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
18.0.132778647348746705647.1	x^18 - 2x^17 + 4x^14 + 2x^13 - 6x^12 - 6x^11 + 5x^10 - 6x^9 + 2x^8 + 23x^7 + 9x^6 - 26x^5 - 16x^4 + 3x^3 + 9x^2 + 4x + 1	\( -\,11^{4}\cdot 23^{8}\cdot 115807 \)	18T881	Trivial
18.0.300561500864281575424.2	x^18 + 4x^16 + 8x^14 + 12x^12 + 15x^10 + 18x^8 + 19x^6 + 15x^4 + 8x^2 + 1	\( -\,2^{18}\cdot 11^{4}\cdot 23^{8} \)	18T881	Trivial
18.2.5341691162750700308441.1	x^18 - 9x^17 + 26x^16 - 4x^15 - 110x^14 + 126x^13 + 196x^12 - 344x^11 - 227x^10 + 475x^9 + 250x^8 - 380x^7 - 272x^6 + 144x^5 + 202x^4 + 20x^3 - 65x^2 - 29x - 1	\( 11^{4}\cdot 23^{8}\cdot 43\cdot 108347 \)	18T881	Trivial
18.2.6912914519878476234752.1	x^18 + 4x^16 + 7x^14 - 3x^12 - 30x^10 - 61x^8 - 74x^6 - 76x^4 - 38x^2 - 23	\( 2^{18}\cdot 11^{4}\cdot 23^{9} \)	18T881	Trivial
18.6.106464657240127078400000.1	x^18 - 6x^17 + 14x^16 - 20x^15 + 30x^14 - 20x^13 - 102x^12 + 264x^11 - 178x^10 - 50x^9 + 76x^8 - 22x^7 + 64x^6 - 150x^5 + 110x^4 - 30x^3 + 20x^2 + 34x + 2	\( 2^{18}\cdot 5^{5}\cdot 37^{9} \)	18T881	Trivial
18.4.147324066234986659840000.1	x^18 - 7x^16 + 16x^14 - 16x^12 + 6x^10 + 22x^8 - 16x^6 + 9x^2 + 1	\( -\,2^{26}\cdot 5^{4}\cdot 37^{8} \)	18T881	Trivial
18.2.184155082793733324800000.1	x^18 - 2x^17 + 2x^16 + 2x^15 - 14x^14 + 44x^13 - 70x^12 + 28x^11 + 54x^10 + 24x^9 - 308x^8 + 466x^7 - 262x^6 - 40x^5 + 118x^4 - 36x^3 - 16x^2 + 12x - 2	\( 2^{24}\cdot 5^{5}\cdot 37^{8} \)	18T881	Trivial
18.6.184155082793733324800000.1	x^18 - 4x^17 + 6x^16 - 12x^15 + 26x^14 - 28x^13 + 28x^12 - 16x^11 - 24x^10 + 20x^9 - 20x^8 - 6x^7 + 62x^6 + 24x^5 - 36x^4 - 28x^3 + 2x^2 + 8x + 2	\( 2^{24}\cdot 5^{5}\cdot 37^{8} \)	18T881	Trivial
18.2.425858628960508313600000.1	x^18 - 4x^17 + 8x^16 - 14x^15 + 28x^14 - 42x^13 + 44x^12 - 76x^11 + 142x^10 - 182x^9 + 242x^8 - 340x^7 + 366x^6 - 360x^5 + 270x^4 - 70x^3 - 20x^2 - 20x - 10	\( 2^{20}\cdot 5^{5}\cdot 37^{9} \)	18T881	Trivial
18.4.589296264939946639360000.1	x^18 - 3x^16 - 20x^14 - 24x^12 + 46x^10 + 210x^8 + 260x^6 + 104x^4 + 17x^2 + 1	\( -\,2^{28}\cdot 5^{4}\cdot 37^{8} \)	18T881	Trivial
18.8.736620331174933299200000.1	x^18 - 11x^16 + 24x^14 - 4x^12 - 30x^10 + 82x^8 - 116x^6 + 60x^4 - 15x^2 + 5	\( -\,2^{26}\cdot 5^{5}\cdot 37^{8} \)	18T881	Trivial
