2]$ (GRH)
18.16.691976677792049302709773533184.1	x^18 - 20x^16 + 157x^14 - 628x^12 + 1403x^10 - 1789x^8 + 1258x^6 - 435x^4 + 53x^2 + 1	\( -\,2^{18}\cdot 1129^{8} \)	18T548	Trivial (GRH)
18.16.691976677792049302709773533184.2	x^18 - 18x^16 + 125x^14 - 412x^12 + 617x^10 - 255x^8 - 177x^6 + 121x^4 - 20x^2 + 1	\( -\,2^{18}\cdot 1129^{8} \)	18T548	Trivial (GRH)
18.14.12411911948529921080616714217889.1	x^18 - 9x^17 + 28x^16 - 20x^15 - 86x^14 + 238x^13 - 162x^12 - 380x^11 + 897x^10 - 239x^9 - 1165x^8 + 1160x^7 + 326x^6 - 1198x^5 + 419x^4 + 580x^3 - 276x^2 - 114x + 37	\( 11\cdot 31\cdot 1129^{8}\cdot 13789 \)	18T548	Trivial (GRH)
18.10.165636102028037750762643320515237.1	x^18 - 7x^17 + 6x^16 + 93x^15 - 542x^14 + 1046x^13 + 2174x^12 - 11483x^11 + 16416x^10 - 15120x^9 - 19620x^8 + 148654x^7 - 267681x^6 + 389944x^5 - 482205x^4 + 162968x^3 + 162148x^2 - 77298x - 7111	\( 13^{7}\cdot 1129^{8} \)	18T548	Trivial (GRH)
18.2.165636102028037750762643320515237.1	x^18 - 5x^17 + 29x^16 - 151x^15 + 546x^14 - 2050x^13 + 6552x^12 - 18629x^11 + 48459x^10 - 101029x^9 + 186392x^8 - 232526x^7 + 193707x^6 - 33264x^5 - 148113x^4 + 148993x^3 - 262653x^2 + 309165x - 151967	\( 13^{7}\cdot 1129^{8} \)	18T548	$[2, 2, 2]$ (GRH)
18.12.781241669227223662759334318964736.1	x^18 - 32x^16 + 280x^14 + 169x^12 - 8286x^10 + 2105x^8 + 35713x^6 + 12603x^4 - 10161x^2 + 1129	\( -\,2^{18}\cdot 1129^{9} \)	18T548	Trivial (GRH)
18.0.781241669227223662759334318964736.2	x^18 + 45x^16 + 820x^14 + 7778x^12 + 40947x^10 + 117713x^8 + 170336x^6 + 108090x^4 + 20322x^2 + 1129	\( -\,2^{18}\cdot 1129^{9} \)	18T548	$[2, 1888]$ (GRH)
18.12.781241669227223662759334318964736.2	x^18 - 15x^16 + 6x^14 + 703x^12 - 1987x^10 - 6410x^8 + 18951x^6 + 12016x^4 - 21451x^2 + 1129	\( -\,2^{18}\cdot 1129^{9} \)	18T548	Trivial (GRH)
18.10.2229465265050635102380004893016461.1	x^18 - 6x^17 - 38x^16 + 235x^15 + 407x^14 - 1243x^13 - 10299x^12 - 3419x^11 + 125021x^10 + 81703x^9 - 677796x^8 - 505964x^7 + 1059178x^6 + 2300482x^5 + 1956448x^4 - 3708549x^3 - 6608342x^2 - 1299397x + 890171	\( 61^{5}\cdot 1129^{8} \)	18T548	Trivial (GRH)
18.10.2229465265050635102380004893016461.2	x^18 - 2x^17 - 60x^16 + 46x^15 + 1213x^14 + 349x^13 - 8432x^12 - 5972x^11 + 6606x^10 - 29270x^9 + 24935x^8 + 185038x^7 + 95120x^6 + 222354x^5 + 189593x^4 - 567330x^3 - 299200x^2 - 798477x - 977029	\( 61^{5}\cdot 1129^{8} \)	18T548	Trivial (GRH)
18.18.10123826964023658466918145250910541.1	x^18 - 9x^17 + x^16 + 196x^15 - 326x^14 - 1862x^13 + 4248x^12 + 10288x^11 - 26385x^10 - 37409x^9 + 93542x^8 + 94832x^7 - 192496x^6 - 163276x^5 + 210989x^4 + 162244x^3 - 95829x^2 - 58749x + 12331	\( 1129^{8}\cdot 3835245581 \)	18T548	Trivial (GRH)
18.14.14013048589890280900016270351996681.1	x^18 - 2x^17 - 33x^16 - 32x^15 - 104x^14 + 4558x^13 + 12605x^12 - 79614x^11 - 131301x^10 + 398596x^9 + 391180x^8 - 520302x^7 - 217105x^6 + 203636x^5 - 402716x^4 - 412143x^3 - 30236x^2 + 30910x + 1529	\( 11\cdot 31\cdot 1129^{9}\cdot 13789 \)	18T548	$[2]$ (GRH)
18.10.27743318282861835289866224169592661.1	x^18 - 5x^17 + 17x^16 - 73x^15 - 144x^14 + 240x^12 + 20515x^11 - 21536x^10 + 57559x^9 - 221081x^8 - 1518837x^7 + 2729255x^6 - 849928x^5 + 3820465x^4 + 34629088x^3 - 54139751x^2 - 56431495x + 47694371	\( 101^{5}\cdot 1129^{8} \)	18T548	Trivial (GRH)
18.2.27743318282861835289866224169592661.1	x^18 - 3x^17 + 66x^16 - 213x^15 + 1892x^14 - 6691x^13 + 23960x^12 - 91827x^11 + 121105x^10 - 350894x^9 + 426906x^8 + 2317649x^7 - 2369746x^6 + 3256845x^5 - 18491746x^4 + 6297689x^3 + 49580003x^2 - 4971898x - 90710077	\( 101^{5}\cdot 1129^{8} \)	18T548	$[2, 6]$ (GRH)
18.0.882021844557535515255288446111186944.2	x^18 + 101x^16 + 4109x^14 + 87716x^12 + 1065692x^10 + 7439224x^8 + 28481283x^6 + 52334795x^4 + 31866025x^2 + 1274641	\( -\,2^{18}\cdot 1129^{10} \)	18T548	$[2, 53644]$ (GRH)
18.18.11429800642382710409150585988278000789.1	x^18 - 2x^17 - 163x^16 + 302x^15 + 10352x^14 - 15492x^13 - 339160x^12 + 332304x^11 + 6338303x^10 - 2252744x^9 - 68963585x^8 - 21248050x^7 + 407115640x^6 + 393026168x^5 - 975375086x^4 - 1665426864x^3 - 327762447x^2 + 499248799x + 195862313	\( 1129^{9}\cdot 3835245581 \)	18T548	$[2]$ (GRH)
18.6.713018177978617901961549930892502499328.1	x^18 + 142x^16 + 5949x^14 + 17966x^12 - 4359003x^10 - 99635083x^8 - 683133017x^6 + 393991011x^4 + 12981013942x^2 - 1030407817	\( 2^{18}\cdot 97^{3}\cdot 1129^{9} \)	18T548	$[2]$ (GRH)
18.6.713018177978617901961549930892502499328.2	x^18 + 43x^16 - 5743x^14 - 204003x^12 + 5567280x^10 + 129338693x^8 + 807512022x^6 + 1693755509x^4 + 403664918x^2 - 1030407817	\( 2^{18}\cdot 97^{3}\cdot 1129^{9} \)	18T548	$[2]$ (GRH)