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 86)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.3267434519824695296.1	x^16 - 8x^15 + 36x^14 - 110x^13 + 251x^12 - 446x^11 + 634x^10 - 750x^9 + 765x^8 - 684x^7 + 536x^6 - 364x^5 + 216x^4 - 112x^3 + 48x^2 - 16x + 4	\( 2^{24}\cdot 41^{7} \)	$D_{16}$ (as 16T56)	Trivial
16.0.15426507143923491573.1	x^16 - x^15 - x^14 + 8x^13 + 15x^12 + 11x^11 + 36x^10 + 71x^9 + 58x^8 + 7x^7 - 18x^6 - 23x^5 - 18x^4 - 2x^3 + 5x^2 + x + 1	\( 3^{8}\cdot 157^{7} \)	$D_{16}$ (as 16T56)	Trivial
16.0.20349490953459368173.1	x^16 - 3x^15 + 2x^14 - 3x^13 + 6x^12 + x^11 + 7x^10 - 29x^9 + 63x^8 - 77x^7 + 24x^6 + 37x^5 - 56x^4 + 29x^3 + 11x^2 - 17x + 5	\( 11^{8}\cdot 37^{7} \)	$D_{16}$ (as 16T56)	Trivial
16.2.33491203828203126784.1	x^16 - x^14 + 4x^12 - 5x^10 + 12x^8 - 9x^6 - 5x^4 - 36x^2 - 4	\( -\,2^{22}\cdot 41^{8} \)	$D_{16}$ (as 16T56)	Trivial
16.2.68448287752545147491.1	x^16 - x^15 + 2x^14 - x^13 + 9x^12 + 2x^11 + 15x^10 + 12x^8 + 4x^6 - 19x^5 - 17x^4 - 33x^3 - 4x^2 - 10x - 1	\( -\,11^{7}\cdot 37^{8} \)	$D_{16}$ (as 16T56)	Trivial
16.2.221730791619531718147.1	x^16 - x^15 + 2x^13 + x^12 - 14x^11 + 51x^10 - 98x^9 + 123x^8 - 83x^7 - 18x^6 + 139x^5 - 196x^4 + 161x^3 - 78x^2 + 20x - 1	\( -\,13^{8}\cdot 43^{7} \)	$D_{16}$ (as 16T56)	Trivial
16.0.733417233818451067717.1	x^16 - 8x^14 - 9x^13 + 35x^12 + 60x^11 - 40x^10 - 126x^9 + 53x^8 + 177x^7 + 41x^6 - 63x^5 - 62x^4 - 30x^3 + 16x^2 + 27x + 9	\( 13^{7}\cdot 43^{8} \)	$D_{16}$ (as 16T56)	Trivial
16.2.807320540531996058987.1	x^16 - 2x^15 + 5x^14 - 6x^13 + 14x^12 + 3x^11 + 25x^10 + 27x^9 + 34x^8 + 78x^7 + 111x^6 + 191x^5 + 206x^4 + 199x^3 + 133x^2 + 53x + 17	\( -\,3^{7}\cdot 157^{8} \)	$D_{16}$ (as 16T56)	Trivial
16.0.836463237075121995776.1	x^16 - 4x^14 + 6x^12 + 19x^8 + 62x^4 + 44x^2 + 41	\( 2^{32}\cdot 41^{7} \)	$D_{16}$ (as 16T56)	Trivial
16.2.3534080002352411615183.1	x^16 - 3x^15 + 9x^14 - 9x^13 - 6x^12 + 21x^11 - 39x^10 + 6x^9 + 52x^8 - 24x^7 + 18x^6 + 18x^5 - 75x^4 - 30x^3 + 39x^2 + 30x + 1	\( -\,17^{8}\cdot 47^{7} \)	$D_{16}$ (as 16T56)	Trivial
16.2.4722366482869645213696.2	x^16 - 4x^8 - 4	\( -\,2^{72} \)	$D_{16}$ (as 16T56)	Trivial (GRH)
16.0.9770691771209608583153.1	x^16 - 3x^15 + 19x^13 - 18x^12 - 24x^11 + 64x^10 - 36x^9 - 48x^8 + 80x^7 - 42x^6 + 90x^5 + 36x^4 - 21x^3 + 162x^2 - 68x + 51	\( 17^{7}\cdot 47^{8} \)	$D_{16}$ (as 16T56)	$[5]$