18.8.1230465333601232081649664.1	x^18 - 11x^16 + 47x^14 - 111x^12 + 184x^10 - 240x^8 + 268x^6 - 200x^4 + 56x^2 + 4	\( -\,2^{22}\cdot 17^{4}\cdot 37^{8} \)	18T881	Trivial
18.6.1703434515842033254400000.1	x^18 - 5x^16 - 10x^15 + 10x^14 + 76x^13 + 72x^12 - 94x^11 - 340x^10 - 440x^9 - 268x^8 + 122x^7 + 478x^6 + 522x^5 + 340x^4 + 138x^3 + 31x^2 + 2x - 1	\( 2^{22}\cdot 5^{5}\cdot 37^{9} \)	18T881	Trivial
18.8.2357185059759786557440000.1	x^18 - 7x^16 + 26x^14 - 52x^12 + 72x^10 - 54x^8 - 6x^6 + 24x^4 - 9x^2 + 1	\( -\,2^{30}\cdot 5^{4}\cdot 37^{8} \)	18T881	Trivial (GRH)
18.8.2906771335579314480480256.1	x^18 - 6x^16 + 4x^14 + 28x^12 - 44x^10 - 40x^8 + 72x^6 + 20x^4 - 28x^2 + 4	\( -\,2^{28}\cdot 101^{8} \)	18T881	Trivial
18.2.3939192317884701900800000.1	x^18 - 4x^17 + 5x^16 - 10x^15 + 22x^14 - 18x^13 + 30x^12 - 46x^11 + 16x^10 - 66x^9 + 16x^8 - 46x^7 + 30x^6 - 18x^5 + 22x^4 - 10x^3 + 5x^2 - 4x + 1	\( 2^{18}\cdot 5^{5}\cdot 37^{10} \)	18T881	Trivial
18.2.6813738063368133017600000.1	x^18 - 4x^17 + 7x^16 - 10x^15 + 22x^14 - 50x^13 + 120x^12 - 198x^11 + 256x^10 - 438x^9 + 750x^8 - 686x^7 + 550x^6 - 566x^5 + 756x^4 - 42x^3 - 149x^2 - 22x - 1	\( 2^{24}\cdot 5^{5}\cdot 37^{9} \)	18T881	$[2]$
18.6.6813738063368133017600000.1	x^18 - 2x^17 - 6x^16 + 12x^15 + 8x^14 - 16x^13 - 50x^12 + 102x^11 - 14x^10 - 308x^9 + 464x^8 + 130x^7 - 766x^6 + 392x^5 + 404x^4 - 284x^3 + 8x^2 + 16x - 2	\( 2^{24}\cdot 5^{5}\cdot 37^{9} \)	18T881	Trivial
18.6.6813738063368133017600000.2	x^18 - 4x^17 - x^16 + 26x^15 - 48x^14 - 2x^13 + 86x^12 - 84x^11 + 38x^10 - 270x^9 + 292x^8 + 288x^7 - 716x^6 + 456x^5 - 238x^4 - 130x^3 + 105x^2 - 64x - 37	\( 2^{24}\cdot 5^{5}\cdot 37^{9} \)	18T881	Trivial
18.4.9428740239039146229760000.2	x^18 + x^16 - 18x^14 - 28x^12 + 48x^10 + 122x^8 + 110x^6 + 48x^4 + 11x^2 + 1	\( -\,2^{32}\cdot 5^{4}\cdot 37^{8} \)	18T881	Trivial
18.4.11785925298798932787200000.1	x^18 + 7x^16 + 2x^14 + 10x^12 + 24x^10 - 12x^8 + 14x^6 - 10x^4 - 25x^2 + 5	\( -\,2^{30}\cdot 5^{5}\cdot 37^{8} \)	18T881	Trivial
18.6.11785925298798932787200000.1	x^18 - 7x^16 + 2x^14 - 10x^12 + 24x^10 + 12x^8 + 14x^6 + 10x^4 - 25x^2 - 5	\( 2^{30}\cdot 5^{5}\cdot 37^{8} \)	18T881	Trivial
