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 matches 1-50 of 93)

Label	Polynomial	Discriminant	Galois group	Class group
6.0.276459339026136384.4	x^6 - 2x^5 + 343x^4 - 4302x^3 + 196062x^2 - 677160x + 3920400	\( -\,2^{6}\cdot 3^{3}\cdot 54287^{3} \)	$S_3$ (as 6T2)	$[2, 2, 90, 3780]$ (GRH)
6.0.487294769549888000.1	x^6 - 2x^5 + 169x^4 + 6064x^3 + 197554x^2 + 2097328x + 12857136	\( -\,2^{9}\cdot 5^{3}\cdot 103^{3}\cdot 191^{3} \)	$S_3$ (as 6T2)	$[2, 2, 4, 84, 756]$ (GRH)
6.0.827762709645597375.1	x^6 - x^5 + 251x^4 - 3343x^3 + 575252x^2 + 4609088x + 225366016	\( -\,3^{3}\cdot 5^{3}\cdot 13^{4}\cdot 97^{5} \)	$C_6$ (as 6T1)	$[2, 14, 84, 588]$ (GRH)
6.0.885997347750498816.1	x^6 - 596x^4 + 88804x^2 + 34576416	\( -\,2^{9}\cdot 3^{3}\cdot 7^{3}\cdot 5717^{3} \)	$S_3$ (as 6T2)	$[2, 258, 5418]$ (GRH)
6.0.986929364330330624.1	x^6 - 2x^5 + 25x^4 - 5288x^3 + 254314x^2 - 4045664x + 22857408	\( -\,2^{9}\cdot 7^{3}\cdot 23^{3}\cdot 773^{3} \)	$S_3$ (as 6T2)	$[2, 166, 3984]$ (GRH)
6.0.1376476767489195072.2	x^6 - 380x^4 + 36100x^2 + 4449552	\( -\,2^{6}\cdot 3^{3}\cdot 92699^{3} \)	$S_3$ (as 6T2)	$[2, 2, 104, 2600]$ (GRH)
6.0.1429485351030646272.1	x^6 + 324x^4 + 26244x^2 + 40553568	\( -\,2^{9}\cdot 3^{3}\cdot 11^{3}\cdot 17^{3}\cdot 251^{3} \)	$S_3$ (as 6T2)	$[2, 2, 202, 1414]$ (GRH)
6.0.1456638979489726976.1	x^6 + 1228x^4 + 376996x^2 + 40808736	\( -\,2^{9}\cdot 141697^{3} \)	$S_3$ (as 6T2)	$[91, 22568]$ (GRH)
6.0.1819458271609754112.3	x^6 + 810x^4 + 164025x^2 + 10987272	\( -\,2^{9}\cdot 3^{3}\cdot 50867^{3} \)	$S_3$ (as 6T2)	$[2, 4, 96, 1440]$ (GRH)
6.0.2136023191251656000.1	x^6 + 412x^4 + 42436x^2 + 5151440	\( -\,2^{6}\cdot 5^{3}\cdot 7^{3}\cdot 9199^{3} \)	$S_3$ (as 6T2)	$[6, 138, 1518]$ (GRH)
6.0.2519231070906432000.1	x^6 + 628x^4 + 98596x^2 + 5442720	\( -\,2^{9}\cdot 3^{3}\cdot 5^{3}\cdot 17^{3}\cdot 23^{3}\cdot 29^{3} \)	$S_3$ (as 6T2)	$[2, 2, 2, 254, 1270]$ (GRH)
6.0.3508315833384935936.1	x^6 - 348x^4 + 30276x^2 + 6077984	\( -\,2^{9}\cdot 11^{3}\cdot 31^{3}\cdot 557^{3} \)	$S_3$ (as 6T2)	$[2, 2, 2, 130, 5330]$ (GRH)
6.0.3583740427054978112.1	x^6 + 310x^4 + 24025x^2 + 55091088	\( -\,2^{6}\cdot 13^{3}\cdot 29429^{3} \)	$S_3$ (as 6T2)	$[5, 190, 2280]$ (GRH)
6.0.7188252085144290816.1	x^6 - 5496x^4 - 1838x^3 + 7601157x^2 + 5100450x + 46649575	\( -\,2^{9}\cdot 3^{9}\cdot 919^{4} \)	$C_6$ (as 6T1)	$[3, 3, 111462]$ (GRH)
6.0.16383365122075470000.1	x^6 - 3x^5 + 4x^4 - 3x^3 - 9302x^2 + 9303x + 28848603	\( -\,2^{4}\cdot 3^{3}\cdot 5^{4}\cdot 2791^{4} \)	$S_3$ (as 6T2)	$[3, 3, 216, 648]$ (GRH)
6.0.21987774715562940375.1	x^6 - 3x^5 - 10359x^4 - 262833x^3 + 27314802x^2 + 1446882480x + 19471804416	\( -\,3^{9}\cdot 5^{3}\cdot 7^{4}\cdot 13^{4}\cdot 19^{4} \)	$C_6$ (as 6T1)	$[3, 3, 3, 3, 54666]$ (GRH)
