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 24 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.4.3511479662680207261696.1	x^18 - x^16 - 5x^14 + 5x^12 + 7x^10 + 2x^8 - 26x^6 + 23x^4 - 8x^2 + 1	\( -\,2^{22}\cdot 307^{6} \)	18T521	Trivial
18.4.6365874812991930630144.1	x^18 - 3x^16 + x^14 + 6x^12 - 11x^10 + 2x^8 - 5x^6 - 6x^4 - 2x^2 + 1	\( -\,2^{22}\cdot 3^{6}\cdot 113^{6} \)	18T521	Trivial
18.0.33478694232985600000000.1	x^18 + 5x^16 + 8x^14 + 4x^12 + 3x^10 + 9x^8 + 6x^6 + x^4 + 3x^2 + 1	\( -\,2^{18}\cdot 5^{8}\cdot 83^{6} \)	18T521	Trivial
18.0.56183674602883316187136.1	x^18 + 4x^16 + 9x^14 + 10x^12 + 4x^10 + 5x^8 + 3x^6 - 5x^4 - x^2 + 1	\( -\,2^{26}\cdot 307^{6} \)	18T521	Trivial
18.2.116558457571798959765625.1	x^18 - x^17 - 5x^16 + 10x^15 + 6x^14 - 43x^13 + 26x^12 + 63x^11 - 132x^10 - 22x^9 + 71x^8 - 458x^7 - 194x^6 + 423x^5 - 175x^4 - 192x^3 + 462x^2 + 60x - 193	\( 5^{8}\cdot 83^{6}\cdot 97^{3} \)	18T521	Trivial
18.2.171878619950782127013888.1	x^18 - 4x^16 + 25x^14 - 20x^12 + 34x^10 + 81x^8 + 181x^6 + 93x^4 - 207x^2 - 27	\( 2^{22}\cdot 3^{9}\cdot 113^{6} \)	18T521	Trivial
18.6.2750057919212514032222208.1	x^18 - 9x^16 + 43x^14 - 167x^12 + 535x^10 - 1096x^8 + 1312x^6 - 861x^4 + 270x^2 - 27	\( 2^{26}\cdot 3^{9}\cdot 113^{6} \)	18T521	Trivial (GRH)
18.6.4387390128075571200000000.1	x^18 - 9x^16 + 33x^14 - 78x^12 + 144x^10 - 207x^8 + 225x^6 - 189x^4 + 108x^2 - 27	\( 2^{30}\cdot 3^{21}\cdot 5^{8} \)	18T521	Trivial
18.4.68835522420844686611068124224.1	x^18 + 10x^16 - 10x^14 - 385x^12 - 1326x^10 - 1365x^8 + 371x^6 + 1144x^4 + 496x^2 + 64	\( -\,2^{6}\cdot 32009^{6} \)	18T521	Trivial (GRH)
18.12.68835522420844686611068124224.2	x^18 + 3x^16 - 86x^14 + 183x^12 + 430x^10 - 890x^8 - 301x^6 + 1012x^4 - 480x^2 + 64	\( -\,2^{6}\cdot 32009^{6} \)	18T521	Trivial (GRH)
18.12.68835522420844686611068124224.3	x^18 - 9x^17 + 24x^16 + 10x^15 - 140x^14 + 165x^13 - 162x^12 + 1230x^11 - 2153x^10 - 2102x^9 + 7596x^8 - 2279x^7 - 5660x^6 + 1927x^5 + 2108x^4 - 72x^3 - 293x^2 - 54x - 1	\( -\,2^{6}\cdot 32009^{6} \)	18T521	Trivial (GRH)
18.4.4405473434934059943108359950336.1	x^18 + 10x^16 - 51x^14 - 316x^12 + 338x^10 + 2450x^8 + 2872x^6 + 1091x^4 + 68x^2 + 1	\( -\,2^{12}\cdot 32009^{6} \)	18T521	$[2]$ (GRH)
18.8.17621893739736239772433439801344.1	x^18 + 22x^16 + 122x^14 - 306x^12 - 3655x^10 - 3106x^8 + 11629x^6 + 1332x^4 - 9435x^2 + 3364	\( -\,2^{14}\cdot 32009^{6} \)	18T521	Trivial (GRH)
18.8.17621893739736239772433439801344.2	x^18 + 2x^16 - 73x^14 - 206x^12 + 1152x^10 + 3126x^8 - 6344x^6 - 14675x^4 + 10000x^2 + 15625	\( -\,2^{14}\cdot 32009^{6} \)	18T521	Trivial (GRH)
18.14.35243787479472479544866879602688.1	x^18 - 15x^16 + 81x^14 - 191x^12 + 163x^10 + 61x^8 - 149x^6 + 34x^4 + 24x^2 - 8	\( 2^{15}\cdot 32009^{6} \)	18T521	Trivial (GRH)
