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 19 matches)

Label	Polynomial	Discriminant	Galois group	Class group
15.5.464317130069216763190044343471527099609375.1	x^15 - 1870x^12 - 32010x^11 + 777876x^10 - 6851625x^9 + 30190710x^8 - 74603760x^7 + 2486105930x^6 - 13069638582x^5 - 50184822600x^4 - 124388611655x^3 + 1660824701580x^2 + 7902686294580x + 5476184846968	\( -\,3^{6}\cdot 5^{24}\cdot 11^{12}\cdot 23^{7} \)	15T40	$[5, 5, 5]$ (GRH)
15.5.464317130069216763190044343471527099609375.2	x^15 - 330x^13 - 4620x^12 + 12650x^11 + 1106633x^10 + 4277350x^9 - 70074125x^8 - 1077527385x^7 + 10086284725x^6 + 100194176808x^5 + 168219899100x^4 - 16147355822675x^3 - 69620528681495x^2 + 79865978259705x + 368982332191957	\( -\,3^{6}\cdot 5^{24}\cdot 11^{12}\cdot 23^{7} \)	15T40	$[5, 5, 5]$ (GRH)
15.3.881985079509661940222184560156250000000000.1	x^15 - 25377x^10 + 370293x^5 + 1185921	\( 2^{10}\cdot 3^{13}\cdot 5^{17}\cdot 11^{13}\cdot 29^{5} \)	$F_5 \times S_3$ (as 15T11)	$[5, 30]$ (GRH)
15.1.2628311466391066187500000000000000000000000.1	x^15 - 5x^14 + 20x^12 + 25x^11 + 10769x^10 - 36230x^9 + 180490x^8 + 505680x^7 - 1263140x^6 + 40460928x^5 - 62922700x^4 + 648860840x^3 - 1694606600x^2 + 1630311940x + 46251096148	\( -\,2^{23}\cdot 5^{27}\cdot 19^{13} \)	$F_5 \times S_3$ (as 15T11)	$[2, 10, 20]$ (GRH)
15.3.140685733870773315116885561600000000000000000.1	x^15 - 5x^14 - 80x^13 + 460x^12 + 2265x^11 - 15553x^10 - 24090x^9 + 392310x^8 - 976120x^7 + 1638320x^6 - 2453272x^5 + 68720x^4 - 5194480x^3 + 231378160x^2 + 420777040x - 520184176	\( 2^{23}\cdot 5^{17}\cdot 89^{13} \)	$F_5 \times S_3$ (as 15T11)	$[4, 40]$ (GRH)
15.1.776673564181413299414214047596093750000000000.1	x^15 + 10x^13 - 850x^12 + 2070x^11 + 30349x^10 - 183910x^9 - 3083670x^8 - 13206720x^7 + 473102930x^6 + 2772478367x^5 - 8431068230x^4 - 57993380220x^3 + 184194250760x^2 + 2061802323020x + 4449241879687	\( -\,2^{10}\cdot 5^{17}\cdot 7^{13}\cdot 29^{13} \)	$F_5 \times S_3$ (as 15T11)	$[2, 2, 30]$ (GRH)
15.1.898400045220655932623997317447073792000000000.1	x^15 - 17028x^10 + 265060026x^5 - 41497747632	\( -\,2^{23}\cdot 3^{13}\cdot 5^{9}\cdot 11^{13}\cdot 251^{5} \)	$F_5 \times S_3$ (as 15T11)	$[5, 85]$ (GRH)
15.1.923759194031620398058860778808593750000000000.1	x^15 - 5x^14 + 25x^13 - 95x^12 + 285x^11 + 19844x^10 - 66945x^9 - 175530x^8 + 3169175x^7 - 5716705x^6 + 145166318x^5 - 219639400x^4 - 2382376375x^3 - 3290217500x^2 + 6382037500x + 325852261250	\( -\,2^{10}\cdot 5^{27}\cdot 11^{12}\cdot 131^{5} \)	$F_5 \times S_3$ (as 15T11)	$[5, 40]$ (GRH)
15.1.6184814803411251939738171243533875000000000000.1	x^15 - 5x^13 - 160x^12 + 10x^11 + 376x^10 + 10230x^9 - 2280x^8 - 284155x^7 - 328800x^6 + 11711x^5 - 11509040x^4 + 5331200x^3 - 5059000x^2 - 48405120x - 35925416	\( -\,2^{12}\cdot 5^{15}\cdot 11^{12}\cdot 6911^{5} \)	$F_5 \times S_3$ (as 15T11)	$[5, 5, 5]$ (GRH)