18.10.15756769271538807603200000.1	x^18 - 4x^17 - 5x^16 + 30x^15 - 14x^14 - 64x^13 + 150x^12 + 20x^11 - 352x^10 + 68x^9 + 248x^8 - 176x^7 - 56x^6 + 110x^5 - 30x^4 - 20x^3 + 25x^2 - 5	\( 2^{20}\cdot 5^{5}\cdot 37^{10} \)	18T881	Trivial
18.4.20917910671220945388044288.1	x^18 - 2x^17 - 6x^16 + 6x^15 + 23x^14 - 20x^12 - 58x^11 - 129x^10 + 316x^9 + 228x^8 - 632x^7 + 37x^6 + 610x^5 - 636x^4 + 508x^3 - 388x^2 + 188x - 38	\( -\,2^{22}\cdot 17^{5}\cdot 37^{8} \)	18T881	Trivial
18.4.27254952253472532070400000.1	x^18 - 8x^17 + 27x^16 - 48x^15 + 52x^14 - 86x^13 + 142x^12 + 112x^11 - 572x^10 + 356x^9 + 32x^8 + 728x^7 - 994x^6 - 94x^5 + 72x^4 + 488x^3 - 77x^2 - 80x - 61	\( -\,2^{26}\cdot 5^{5}\cdot 37^{9} \)	18T881	Trivial
18.0.47143701195195731148800000.2	x^18 + 6x^16 + 2x^14 - 34x^12 - 24x^10 + 140x^8 + 312x^6 + 280x^4 + 120x^2 + 20	\( -\,2^{32}\cdot 5^{5}\cdot 37^{8} \)	18T881	$[2]$
18.10.47143701195195731148800000.1	x^18 - 6x^16 + 2x^14 + 34x^12 - 24x^10 - 140x^8 + 312x^6 - 280x^4 + 120x^2 - 20	\( 2^{32}\cdot 5^{5}\cdot 37^{8} \)	18T881	Trivial (GRH)
18.0.109019809013890128281600000.1	x^18 - 6x^17 + 25x^16 - 78x^15 + 172x^14 - 342x^13 + 648x^12 - 1212x^11 + 2470x^10 - 4116x^9 + 5132x^8 - 5838x^7 + 5868x^6 - 4482x^5 + 4174x^4 - 4704x^3 + 6397x^2 - 6638x + 2803	\( -\,2^{28}\cdot 5^{5}\cdot 37^{9} \)	18T881	$[2]$
18.4.2668486391446898222999679123.1	x^18 + 20x^16 + 94x^14 - 114x^12 - 1423x^10 - 2514x^8 - 1191x^6 + 147x^4 + 186x^2 + 27	\( -\,3^{9}\cdot 53^{4}\cdot 107^{8} \)	18T881	Trivial
18.8.24016377523022084006997112107.1	x^18 + 11x^16 - 66x^14 - 427x^12 + 352x^10 + 2676x^8 + 579x^6 - 3987x^4 - 2241x^2 + 243	\( -\,3^{11}\cdot 53^{4}\cdot 107^{8} \)	18T881	Trivial (GRH)
18.8.24016377523022084006997112107.2	x^18 - 6x^17 + 20x^16 - 19x^15 - 90x^14 + 448x^13 - 996x^12 + 978x^11 + 624x^10 - 4011x^9 + 6096x^8 - 3930x^7 - 468x^6 + 2208x^5 + 5544x^4 - 8442x^3 - 1971x^2 + 4212x - 729	\( -\,3^{11}\cdot 53^{4}\cdot 107^{8} \)	18T881	Trivial (GRH)
18.12.95176014628272703286988555387.1	x^18 - 3x^17 - 14x^16 + 61x^15 + 54x^14 - 373x^13 - 128x^12 + 855x^11 + 735x^10 - x^9 - 2985x^8 - 4291x^7 + 3921x^6 + 8763x^5 + 2072x^4 - 2414x^3 - 1068x^2 + 9x + 27	\( -\,3^{8}\cdot 53^{4}\cdot 107^{9} \)	18T881	Trivial (GRH)
