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 16 matches)

Label	Polynomial	Discriminant	Galois group	Class group
15.1.16477038080000000000000000.1	x^15 + 5x^11 - 4x^10 + 50x^7 - 80x^6 + 32x^5 + 125x^3 - 300x^2 + 240x - 64	\( -\,2^{24}\cdot 5^{16}\cdot 23^{5} \)	15T100	Trivial (GRH)
15.3.60610193289198080000000000000000.1	x^15 + 25x^11 - 20x^10 - 125x^3 + 300x^2 - 240x + 64	\( 2^{24}\cdot 5^{16}\cdot 11^{5}\cdot 43^{5} \)	15T100	Trivial (GRH)
15.1.312915159730527430614453923840000000.1	x^15 + 9x^13 - 216x^12 + 357x^11 - 4876x^10 + 8631x^9 - 28224x^8 + 94472x^7 + 213276x^6 - 699720x^5 - 236880x^4 + 1294300x^3 - 1089200x^2 + 392000x - 56000	\( -\,2^{18}\cdot 5^{7}\cdot 7^{9}\cdot 101^{2}\cdot 6092363^{2} \)	15T100	Trivial (GRH)
15.7.7289180414320769222686507858001920000000.1	x^15 - 63x^13 - 1980x^12 + 12096x^11 + 117274x^10 - 1181655x^9 - 359352x^8 + 14691665x^7 + 13797194x^6 - 39366720x^5 - 83106360x^4 - 60970700x^3 - 20741400x^2 - 3220000x - 184000	\( 2^{23}\cdot 5^{7}\cdot 23^{4}\cdot 73^{7}\cdot 59981^{2} \)	15T100	Trivial (GRH)
15.7.13790324594017072909477729953120256000000.1	x^15 + 198x^13 - 864x^12 + 7130x^11 + 21512x^10 - 383472x^9 - 712512x^8 + 3971312x^7 + 10176624x^6 - 3671840x^5 - 23912640x^4 - 8010400x^3 + 14440000x^2 + 8512000x + 1216000	\( 2^{24}\cdot 5^{6}\cdot 19^{4}\cdot 23^{2}\cdot 37^{2}\cdot 43^{2}\cdot 79^{5}\cdot 313^{2} \)	15T100	Trivial (GRH)
15.7.18866366579450294354517385665314816000000.1	x^15 - 162x^13 - 432x^12 + 10504x^11 + 24992x^10 - 1130400x^9 - 8695296x^8 + 19025280x^7 + 499850752x^6 + 2453729280x^5 + 5506375680x^4 + 6367436800x^3 + 3859251200x^2 + 1146880000x + 131072000	\( 2^{27}\cdot 5^{6}\cdot 37^{2}\cdot 163^{5}\cdot 7557157^{2} \)	15T100	Trivial (GRH)
15.5.29055909763442875483084887483088896000000.1	x^15 + 189x^13 - 108x^12 + 9756x^11 + 162330x^10 + 942597x^9 + 717984x^8 - 10844463x^7 - 50109174x^6 - 115536600x^5 - 164593080x^4 - 149548300x^3 - 82188600x^2 - 21588000x - 2056000	\( -\,2^{23}\cdot 3^{15}\cdot 5^{6}\cdot 37^{2}\cdot 181^{2}\cdot 257^{4}\cdot 281^{2} \)	15T100	Trivial (GRH)
15.7.98539808552158008427621845251903488000000.1	x^15 + 99x^13 - 432x^12 + 2795x^11 - 15324x^10 + 63459x^9 - 301752x^8 + 978344x^7 - 1379644x^6 - 460300x^5 + 2896920x^4 - 1561300x^3 - 676000x^2 + 364000x + 104000	\( 2^{18}\cdot 5^{6}\cdot 13^{4}\cdot 37^{5}\cdot 3485257483^{2} \)	15T100	Trivial (GRH)
15.5.19716834062238531710965065164233726976000000.1	x^15 - 297x^13 - 3204x^12 + 46185x^11 + 463062x^10 - 710082x^9 - 14595012x^8 - 169764568x^7 - 766844496x^6 - 1490235840x^5 - 3865098240x^4 - 5079654400x^3 - 5918720000x^2 - 5849088000x - 2228224000	\( -\,2^{16}\cdot 5^{6}\cdot 17^{4}\cdot 41^{2}\cdot 431^{5}\cdot 3036643^{2} \)	15T100	Trivial (GRH)