16.0.15251399075306833745561.1	x^16 - 8x^15 + 32x^14 - 84x^13 + 180x^12 - 352x^11 + 598x^10 - 812x^9 + 816x^8 - 548x^7 + 116x^6 + 248x^5 - 194x^4 - 78x^3 + 432x^2 - 347x + 213	\( 23^{8}\cdot 41^{7} \)	$D_{16}$ (as 16T56)	$[3]$ (GRH)
16.2.27187276612503486242087.1	x^16 - 5x^15 + 8x^14 - x^13 + 11x^11 - 38x^10 - 2x^9 + 58x^8 - 28x^7 - 59x^6 + 46x^5 + 66x^4 - 32x^3 - 55x^2 + 38x + 1	\( -\,23^{7}\cdot 41^{8} \)	$D_{16}$ (as 16T56)	Trivial (GRH)
16.2.42278054078586972458443.1	x^16 - 6x^15 + 24x^14 - 66x^13 + 146x^12 - 224x^11 + 232x^10 - 94x^9 - 104x^8 + 202x^7 - 50x^6 - 288x^5 + 519x^4 - 428x^3 + 96x^2 + 88x - 64	\( -\,17^{8}\cdot 67^{7} \)	$D_{16}$ (as 16T56)	Trivial (GRH)
16.0.53374971077213779099861.1	x^16 - 4x^15 + 15x^14 - 23x^13 + 24x^12 + 20x^11 - 36x^10 + 52x^9 + 64x^8 - 56x^7 + 57x^6 + 2x^5 + 165x^4 - 80x^3 + 45x^2 + 26x + 169	\( 19^{8}\cdot 61^{7} \)	$D_{16}$ (as 16T56)	Trivial (GRH)
16.0.166625271956783950277393.1	x^16 - 7x^15 + 19x^14 - 12x^13 - 45x^12 + 145x^11 - 132x^10 - 71x^9 + 377x^8 - 372x^7 + 61x^6 + 335x^5 - 269x^4 + 62x^3 + 180x^2 - 80x + 64	\( 17^{7}\cdot 67^{8} \)	$D_{16}$ (as 16T56)	Trivial (GRH)
16.2.171361749247896869741659.1	x^16 - 5x^15 + x^14 + 23x^13 - 22x^12 - 32x^11 + 106x^10 - 34x^9 - 114x^8 + 137x^7 + 95x^6 - 245x^5 + 106x^4 + 191x^3 - 190x^2 + 64x - 1	\( -\,19^{7}\cdot 61^{8} \)	$D_{16}$ (as 16T56)	Trivial (GRH)
16.2.3031849240553934703791403.1	x^16 - 8x^15 + 23x^14 - 5x^13 - 135x^12 + 284x^11 + 123x^10 - 1204x^9 + 1099x^8 + 1747x^7 - 3431x^6 - 398x^5 + 4310x^4 - 1715x^3 - 650x^2 + 1061x - 383	\( -\,29^{8}\cdot 67^{7} \)	$D_{16}$ (as 16T56)	Trivial (GRH)
16.0.7004617210934952591518069.1	x^16 - 19x^14 + 149x^12 - 600x^10 + 1272x^8 - 1630x^6 + 3984x^4 - 12529x^2 + 15341	\( 29^{7}\cdot 67^{8} \)	$D_{16}$ (as 16T56)	Trivial (GRH)
16.0.944386531066764936008646913.1	x^16 - x^15 + x^14 - 32x^13 + 17x^12 - 47x^11 + 303x^10 + 108x^9 + 183x^8 + 19x^7 - 1081x^6 + 1522x^5 - 280x^4 + 328x^3 + 2192x^2 - 3648x + 2304	\( 43^{8}\cdot 97^{7} \)	$D_{16}$ (as 16T56)	Trivial (GRH)
16.2.2130360314266888344019505827.1	x^16 - 3x^15 + 2x^14 + 28x^13 - 80x^12 - 200x^11 + 450x^10 + 1182x^9 - 736x^8 - 3960x^7 - 3584x^6 + 8672x^5 + 15269x^4 - 4171x^3 - 28458x^2 + 2916x + 13824	\( -\,43^{7}\cdot 97^{8} \)	$D_{16}$ (as 16T56)	Trivial (GRH)