18.12.141429778746685605818982993519.1	x^18 - 4x^17 - 23x^16 + 43x^15 + 219x^14 - 82x^13 - 910x^12 - 357x^11 + 2067x^10 + 993x^9 - 2153x^8 - 1167x^7 + 1020x^6 + 732x^5 - 183x^4 - 207x^3 - 9x^2 + 18x + 3	\( -\,3^{9}\cdot 53^{5}\cdot 107^{8} \)	18T881	Trivial (GRH)
18.8.330547723709515877115643871232.1	x^18 + 24x^16 + 36x^14 - 748x^12 - 96x^10 + 4512x^8 - 4496x^6 - 768x^4 + 1344x^2 + 192	\( -\,2^{14}\cdot 3^{25}\cdot 47^{8} \)	18T881	Trivial (GRH)
18.8.330547723709515877115643871232.2	x^18 - 9x^17 + 21x^16 + 35x^15 - 168x^14 - 117x^13 + 1331x^12 - 2265x^11 - 735x^10 + 7830x^9 - 8949x^8 + 459x^7 + 8037x^6 - 6273x^5 - 612x^4 + 1515x^3 - 315x^2 + 81x - 3	\( -\,2^{14}\cdot 3^{25}\cdot 47^{8} \)	18T881	Trivial (GRH)
18.10.424289336240056817456948980557.1	x^18 - 9x^17 + 27x^16 - 12x^15 - 277x^14 + 1435x^13 - 3800x^12 + 6251x^11 - 5259x^10 - 2668x^9 + 13083x^8 - 15507x^7 + 4893x^6 + 9824x^5 - 10793x^4 + 1504x^3 + 2708x^2 - 1401x - 293	\( 3^{10}\cdot 53^{5}\cdot 107^{8} \)	18T881	Trivial (GRH)
18.6.424289336240056817456948980557.1	x^18 - 3x^17 + 23x^15 - 116x^14 + 148x^13 - 212x^12 - 266x^11 + 3754x^10 - 9377x^9 + 12783x^8 - 3270x^7 - 47398x^6 + 128677x^5 - 156665x^4 + 101722x^3 - 36863x^2 + 7918x - 963	\( 3^{10}\cdot 53^{5}\cdot 107^{8} \)	18T881	$[2]$ (GRH)
18.10.424289336240056817456948980557.2	x^18 - 6x^17 + 5x^16 + 60x^15 - 300x^14 + 735x^13 - 1051x^12 + 1491x^11 - 4025x^10 + 7014x^9 - 891x^8 - 12402x^7 + 7815x^6 + 17118x^5 - 24660x^4 + 6885x^3 + 4644x^2 - 2673x + 243	\( 3^{10}\cdot 53^{5}\cdot 107^{8} \)	18T881	Trivial (GRH)
18.4.856584131654454329582896998483.1	x^18 - 3x^17 - 3x^16 + 21x^15 - 53x^14 + 117x^13 - 60x^12 - 717x^11 - 190x^10 - 2224x^9 - 1931x^8 - 734x^7 - 3665x^6 - 8322x^5 - 11774x^4 + 7582x^3 + 5410x^2 + 641x - 1907	\( -\,3^{10}\cdot 53^{4}\cdot 107^{9} \)	18T881	$[2, 2]$ (GRH)
18.16.1322190894838063508462575484928.1	x^18 - 24x^16 + 180x^14 - 351x^12 - 1620x^10 + 9072x^8 - 16497x^6 + 12960x^4 - 3888x^2 + 243	\( -\,2^{16}\cdot 3^{25}\cdot 47^{8} \)	18T881	Trivial (GRH)