15.1.37362650893059880826731834411621093750000000000.1	x^15 - 5x^14 - 15x^13 - 25x^12 + 565x^11 + 794x^10 - 1125x^9 - 29310x^8 - 139405x^7 + 309215x^6 + 186450x^5 - 3565970x^4 + 4878805x^3 - 4003430x^2 - 19039100x - 9329068	\( -\,2^{10}\cdot 5^{28}\cdot 11^{12}\cdot 199^{5} \)	$F_5 \times S_3$ (as 15T11)	$[5, 30]$ (GRH)
15.1.74813147538844994892441022008177343750000000000.1	x^15 - 85701x^10 + 18380656217x^5 - 28950040844263	\( -\,2^{10}\cdot 5^{17}\cdot 7^{13}\cdot 11^{13}\cdot 31^{5} \)	$F_5 \times S_3$ (as 15T11)	$[5, 30]$ (GRH)
15.1.244029338779125043943806918241370375000000000000.1	x^15 - 5x^14 + 145x^13 - 370x^12 + 7385x^11 + 377x^10 + 165195x^9 + 114930x^8 + 88155x^7 + 27605475x^6 + 15925923x^5 + 438449760x^4 - 1007584920x^3 + 5251526460x^2 - 2872916100x + 13217245308	\( -\,2^{12}\cdot 3^{12}\cdot 5^{15}\cdot 7^{13}\cdot 2069^{5} \)	$F_5 \times S_3$ (as 15T11)	$[5, 40]$ (GRH)
15.3.2040831918205308698658487548828125000000000000000.1	x^15 - 5x^14 - 65x^13 + 265x^12 + 1905x^11 - 4006x^10 - 34875x^9 + 124650x^8 + 377075x^7 + 1279775x^6 - 2527180x^5 - 9127000x^4 + 68380625x^3 - 20459750x^2 + 244074250x - 401691100	\( 2^{15}\cdot 5^{28}\cdot 73^{13} \)	$F_5 \times S_3$ (as 15T11)	$[6, 30]$ (GRH)
15.1.2194927079071729169273313590285013843750000000000.1	x^15 - 33759x^10 + 715190553x^5 + 163598974587	\( -\,2^{10}\cdot 3^{13}\cdot 5^{15}\cdot 31^{13}\cdot 71^{5} \)	$F_5 \times S_3$ (as 15T11)	$[5, 45]$ (GRH)
15.1.2844058494074397240031532493118252843750000000000.1	x^15 - 39711x^10 - 288331x^5 - 923521	\( -\,2^{10}\cdot 5^{15}\cdot 31^{13}\cdot 1301^{5} \)	$F_5 \times S_3$ (as 15T11)	$[5, 10, 10]$ (GRH)
15.1.5617330134094061678662632074276610010758000000000.1	x^15 - 145860x^10 - 243079056x^5 - 4696791102432	\( -\,2^{10}\cdot 3^{12}\cdot 5^{9}\cdot 11^{13}\cdot 10889^{5} \)	$F_5 \times S_3$ (as 15T11)	$[165]$ (GRH)
15.1.11062882564988453344561367303320248843750000000000.1	x^15 - 47157x^10 - 348513x^5 - 1185921	\( -\,2^{10}\cdot 3^{13}\cdot 5^{15}\cdot 11^{13}\cdot 1451^{5} \)	$F_5 \times S_3$ (as 15T11)	$[15, 45]$ (GRH)
15.1.35347664861463185809488152464433328209920000000000.1	x^15 - 2x^14 - 623x^13 + 956x^12 + 148616x^11 + 1678622x^10 - 22740148x^9 - 945266382x^8 + 4164671679x^7 + 68139475134x^6 + 2607605182191x^5 - 47700853439788x^4 + 481533826058428x^3 - 5829949369516366x^2 + 57762542818688054x - 294690202775308898	\( -\,2^{23}\cdot 5^{10}\cdot 19^{13}\cdot 29^{13} \)	$F_5 \times S_3$ (as 15T11)	$[5, 5, 10]$ (GRH)
15.3.152254411749787445620075030097255524878656250000000000.1	x^15 - 199629x^10 + 1618399683x^5 + 500575083867	\( 2^{10}\cdot 3^{13}\cdot 5^{15}\cdot 11^{5}\cdot 29^{5}\cdot 41^{13} \)	$F_5 \times S_3$ (as 15T11)	$[5, 5, 5]$ (GRH)