6.0.45038029553267697072.1	x^6 - 3x^5 + 4x^4 - 3x^3 - 11978x^2 + 11979x + 47832147	\( -\,2^{4}\cdot 3^{3}\cdot 7^{4}\cdot 17^{4}\cdot 151^{4} \)	$S_3$ (as 6T2)	$[3, 3, 3, 195, 195]$ (GRH)
6.0.101097431351147483307.1	x^6 - 3x^5 + 6x^4 + 1261011x^3 - 1891521x^2 - 1891530x + 397542860100	\( -\,3^{7}\cdot 11^{4}\cdot 31^{4}\cdot 43^{4} \)	$S_3$ (as 6T2)	$[6, 6, 168, 168]$ (GRH)
6.0.127925328011997166875.1	x^6 + x^4 - 31103x^2 + 80621568	\( -\,3^{3}\cdot 5^{4}\cdot 7^{4}\cdot 31^{4}\cdot 43^{4} \)	$S_3$ (as 6T2)	$[3, 3, 3, 3, 3, 90, 90]$ (GRH)
6.0.127947264962647622427.1	x^6 - 3x^5 + 4x^4 - 3x^3 - 15551x^2 + 15552x + 80621568	\( -\,3^{3}\cdot 13^{4}\cdot 37^{4}\cdot 97^{4} \)	$S_3$ (as 6T2)	$[3, 3, 3, 396, 396]$ (GRH)
6.0.190529774530960489443.1	x^6 - 9919x^3 + 975896298559	\( -\,3^{9}\cdot 7^{4}\cdot 13^{4}\cdot 109^{4} \)	$C_6$ (as 6T1)	$[3, 3, 3, 3, 3, 5187]$ (GRH)
6.0.208086348062159455707.1	x^6 - 3x^5 + 6x^4 + 35119x^3 - 52683x^2 - 52692x + 308494096	\( -\,3^{7}\cdot 7^{4}\cdot 13^{4}\cdot 193^{4} \)	$S_3$ (as 6T2)	$[3, 3, 3, 3, 3, 42, 126]$ (GRH)
6.0.233777450633202016875.1	x^6 - 3x^5 + 4x^4 - 3x^3 - 1717757x^2 + 1717758x + 983564182188	\( -\,3^{3}\cdot 5^{4}\cdot 19^{4}\cdot 571^{4} \)	$S_3$ (as 6T2)	$[3, 3, 420, 420]$ (GRH)
6.0.239886728386521056883.1	x^6 - 2153935x^3 + 1159941793843	\( -\,3^{9}\cdot 7^{4}\cdot 19^{4}\cdot 79^{4} \)	$C_6$ (as 6T1)	$[3, 3, 21, 84, 84]$ (GRH)
6.0.244792767356078885307.1	x^6 + 111520227	\( -\,3^{11}\cdot 7^{4}\cdot 13^{4}\cdot 67^{4} \)	$S_3$ (as 6T2)	$[3, 3, 3, 3, 3, 99, 99]$ (GRH)
6.0.250468392121087200723.1	x^6 - 10621x^3 + 1198108713061	\( -\,3^{9}\cdot 13^{4}\cdot 19^{4}\cdot 43^{4} \)	$C_6$ (as 6T1)	$[3, 3, 3, 3, 3, 9, 819]$ (GRH)
6.0.270016660719732616875.1	x^6 - 3x^5 + 6x^4 + 37483x^3 - 56229x^2 - 56238x + 351412516	\( -\,3^{7}\cdot 5^{4}\cdot 23^{4}\cdot 163^{4} \)	$S_3$ (as 6T2)	$[3, 3, 3, 282, 282]$ (GRH)
6.0.389444934515598390375.1	x^6 - 3x^5 - 21267x^4 - 411477x^3 + 113880042x^2 + 4722731136x + 49567764384	\( -\,3^{9}\cdot 5^{3}\cdot 3547^{4} \)	$C_6$ (as 6T1)	$[2, 4, 4, 4, 13188]$ (GRH)
6.0.421504305441177469923.1	x^6 - 12097x^3 + 1770243636673	\( -\,3^{9}\cdot 12097^{4} \)	$C_6$ (as 6T1)	$[3, 9, 9, 6669]$ (GRH)
6.0.432914561184912730587.1	x^6 + 1174722978243	\( -\,3^{11}\cdot 79^{4}\cdot 89^{4} \)	$S_3$ (as 6T2)	$[3, 420, 1260]$ (GRH)
6.0.452956521111545088027.1	x^6 + 151698963	\( -\,3^{11}\cdot 13^{4}\cdot 547^{4} \)	$S_3$ (as 6T2)	$[3, 1032, 1032]$ (GRH)
6.0.525800232641772270000.1	x^6 - 3x^5 + 4x^4 - 3x^3 - 22142x^2 + 22143x + 163437483	\( -\,2^{4}\cdot 3^{3}\cdot 5^{4}\cdot 7^{4}\cdot 13^{4}\cdot 73^{4} \)	$S_3$ (as 6T2)	$[3, 3, 3, 3, 3, 84, 84]$ (GRH)