15.11.903220055915539404331852313843496708734976000000.1	x^15 + 324x^13 - 2808x^12 + 15414x^11 + 8208x^10 - 715554x^9 + 204120x^8 + 8908788x^7 + 4954824x^6 - 32517240x^5 - 32825520x^4 + 29720600x^3 + 47174400x^2 + 15288000x + 1456000	\( 2^{24}\cdot 3^{15}\cdot 5^{6}\cdot 7^{9}\cdot 13^{4}\cdot 456446131^{2} \)	15T100	Trivial (GRH)
15.3.51525487947813225854981517260718473944855552000000.1	x^15 - 576x^13 - 3456x^12 + 4208x^11 + 1792640x^10 - 1450872x^9 - 133337088x^8 - 23291424x^7 + 2284777472x^6 - 3483015040x^5 - 12492495360x^4 + 46507724800x^3 - 55455129600x^2 + 26292224000x - 4292608000	\( 2^{16}\cdot 5^{6}\cdot 131^{4}\cdot 733^{5}\cdot 2053^{2}\cdot 437693^{2} \)	15T100	Trivial (GRH)
15.11.465354434733444657917549052039955476309397504000000.1	x^15 - 36x^13 - 288x^12 - 59528x^11 - 943808x^10 - 9568440x^9 - 110763072x^8 - 967758176x^7 - 5106134656x^6 - 16395827840x^5 - 33040465920x^4 - 42126246400x^3 - 33061324800x^2 - 14601216000x - 2781184000	\( 2^{18}\cdot 5^{6}\cdot 7^{9}\cdot 19^{2}\cdot 61^{2}\cdot 67^{5}\cdot 97^{4}\cdot 132421^{2} \)	15T100	Trivial (GRH)
15.11.987698322701449818222428064455485979759874048000000.1	x^15 - 6x^14 - 609x^13 + 1918x^12 + 109824x^11 - 351336x^10 - 9177561x^9 + 28595400x^8 + 413865150x^7 - 702248000x^6 - 11065807500x^5 - 14833200000x^4 + 170839125000x^3 + 688080000000x^2 - 1015200000000x - 3008000000000	\( 2^{18}\cdot 3^{25}\cdot 5^{6}\cdot 7^{2}\cdot 11^{5}\cdot 47^{4}\cdot 1153^{2}\cdot 74561^{2} \)	15T100	Trivial (GRH)
15.11.4997116069370523770922817361794182094079365120000000.1	x^15 - 846x^13 - 6768x^12 + 141712x^11 + 2470432x^10 + 17068680x^9 + 97426368x^8 + 617654944x^7 + 3048750464x^6 + 9692440960x^5 + 19512852480x^4 + 24878681600x^3 + 19525171200x^2 + 8623104000x + 1642496000	\( 2^{18}\cdot 5^{7}\cdot 7^{2}\cdot 11^{5}\cdot 79^{5}\cdot 401^{4}\cdot 19713263^{2} \)	15T100	Trivial (GRH)
15.15.1515690136126498500450210146631049938378469084270592000000.1	x^15 - 1656x^13 - 13248x^12 + 853252x^11 + 14049472x^10 - 64056600x^9 - 3309446592x^8 - 34903903136x^7 - 189549759616x^6 - 611135258240x^5 - 1232034693120x^4 - 1570831270400x^3 - 1232812492800x^2 - 544459776000x - 103706624000	\( 2^{18}\cdot 5^{6}\cdot 7^{4}\cdot 257^{5}\cdot 3617^{4}\cdot 9043^{2}\cdot 99103^{2} \)	15T100	Trivial (GRH)
15.15.34548641890596001947725147253590025498737248434540544000000.1	x^15 - 2619x^13 - 7884x^12 + 1702691x^11 + 3664210x^10 - 230491062x^9 - 677187108x^8 + 7850882532x^7 + 25585029672x^6 - 14869135600x^5 - 101017715040x^4 - 37835364800x^3 + 98787324800x^2 + 75851328000x + 14447872000	\( 2^{18}\cdot 5^{6}\cdot 7^{2}\cdot 229^{5}\cdot 56437^{4}\cdot 164142457^{2} \)	15T100	Trivial (GRH)