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
18.0.15034518472210440781824.2	x^18 - 2x^15 + 3x^12 + 4x^9 + 3x^6 - 2x^3 + 1	\( -\,2^{18}\cdot 3^{18}\cdot 23^{6} \)	18T394	Trivial
18.2.68563446071980773298176.1	x^18 - x^15 + 3x^9 - x^3 - 1	\( 2^{12}\cdot 3^{18}\cdot 11^{6}\cdot 29^{3} \)	18T394	Trivial
18.0.71217647711936550273024.1	x^18 + x^16 + 10x^14 + 52x^12 + 121x^10 + 289x^8 + 569x^6 + 593x^4 + 251x^2 + 9	\( -\,2^{24}\cdot 3^{14}\cdot 31^{6} \)	18T394	Trivial (GRH)
18.6.148204394789719081222144.1	x^18 - 6x^16 + 7x^14 - 9x^12 + 51x^10 - 100x^8 + 120x^6 - 159x^4 + 219x^2 - 151	\( 2^{24}\cdot 37^{6}\cdot 151^{3} \)	18T394	Trivial (GRH)
18.6.210931560055756625543168.1	x^18 - 8x^16 + 12x^14 + 32x^12 - 36x^10 - 172x^8 + 92x^6 + 416x^4 - 60x^2 - 428	\( 2^{26}\cdot 37^{6}\cdot 107^{3} \)	18T394	Trivial
18.0.223513629375742151897088.1	x^18 - 5x^15 + 10x^12 - 11x^9 + 10x^6 - 5x^3 + 1	\( -\,2^{12}\cdot 3^{18}\cdot 11^{6}\cdot 43^{3} \)	18T394	Trivial
18.2.514687157793406972592128.1	x^18 - 9x^16 + 39x^14 - 109x^12 + 220x^10 - 252x^8 + 355x^6 - 547x^4 + 886x^2 - 1303	\( 2^{18}\cdot 31^{6}\cdot 1303^{3} \)	18T394	Trivial
18.4.2775641410382903738630144.1	x^18 - 2x^17 + x^16 - 18x^15 + 30x^14 - 18x^13 + 116x^12 - 194x^11 + 176x^10 - 298x^9 + 514x^8 - 574x^7 + 242x^6 + 618x^5 - 1620x^4 + 1970x^3 - 1353x^2 + 484x - 67	\( -\,2^{24}\cdot 37^{6}\cdot 401^{3} \)	18T394	Trivial
18.0.5362395958062483294921875.1	x^18 - 6x^17 + 19x^16 - 62x^15 + 196x^14 - 506x^13 + 1233x^12 - 2872x^11 + 5752x^10 - 11013x^9 + 20122x^8 - 29253x^7 + 42430x^6 - 56818x^5 + 58710x^4 - 74047x^3 + 61944x^2 - 32778x + 55269	\( -\,5^{9}\cdot 23^{6}\cdot 2647^{3} \)	18T394	$[6]$
18.4.5484891214174855928741888.1	x^18 - 2x^17 - 7x^16 + 20x^15 - 110x^13 + 184x^12 + 164x^11 - 972x^10 + 1676x^9 - 1184x^8 - 248x^7 + 1570x^6 - 1598x^5 + 942x^4 - 292x^3 + 75x^2 - 6x + 1	\( -\,2^{26}\cdot 37^{6}\cdot 317^{3} \)	18T394	Trivial
18.6.53321094333449969673424896.2	x^18 - 18x^14 - 90x^12 + 9x^10 + 1242x^8 - 543x^6 - 5652x^4 + 8928x^2 - 3904	\( 2^{12}\cdot 3^{18}\cdot 23^{6}\cdot 61^{3} \)	18T394	Trivial (GRH)
18.0.70669362444743672000000000.1	x^18 - x^17 - 5x^16 - 19x^15 + 65x^14 + 43x^13 - 12x^12 - 529x^11 + 264x^10 + 175x^9 + 2247x^8 - 3987x^7 + 6440x^6 - 21524x^5 + 37660x^4 - 37965x^3 + 37556x^2 - 34509x + 14549	\( -\,2^{12}\cdot 5^{9}\cdot 37^{6}\cdot 151^{3} \)	18T394	$[2, 4]$
18.6.182924986251384432992452608.1	x^18 - 2x^15 - 18x^14 - 24x^13 - 48x^12 + 54x^11 + 45x^10 + 274x^9 + 549x^8 + 186x^7 + 38x^6 - 450x^5 + 99x^4 + 436x^3 + 234x^2 + 282x - 43	\( 2^{18}\cdot 3^{18}\cdot 23^{9} \)	18T394	Trivial (GRH)
18.12.225541330581011212170952704.1	x^18 - 6x^16 + 8x^14 - 43x^12 + 295x^10 - 565x^8 + 169x^6 + 322x^4 - 153x^2 + 9	\( -\,2^{30}\cdot 3^{6}\cdot 257^{6} \)	18T394	Trivial (GRH)