18.6.1322190894838063508462575484928.1	x^18 + 9x^16 - 132x^14 - 944x^12 - 642x^10 + 2226x^8 + 604x^6 - 456x^4 - 87x^2 - 3	\( 2^{16}\cdot 3^{25}\cdot 47^{8} \)	18T881	Trivial (GRH)
18.4.5288763579352254033850301939712.1	x^18 + 27x^16 + 198x^14 - 461x^12 - 12042x^10 - 55593x^8 - 100899x^6 - 54108x^4 + 17496x^2 + 3888	\( -\,2^{18}\cdot 3^{25}\cdot 47^{8} \)	18T881	$[2]$ (GRH)
18.10.5288763579352254033850301939712.1	x^18 - 3x^16 - 180x^14 + 639x^12 + 4212x^10 - 15309x^8 + 2187x^6 + 24786x^4 - 8748x^2 - 8748	\( 2^{18}\cdot 3^{25}\cdot 47^{8} \)	18T881	Trivial (GRH)
18.2.5288763579352254033850301939712.1	x^18 + 6x^16 - 7x^15 + 105x^14 + 78x^13 - 75x^12 + 1626x^11 + 441x^10 + 6387x^9 + 8199x^8 + 5841x^7 + 23235x^6 - 7398x^5 + 23706x^4 - 18102x^3 + 9054x^2 - 1566x + 2538	\( 2^{18}\cdot 3^{25}\cdot 47^{8} \)	18T881	$[2]$ (GRH)
18.10.5288763579352254033850301939712.2	x^18 - 21x^16 + 129x^14 - 47x^12 - 1440x^10 + 1056x^8 + 5344x^6 - 1536x^4 - 6144x^2 - 768	\( 2^{18}\cdot 3^{25}\cdot 47^{8} \)	18T881	Trivial (GRH)
18.16.10914998836481629364809687506111.1	x^18 - 9x^17 + 18x^16 + 60x^15 - 253x^14 + 7x^13 + 1019x^12 - 823x^11 - 1809x^10 + 2313x^9 + 1408x^8 - 2719x^7 - 213x^6 + 1477x^5 - 276x^4 - 336x^3 + 114x^2 + 21x - 9	\( -\,3^{8}\cdot 7\cdot 53^{4}\cdot 107^{8}\cdot 1753 \)	18T881	Trivial (GRH)
18.14.15132986325895359822631180306533.1	x^18 - 9x^17 + 15x^16 + 21x^15 + 96x^14 - 2396x^12 + 1212x^11 + 9866x^10 - 6183x^9 - 9901x^8 + 16554x^7 - 1386x^6 - 17523x^5 + 2133x^4 + 6732x^3 + 864x^2 - 216x - 27	\( 3^{9}\cdot 53^{5}\cdot 107^{9} \)	18T881	Trivial (GRH)
18.8.15866290738056762101550905819136.1	x^18 + 33x^16 + 267x^14 - 27x^12 - 1332x^10 + 396x^8 + 1560x^6 - 720x^4 - 288x^2 + 144	\( -\,2^{18}\cdot 3^{26}\cdot 47^{8} \)	18T881	Trivial (GRH)
18.14.20714324019129661632580349263872.1	x^18 - 9x^17 + 21x^16 - 8x^15 + 177x^14 - 903x^13 + 160x^12 + 8553x^11 - 33273x^10 + 67562x^9 - 44991x^8 - 96585x^7 + 188851x^6 - 38604x^5 - 117552x^4 + 57532x^3 + 19776x^2 - 9414x - 1538	\( 2^{16}\cdot 3^{24}\cdot 47^{9} \)	18T881	Trivial (GRH)
18.10.21155054317409016135401207758848.1	x^18 - 6x^16 - 132x^14 - 205x^12 + 1104x^10 + 636x^8 - 1821x^6 + 126x^4 + 72x^2 - 3	\( 2^{20}\cdot 3^{25}\cdot 47^{8} \)	18T881	Trivial (GRH)