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 32 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.2.11410125096185151906816.1	x^20 - x^16 - 8x^12 + 13x^8 + 3x^4 - 9	\( -\,2^{10}\cdot 3^{6}\cdot 11119^{4} \)	20T807	Trivial (GRH)
20.2.17895043229790736000000.1	x^20 - 2x^19 + 5x^17 - 5x^16 - 9x^15 + 8x^14 + 11x^13 - 31x^12 - 15x^11 + 58x^10 - 6x^9 - 38x^8 + 34x^7 - 14x^6 - 36x^5 + 9x^4 - 7x^3 - 8x^2 + 3x - 1	\( -\,2^{10}\cdot 5^{6}\cdot 5783^{4} \)	20T807	Trivial
20.2.2106529534966324491452416.1	x^20 - 10x^18 + 40x^16 - 80x^14 + 81x^12 - 38x^10 + 13x^8 - 12x^6 + 6x^4 - 4x^2 - 1	\( -\,2^{36}\cdot 13^{4}\cdot 181^{4} \)	20T807	Trivial (GRH)
20.2.3933022591662545799479296.1	x^20 - x^18 + x^16 - 17x^14 + 26x^12 - 3x^10 - 16x^8 + 25x^6 - 11x^4 + 4x^2 - 1	\( -\,2^{32}\cdot 5501^{4} \)	20T807	Trivial (GRH)
20.6.18546881403289244170576896.1	x^20 - 19x^16 + 19x^12 + 40x^8 - 15x^4 - 9	\( -\,2^{10}\cdot 3^{6}\cdot 17^{4}\cdot 4153^{4} \)	20T807	Trivial (GRH)
20.6.455293169564857148863676416.3	x^20 - 2x^14 - 41x^12 - 52x^10 - 16x^8 - 26x^6 - 12x^4 + 12x^2 - 1	\( -\,2^{40}\cdot 13^{4}\cdot 347^{4} \)	20T807	Trivial (GRH)
20.6.635400276596182371643949056.1	x^20 - 2x^18 - 10x^16 + 14x^14 + 7x^12 - 36x^10 - 4x^8 - 4x^6 - 14x^4 + 8x^2 - 1	\( -\,2^{40}\cdot 4903^{4} \)	20T807	Trivial (GRH)
20.6.5360048725550591565296722944.1	x^20 - 3x^19 - 2x^18 + 24x^17 - 70x^16 + 38x^15 + 133x^14 - 435x^13 + 592x^12 - 398x^11 - 25x^10 - 556x^9 + 839x^8 - 495x^7 + 496x^6 - 185x^5 + 3x^4 - 57x^3 + 35x^2 - 9x + 1	\( -\,2^{10}\cdot 3^{6}\cdot 17^{6}\cdot 4153^{4} \)	20T807	Trivial (GRH)
20.0.14569381426075428763637645312.2	x^20 + 8x^18 + 20x^16 + 56x^14 + 356x^12 + 1168x^10 + 1864x^8 + 1600x^6 + 784x^4 + 224x^2 + 32	\( 2^{45}\cdot 13^{4}\cdot 347^{4} \)	20T807	Trivial (GRH)
20.0.20349401981991717600380321792.1	x^20 + 10x^18 + 44x^16 + 112x^14 + 184x^12 + 208x^10 + 168x^8 + 96x^6 + 38x^4 + 12x^2 + 2	\( 2^{57}\cdot 613^{4} \)	20T807	Trivial (GRH)
20.2.320097689127091513657129959424.1	x^20 - 10x^18 + 38x^16 + 252x^14 + 341x^12 + 2749x^10 + 8760x^8 + 3569x^6 - 12450x^4 - 13778x^2 - 6889	\( -\,2^{20}\cdot 83^{6}\cdot 983^{4} \)	20T807	Trivial (GRH)
20.2.320097689127091513657129959424.2	x^20 - 18x^18 + 118x^16 - 172x^14 - 1774x^12 + 9158x^10 - 21989x^8 + 32868x^6 - 32287x^4 + 20667x^2 - 6889	\( -\,2^{20}\cdot 83^{6}\cdot 983^{4} \)	20T807	Trivial (GRH)
20.10.1950870747766649155582852857856.2	x^20 - 6x^18 - 54x^16 + 56x^14 + 193x^12 - 136x^10 - 191x^8 + 110x^6 + 33x^4 - 14x^2 - 1	\( -\,2^{40}\cdot 36497^{4} \)	20T807	Trivial (GRH)