6.0.532416591510403300272.1	x^6 + x^4 - 577529x^2 + 27795075075	\( -\,2^{4}\cdot 3^{3}\cdot 11^{4}\cdot 13^{4}\cdot 233^{4} \)	$S_3$ (as 6T2)	$[3, 3, 3, 171, 513]$ (GRH)
6.0.609249596128325902512.1	x^6 + 175934892	\( -\,2^{4}\cdot 3^{11}\cdot 7^{4}\cdot 547^{4} \)	$S_3$ (as 6T2)	$[3, 6, 6, 114, 114]$ (GRH)
6.0.609792683196193005843.1	x^6 - 13267x^3 + 2335168305163	\( -\,3^{9}\cdot 13267^{4} \)	$C_6$ (as 6T1)	$[3, 1616709]$ (GRH)
6.0.664497231954275773872.1	x^6 + 9003202572	\( -\,2^{4}\cdot 3^{11}\cdot 7^{4}\cdot 13^{4}\cdot 43^{4} \)	$S_3$ (as 6T2)	$[3, 3, 3, 3, 3, 87, 87]$ (GRH)
6.0.723419777319917518512.1	x^6 - 3x^5 + 6x^4 + 95921x^3 - 143886x^2 - 143895x + 2300641225	\( -\,2^{4}\cdot 3^{11}\cdot 7^{4}\cdot 571^{4} \)	$S_3$ (as 6T2)	$[3, 3, 3, 3, 78, 234]$ (GRH)
6.0.772914998516735490003.1	x^6 - 14077x^3 + 2789525474533	\( -\,3^{9}\cdot 7^{4}\cdot 2011^{4} \)	$C_6$ (as 6T1)	$[3, 3, 3, 12, 5436]$ (GRH)
6.0.819043793650127635632.1	x^6 + 203989548	\( -\,2^{4}\cdot 3^{11}\cdot 7^{4}\cdot 19^{4}\cdot 31^{4} \)	$S_3$ (as 6T2)	$[3, 3, 3, 3, 3, 9, 18, 54]$ (GRH)
6.0.867930036502357034163.1	x^6 - 14491x^3 + 3042951772771	\( -\,3^{9}\cdot 43^{4}\cdot 337^{4} \)	$C_6$ (as 6T1)	$[3, 3, 3, 82251]$ (GRH)
6.0.989449862200332316875.1	x^6 + 80939115075	\( -\,3^{11}\cdot 5^{4}\cdot 7^{4}\cdot 13^{4}\cdot 19^{4} \)	$S_3$ (as 6T2)	$[3, 3, 3, 3, 3, 3, 72, 72]$ (GRH)
6.0.1078855752548052610992.1	x^6 + 234118668	\( -\,2^{4}\cdot 3^{11}\cdot 7^{4}\cdot 631^{4} \)	$S_3$ (as 6T2)	$[3, 3, 3, 3, 3, 93, 93]$ (GRH)
6.0.1164846423393322216875.1	x^6 + 6081751875	\( -\,3^{11}\cdot 5^{4}\cdot 1801^{4} \)	$S_3$ (as 6T2)	$[2, 2, 2, 6, 234, 234]$ (GRH)
6.0.1217048555319410394243.1	x^6 - 15769x^3 + 3921141001609	\( -\,3^{9}\cdot 13^{4}\cdot 1213^{4} \)	$C_6$ (as 6T1)	$[3, 3, 3, 58539]$ (GRH)
6.0.1417326199717624035867.1	x^6 - 3x^5 + 6x^4 + 56739x^3 - 85113x^2 - 85122x + 805083876	\( -\,3^{7}\cdot 17^{4}\cdot 1669^{4} \)	$S_3$ (as 6T2)	$[1056, 1056]$ (GRH)
6.0.1513047546760387962483.1	x^6 - 16651x^3 + 4616586342451	\( -\,3^{9}\cdot 16651^{4} \)	$C_6$ (as 6T1)	$[2, 2, 6, 54834]$ (GRH)
6.0.1604142321628736716875.1	x^6 + 7137001875	\( -\,3^{11}\cdot 5^{4}\cdot 1951^{4} \)	$S_3$ (as 6T2)	$[2, 6, 516, 516]$ (GRH)
6.0.2811678717188691670563.1	x^6 - 19441x^3 + 7347774183121	\( -\,3^{9}\cdot 19441^{4} \)	$C_6$ (as 6T1)	$[9, 9, 9, 5859]$ (GRH)
6.0.3002454118928066670000.1	x^6 + 1562257200	\( -\,2^{4}\cdot 3^{11}\cdot 5^{4}\cdot 7^{4}\cdot 163^{4} \)	$S_3$ (as 6T2)	$[3, 3, 3, 3, 3, 90, 90]$ (GRH)
6.0.3103551637694033697603.1	x^6 - 19927x^3 + 7912719350983	\( -\,3^{9}\cdot 19927^{4} \)	$C_6$ (as 6T1)	$[18, 18, 18, 234]$ (GRH)