Global number field search results

Further refine search

Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying all 8 matches)

Label	Polynomial	Discriminant	Galois group	Class group
15.3.4413675765625000000000000000000.1	x^15 + 40x^13 - 20x^12 + 350x^11 + 1224x^10 - 8050x^9 + 66860x^8 - 242935x^7 + 1089460x^6 - 2540910x^5 + 7722400x^4 - 11638655x^3 + 19943960x^2 - 15150000x + 3225664	\( 2^{18}\cdot 5^{24}\cdot 7^{10} \)	15T92	$[3]$ (GRH)
15.3.227105922614218681297997824000000.1	x^15 - 6x^14 - x^13 + 11x^12 - 1020x^11 + 11410x^10 - 9030x^9 - 182438x^8 - 529425x^7 + 11997606x^6 - 58450939x^5 + 145415117x^4 - 204287273x^3 + 155961176x^2 - 55625899x + 7277179	\( 2^{18}\cdot 5^{6}\cdot 7^{10}\cdot 13^{2}\cdot 1077707^{2} \)	15T92	$[3]$ (GRH)
15.7.695337504354450262881345263439253504000000.1	x^15 - 180x^13 - 144x^12 + 6684x^11 + 22688x^10 - 62424x^9 - 624384x^8 + 10372064x^7 + 60653056x^6 + 29354240x^5 - 267264000x^4 - 302528000x^3 + 277657600x^2 + 415744000x + 118784000	\( 2^{18}\cdot 5^{6}\cdot 7^{10}\cdot 29^{4}\cdot 921789289^{2} \)	15T92	$[3]$ (GRH)
15.11.14510776668759878086782120121838473216000000.1	x^15 - 360x^13 - 648x^12 + 39784x^11 + 127584x^10 - 1599876x^9 - 6284088x^8 + 21382724x^7 + 72393848x^6 + 18576960x^5 - 80928000x^4 - 45803000x^3 + 21018800x^2 + 15736000x + 2248000	\( 2^{18}\cdot 5^{6}\cdot 7^{10}\cdot 281^{4}\cdot 44850007^{2} \)	15T92	$[3]$ (GRH)
15.11.4248332612098651806088183712995608825856000000.1	x^15 - 306x^13 - 288x^12 + 24240x^11 + 2756x^10 - 112752x^9 + 5324544x^8 - 1338292x^7 - 40210112x^6 - 9352320x^5 + 85779360x^4 + 95779000x^3 + 41322000x^2 + 7952000x + 568000	\( 2^{18}\cdot 5^{6}\cdot 7^{10}\cdot 71^{4}\cdot 223^{2}\cdot 1709^{2}\cdot 31541^{2} \)	15T92	$[3]$ (GRH)
15.7.6307022116728638404825373947273030733824000000.1	x^15 - 360x^13 - 2736x^12 + 15004x^11 + 371872x^10 + 1327176x^9 - 12871296x^8 - 80152416x^7 + 521764864x^6 - 260002560x^5 - 2313216000x^4 + 2618432000x^3 + 2403174400x^2 - 3598336000x + 1028096000	\( 2^{18}\cdot 5^{6}\cdot 7^{10}\cdot 251^{4}\cdot 2477^{2}\cdot 473117^{2} \)	15T92	$[3]$ (GRH)
15.15.191462095148251089869153304845837565344604688384000000.1	x^15 - 5082x^13 - 7752x^12 + 10106636x^11 + 37878064x^10 - 10043207752x^9 - 63850635200x^8 + 5167148500176x^7 + 47814832667776x^6 - 1236668673788960x^5 - 15834444242156160x^4 + 80444100448171200x^3 + 1792435586109190400x^2 + 6375394044674816000x + 542000152064000	\( 2^{18}\cdot 5^{6}\cdot 7^{10}\cdot 29^{4}\cdot 41^{4}\cdot 287744824009^{2} \)	15T92	$[3]$ (GRH)
15.15.2951913264025688280807555730603157129805843381784576000000.1	x^15 - 1980x^13 - 2232x^12 + 1066084x^11 - 1229584x^10 - 182612916x^9 + 706537368x^8 + 2232940764x^7 - 7767061528x^6 + 2017438560x^5 + 8709408000x^4 - 4929283000x^3 - 2262026800x^2 + 1693496000x - 241928000	\( 2^{18}\cdot 5^{6}\cdot 7^{10}\cdot 1609^{2}\cdot 30241^{4}\cdot 34326797^{2} \)	15T92	$[3]$ (GRH)