20.10.2433062929616749991460283088896.2	x^20 - 2x^18 - 43x^16 + 4x^14 + 343x^12 - 52x^10 - 749x^8 + 484x^6 + 16x^4 - 38x^2 - 1	\( -\,2^{40}\cdot 38569^{4} \)	20T807	Trivial (GRH)
20.0.2462225461006747461054762057728.1	x^20 + 32x^18 + 434x^16 + 3260x^14 + 14820x^12 + 41768x^10 + 72000x^8 + 73280x^6 + 43920x^4 + 18304x^2 + 5408	\( 2^{45}\cdot 13^{6}\cdot 347^{4} \)	20T807	Trivial (GRH)
20.12.2462225461006747461054762057728.2	x^20 - 14x^18 + 92x^16 - 664x^14 + 4084x^12 - 12344x^10 + 11304x^8 + 12896x^6 - 19344x^4 - 5408x^2 + 5408	\( 2^{45}\cdot 13^{6}\cdot 347^{4} \)	20T807	Trivial (GRH)
20.12.2462225461006747461054762057728.3	x^20 - 32x^18 + 434x^16 - 3260x^14 + 14820x^12 - 41768x^10 + 72000x^8 - 73280x^6 + 43920x^4 - 18304x^2 + 5408	\( 2^{45}\cdot 13^{6}\cdot 347^{4} \)	20T807	Trivial (GRH)
20.0.1741167538834544763439794528727334912.1	x^20 + 61x^18 + 1529x^16 + 20608x^14 + 164027x^12 + 798075x^10 + 2385289x^8 + 4315198x^6 + 4539685x^4 + 2528263x^2 + 571787	\( 2^{36}\cdot 83^{7}\cdot 983^{4} \)	20T807	$[2, 10696]$ (GRH)
20.16.1741167538834544763439794528727334912.3	x^20 - 56x^18 + 1239x^16 - 13660x^14 + 76332x^12 - 170366x^10 - 218299x^8 + 1811192x^6 - 2906660x^4 + 978238x^2 + 571787	\( 2^{36}\cdot 83^{7}\cdot 983^{4} \)	20T807	Trivial (GRH)
20.8.1741167538834544763439794528727334912.3	x^20 - 27x^18 - 153x^16 + 3788x^14 + 32832x^12 + 37230x^10 - 350829x^8 - 919719x^6 + 561246x^4 + 2748711x^2 + 571787	\( 2^{36}\cdot 83^{7}\cdot 983^{4} \)	20T807	Trivial (GRH)
20.8.1741167538834544763439794528727334912.4	x^20 - 31x^18 - 130x^16 + 4509x^14 + 6325x^12 - 183646x^10 - 154680x^8 + 1713278x^6 + 3802479x^4 + 2610931x^2 + 571787	\( 2^{36}\cdot 83^{7}\cdot 983^{4} \)	20T807	Trivial (GRH)
20.4.74891594867646330033252195969701773312.3	x^20 - 2313x^16 + 52870x^14 + 912693x^12 - 32854184x^10 + 134117049x^8 + 2092902102x^6 - 13104257906x^4 - 9952315326x^2 + 117865222327	\( 2^{40}\cdot 4903^{7} \)	20T807	Trivial (GRH)
20.8.74891594867646330033252195969701773312.3	x^20 + 4x^18 - 1697x^16 - 31210x^14 + 386622x^12 + 22467016x^10 + 425115681x^8 + 1410756648x^6 - 61597874609x^4 - 527568869914x^2 + 117865222327	\( 2^{40}\cdot 4903^{7} \)	20T807	Trivial (GRH)
20.4.74891594867646330033252195969701773312.4	x^20 - 28x^18 - 1608x^16 + 50062x^14 + 760301x^12 - 21133322x^10 - 140047794x^8 + 1761805932x^6 - 5607737608x^4 - 22693202096x^2 + 117865222327	\( 2^{40}\cdot 4903^{7} \)	20T807	Trivial (GRH)