16.2.2558639070806765618458574027.1	x^16 - 2x^15 - 13x^14 + 9x^13 - 18x^12 + 393x^11 - 327x^10 + 858x^9 - 2379x^8 - 189x^7 - 1866x^6 + 10311x^5 - 21710x^4 - 14516x^3 - 10408x^2 - 3120x - 288	\( -\,17^{15}\cdot 19^{7} \)	$D_{16}$ (as 16T56)	$[4]$ (GRH)
16.0.5726874571603625384731365629.1	x^16 - 3x^15 - 5x^14 - 5x^13 + 69x^12 + 157x^11 + 2x^10 - 660x^9 - 1443x^8 + 323x^7 + 16030x^6 + 40365x^5 + 57643x^4 + 26263x^3 - 55032x^2 - 57305x + 50919	\( 37^{8}\cdot 149^{7} \)	$D_{16}$ (as 16T56)	$[47]$ (GRH)
16.0.7133896604786078388958797817.1	x^16 - 2x^15 + 4x^14 - 21x^13 - 27x^12 - 165x^11 + 944x^10 + 1930x^9 - 2482x^8 - 5011x^7 + 2662x^6 + 2845x^5 + 1030x^4 - 1167x^3 - 326x^2 - 29x + 107	\( 71^{8}\cdot 73^{7} \)	$D_{16}$ (as 16T56)	$[7]$ (GRH)
16.2.7334851438723714399915383671.1	x^16 - 2x^15 - 4x^14 + 115x^13 - 397x^12 + 965x^11 - 138x^10 - 829x^9 + 2987x^8 + 9275x^7 - 4219x^6 + 8790x^5 + 34336x^4 + 37298x^3 + 3716x^2 + 10610x - 4447	\( -\,71^{7}\cdot 73^{8} \)	$D_{16}$ (as 16T56)	Trivial (GRH)
16.0.19324652256549748184809636393.1	x^16 - 4x^15 - 8x^14 - x^13 + 88x^12 + 96x^11 + 545x^10 + 711x^9 - 416x^8 + 337x^7 + 10x^6 + 1822x^5 + 16660x^4 + 22722x^3 + 34983x^2 + 30240x + 14175	\( 7^{7}\cdot 31^{15} \)	$D_{16}$ (as 16T56)	$[3]$ (GRH)
16.0.23062278680241626549323607533.1	x^16 - 6x^15 + 12x^14 + 18x^13 - 145x^12 + 156x^11 + 1152x^10 - 6153x^9 + 15545x^8 - 22656x^7 + 12273x^6 + 27438x^5 - 72479x^4 + 59010x^3 + 17064x^2 - 61830x + 34425	\( 37^{7}\cdot 149^{8} \)	$D_{16}$ (as 16T56)	$[47]$ (GRH)
16.0.26382542843244145338070455141.1	x^16 - 5x^15 + 22x^14 - 83x^13 + 392x^12 - 717x^11 + 1364x^10 - 2969x^9 + 4036x^8 - 8051x^7 + 24446x^6 - 66537x^5 + 178753x^4 - 353640x^3 + 572700x^2 - 666000x + 360000	\( 3^{7}\cdot 47^{15} \)	$D_{16}$ (as 16T56)	$[5]$ (GRH)
16.0.48614142345328546750712906513.1	x^16 - 4x^15 + 33x^14 - 166x^13 + 664x^12 - 2044x^11 + 6442x^10 - 16316x^9 + 30006x^8 - 48148x^7 + 55708x^6 - 11284x^5 - 10539x^4 + 1424x^3 + 67353x^2 + 44442x + 18684	\( 17^{15}\cdot 19^{8} \)	$D_{16}$ (as 16T56)	$[16]$ (GRH)
16.2.79147628529732436014211365423.1	x^16 - 5x^15 + 22x^14 - 83x^13 + 392x^12 - 905x^11 + 3573x^10 - 12980x^9 + 29369x^8 - 70843x^7 + 155388x^6 - 103855x^5 - 343558x^4 + 1036385x^3 - 1038695x^2 + 244766x + 237988	\( -\,3^{8}\cdot 47^{15} \)	$D_{16}$ (as 16T56)	Trivial (GRH)