18.6.35243787479472479544866879602688.1	x^18 + 9x^16 + 17x^14 - 39x^12 - 113x^10 + 25x^8 + 155x^6 + 10x^4 - 40x^2 - 8	\( 2^{15}\cdot 32009^{6} \)	18T521	Trivial (GRH)
18.14.981630043037493479115365283435793.1	x^18 - 2x^17 - 42x^16 + 167x^15 + 356x^14 - 3424x^13 + 4855x^12 + 18899x^11 - 58939x^10 - 19557x^9 + 158714x^8 + 39695x^7 - 182824x^6 - 98664x^5 + 53095x^4 + 47038x^3 + 2083x^2 - 5140x - 1039	\( 97^{3}\cdot 32009^{6} \)	18T521	Trivial (GRH)
18.6.981630043037493479115365283435793.1	x^18 - 3x^17 - 8x^16 + 124x^15 - 619x^14 - 1029x^13 + 6753x^12 + 11929x^11 - 21709x^10 - 71825x^9 - 37431x^8 + 82141x^7 + 161309x^6 + 178339x^5 + 189414x^4 + 167932x^3 + 94605x^2 + 32247x + 4806	\( 97^{3}\cdot 32009^{6} \)	18T521	Trivial (GRH)
18.10.1261890771353825087664258755140125.1	x^18 - 4x^17 - 27x^16 + 97x^15 + 346x^14 - 825x^13 - 3675x^12 + 4726x^11 + 26892x^10 - 28348x^9 - 104218x^8 + 101955x^7 + 247344x^6 - 207718x^5 - 500820x^4 + 649205x^3 + 34356x^2 - 358992x + 139968	\( 3^{22}\cdot 5^{3}\cdot 11^{8}\cdot 107^{6} \)	18T521	Trivial (GRH)
18.10.1938264224799475334652301447895232.1	x^18 - 31x^16 + 318x^14 - 978x^12 - 2541x^10 + 14859x^8 + 117x^6 - 30843x^4 - 17307x^2 - 2187	\( 2^{6}\cdot 3^{23}\cdot 11^{8}\cdot 107^{6} \)	18T521	Trivial (GRH)
18.0.141014799178804324718955493650305024.1	x^18 + 86x^16 + 2984x^14 + 55319x^12 + 603172x^10 + 3970251x^8 + 15402143x^6 + 32173404x^4 + 28123264x^2 + 2048576	\( -\,2^{12}\cdot 32009^{7} \)	18T521	$[2, 4420]$ (GRH)
18.0.141014799178804324718955493650305024.2	x^18 - 5x^17 + 32x^16 - 150x^15 + 701x^14 - 2365x^13 + 7382x^12 - 28847x^11 + 85736x^10 - 197768x^9 + 575581x^8 - 1390954x^7 + 2097717x^6 - 4684148x^5 + 8327002x^4 - 5442740x^3 + 6865944x^2 - 1604952x + 1403352	\( -\,2^{12}\cdot 32009^{7} \)	18T521	$[2, 4156]$ (GRH)
18.18.596927111187232576466742898477508785559748046759414357.1	x^18 - 9x^17 - 4713x^16 + 37908x^15 + 7582845x^14 - 53744019x^13 - 6048917846x^12 + 36993906789x^11 + 2700519652990x^10 - 13842994500965x^9 - 697169842983026x^8 + 2872146475884161x^7 + 101886839309334295x^6 - 315771580417732762x^5 - 7801208519486086464x^4 + 16132081734514574945x^3 + 257580432375126965074x^2 - 265699584714103969204x - 2050201927532681754088	\( 241^{3}\cdot 1033^{3}\cdot 3301^{3}\cdot 32009^{6} \)	18T521	Trivial (GRH)
18.18.596927111187232576466742898477508785559748046759414357.2	x^18 - 9x^17 - 5529x^16 + 44436x^15 + 10292937x^14 - 72828903x^13 - 8539018588x^12 + 52182911757x^11 + 3447114469486x^10 - 17715656763307x^9 - 742287334083178x^8 + 3076020274067557x^7 + 88069603774193460x^6 - 275049865186735271x^5 - 5623047621043485557x^4 + 11708136094287234244x^3 + 176804857217449151273x^2 - 182705284937259444809x - 2071089383551800498025	\( 241^{3}\cdot 1033^{3}\cdot 3301^{3}\cdot 32009^{6} \)	18T521	Trivial (GRH)