20.8.74891594867646330033252195969701773312.4	x^20 + 28x^18 - 1608x^16 - 50062x^14 + 760301x^12 + 21133322x^10 - 140047794x^8 - 1761805932x^6 - 5607737608x^4 + 22693202096x^2 + 117865222327	\( 2^{40}\cdot 4903^{7} \)	20T807	Trivial (GRH)
20.0.11994903175031178875336744508402610208768.1	x^20 + 168x^18 + 11277x^16 + 397532x^14 + 8089180x^12 + 98149160x^10 + 709808115x^8 + 2994937638x^6 + 7062713024x^4 + 8447581138x^2 + 3939040643	\( 2^{36}\cdot 83^{9}\cdot 983^{4} \)	20T807	$[2, 2, 4, 122668]$ (GRH)
20.16.11994903175031178875336744508402610208768.1	x^20 - 83x^18 + 1218x^16 + 67415x^14 - 2249383x^12 + 3984498x^10 + 634504456x^8 - 8681848472x^6 + 36806500977x^4 - 40292114529x^2 + 3939040643	\( 2^{36}\cdot 83^{9}\cdot 983^{4} \)	20T807	Trivial (GRH)
20.0.1079728333617289649279000342064345892234723328.1	x^20 + 314x^18 + 38988x^16 + 3338072x^14 + 296978572x^12 + 19141645888x^10 + 895279412494x^8 + 47279980062632x^6 + 1473870039126118x^4 + 20773688461030320x^2 + 106118925221763218	\( 2^{57}\cdot 613^{10} \)	20T807	$[2]$ (GRH)
20.12.43638965741625483308617553270102089623548879194554368.1	x^20 - 1012x^18 - 160446x^16 + 230124576x^14 - 1929332416x^12 - 12504794909838x^10 + 286196363372546x^8 + 196854919587541710x^6 - 7056313724597572776x^4 - 627852139000069896440x^2 + 14330725072676595386243	\( 2^{36}\cdot 11^{10}\cdot 83^{7}\cdot 983^{6} \)	20T807	$[2, 2]$ (GRH)
20.20.43638965741625483308617553270102089623548879194554368.1	x^20 - 3300x^18 + 4470103x^16 - 3274244028x^14 + 1432387550077x^12 - 389915282997834x^10 + 66816613758241721x^8 - 7127823539752640054x^6 + 455133581914702571045x^4 - 15821873902801761390288x^2 + 229291601162825526179888	\( 2^{36}\cdot 11^{10}\cdot 83^{7}\cdot 983^{6} \)	20T807	Trivial (GRH)
20.4.43638965741625483308617553270102089623548879194554368.1	x^20 + 2200x^18 + 1651529x^16 + 455819584x^14 - 1705442244x^12 - 21744427673188x^10 - 3520584578300493x^8 - 156133983685665546x^6 + 6721737103902251508x^4 + 702102201216507460490x^2 + 14330725072676595386243	\( 2^{36}\cdot 11^{10}\cdot 83^{7}\cdot 983^{6} \)	20T807	n/a
20.4.42167852567509546640800746931813678080249422928026745700352.1	x^20 + 6732x^18 + 2833578x^16 - 43310745324x^14 - 75078668227101x^12 - 27960060073739838x^10 + 23406765475219102284x^8 + 22525314252979581288872x^6 + 6671346966170800390622211x^4 + 722376753979057069513298634x^2 + 13847621999751594679177362227	\( 2^{36}\cdot 11^{10}\cdot 83^{7}\cdot 983^{8} \)	20T807	n/a