18.2.1804330644648089697367621632.1	x^18 + 14x^16 + 66x^14 + 142x^12 - 87x^10 - 1800x^8 - 5055x^6 - 5102x^4 - 1140x^2 - 72	\( 2^{33}\cdot 3^{6}\cdot 257^{6} \)	18T394	Trivial
18.6.1945837710744813682262462464.1	x^18 - 8x^17 + 9x^16 + 78x^15 - 170x^14 - 441x^13 + 1394x^12 + 1244x^11 - 6374x^10 - 1175x^9 + 18003x^8 - 2566x^7 - 32387x^6 + 10297x^5 + 31543x^4 - 8113x^3 - 18892x^2 + 3315x + 13	\( 2^{12}\cdot 13^{8}\cdot 37^{6}\cdot 61^{3} \)	18T394	Trivial (GRH)
18.2.1957287753903949511628161024.1	x^18 + 19x^16 + 117x^14 + 200x^12 - 592x^10 - 2905x^8 - 4949x^6 - 4489x^4 - 2230x^2 - 479	\( 2^{24}\cdot 101^{6}\cdot 479^{3} \)	18T394	Trivial
18.6.2190864986407862105758203125.1	x^18 - 6x^17 + 11x^16 + 7x^15 - 106x^14 + 254x^13 - 39x^12 - 682x^11 + 1286x^10 - 127x^9 - 3630x^8 + 1618x^7 + 4406x^6 - 397x^5 + 504x^4 + 494x^3 - 1913x^2 - 1561x - 355	\( 5^{8}\cdot 257^{6}\cdot 269^{3} \)	18T394	$[2]$ (GRH)
18.0.188521017135728366078671192064.1	x^18 - 6x^17 + 31x^16 - 124x^15 + 403x^14 - 1144x^13 + 2830x^12 - 6420x^11 + 13956x^10 - 27780x^9 + 51861x^8 - 91584x^7 + 173635x^6 - 319924x^5 + 597495x^4 - 843778x^3 + 865576x^2 - 666536x + 330469	\( -\,2^{24}\cdot 37^{6}\cdot 16361^{3} \)	18T394	$[4, 68]$ (GRH)
18.0.196828034361502629659007778816.1	x^18 + 18x^16 + 135x^14 + 714x^12 + 3303x^10 + 10854x^8 + 26697x^6 + 57150x^4 + 64584x^2 + 65350	\( -\,2^{35}\cdot 37^{6}\cdot 1307^{3} \)	18T394	$[54]$ (GRH)
18.0.442064923298304690829165330432.1	x^18 - 6x^17 + 29x^16 - 102x^15 + 336x^14 - 890x^13 + 2170x^12 - 4566x^11 + 9356x^10 - 15604x^9 + 22168x^8 - 24046x^7 + 21992x^6 - 15918x^5 + 17462x^4 - 15366x^3 + 13571x^2 - 3898x + 6053	\( -\,2^{26}\cdot 37^{6}\cdot 13693^{3} \)	18T394	$[2, 100]$ (GRH)
18.12.3796833129811863922362236940288.1	x^18 - 42x^16 - 28x^15 + 675x^14 + 900x^13 - 5181x^12 - 10962x^11 + 17316x^10 + 64040x^9 + 6615x^8 - 167646x^7 - 198527x^6 + 61236x^5 + 335340x^4 + 342144x^3 + 174960x^2 + 46656x + 5184	\( -\,2^{12}\cdot 3^{31}\cdot 107^{6} \)	18T394	Trivial (GRH)
18.18.35041425235206245760443200000000.1	x^18 - 6x^17 - 42x^16 + 320x^15 + 116x^14 - 4309x^13 + 5483x^12 + 18970x^11 - 42448x^10 - 22590x^9 + 108365x^8 - 23256x^7 - 107909x^6 + 46896x^5 + 44304x^4 - 14953x^3 - 8607x^2 - 505x + 1	\( 2^{12}\cdot 5^{8}\cdot 37^{6}\cdot 107^{3}\cdot 191^{3} \)	18T394	Trivial (GRH)
18.18.89893826072563345946632000000000.1	x^18 - 2x^17 - 67x^16 + 115x^15 + 1769x^14 - 2449x^13 - 23841x^12 + 24381x^11 + 178681x^10 - 120414x^9 - 760652x^8 + 280327x^7 + 1794673x^6 - 231163x^5 - 2145279x^4 - 47748x^3 + 1037777x^2 + 45603x - 111031	\( 2^{12}\cdot 5^{9}\cdot 37^{6}\cdot 16361^{3} \)	18T394	$[2]$ (GRH)