16.2.135272565795848237293667454751.1	x^16 - 6x^15 + 13x^14 - 15x^13 + 120x^12 - 1565x^11 + 4081x^10 + 2766x^9 + 24690x^8 - 169895x^7 + 90832x^6 + 285015x^5 - 18016x^4 + 35647x^3 - 1002x^2 + 450x + 81	\( -\,7^{8}\cdot 31^{15} \)	$D_{16}$ (as 16T56)	Trivial (GRH)
16.2.778059858262058848230673812851.1	x^16 - 17x^14 - 17x^13 + 85x^12 + 255x^11 + 255x^10 - 1241x^9 - 4845x^8 + 3757x^7 + 9639x^6 + 19125x^5 - 8772x^4 - 92531x^3 - 33830x^2 + 328440x - 239904	\( -\,17^{15}\cdot 43^{7} \)	$D_{16}$ (as 16T56)	$[4]$ (GRH)
16.2.1450169698441125460523978872159.7	x^16 - 3x^15 + 26x^14 - 27x^13 + 302x^12 - 226x^11 + 3279x^10 - 7406x^9 + 19736x^8 - 46509x^7 + 67736x^6 - 275084x^5 + 782497x^4 - 1180866x^3 + 1073416x^2 - 561890x + 3775	\( -\,17^{15}\cdot 47^{7} \)	$D_{16}$ (as 16T56)	$[8]$ (GRH)
16.2.7123573377320035993002625946467.2	x^16 - 8x^15 + 30x^14 - 19x^13 - 137x^12 - 570x^11 - 81x^10 + 6377x^9 + 17324x^8 + 4055x^7 - 69143x^6 - 222838x^5 - 241792x^4 + 378479x^3 + 1414438x^2 + 1527452x + 594304	\( -\,17^{15}\cdot 59^{7} \)	$D_{16}$ (as 16T56)	$[4]$ (GRH)
16.0.9934686090879658520416349720249.1	x^16 - 8x^15 + 30x^14 + 24x^13 - 603x^12 - 489x^11 + 3515x^10 + 9152x^9 + 13887x^8 + 13145x^7 + 7913x^6 + 30336x^5 + 25264x^4 - 9440x^3 + 26472x^2 - 5929x + 4781	\( 7^{7}\cdot 47^{15} \)	$D_{16}$ (as 16T56)	$[15]$ (GRH)
16.2.17348320607629615993685048266139.8	x^16 - 8x^15 + 47x^14 - 189x^13 + 934x^12 - 3511x^11 + 5529x^10 + 988x^9 + 4489x^8 - 56499x^7 + 1123050x^6 - 3134921x^5 + 3626014x^4 - 2111188x^3 + 637232x^2 - 91968x + 4608	\( -\,17^{15}\cdot 67^{7} \)	$D_{16}$ (as 16T56)	$[8]$ (GRH)
16.0.20974934542740813230114132554789.1	x^16 - 2x^15 - 2x^14 - 66x^13 + 145x^12 + 158x^11 + 71x^10 - 7146x^9 + 110277x^8 - 608662x^7 + 1780247x^6 - 3845538x^5 + 7004864x^4 - 9260696x^3 + 7860421x^2 - 4451244x + 1532768	\( 19^{7}\cdot 31^{15} \)	$D_{16}$ (as 16T56)	$[3]$ (GRH)
16.0.33456573905268530473918973952593.1	x^16 - 17x^14 + 170x^12 - 2057x^10 + 11322x^8 - 20893x^6 + 345253x^4 - 2310028x^2 + 4250000	\( 17^{15}\cdot 43^{8} \)	$D_{16}$ (as 16T56)	$[48]$ (GRH)
16.0.68157975826732896644627006991473.12	x^16 - 6x^15 + 53x^14 - 131x^13 + 1075x^12 - 1163x^11 + 17093x^10 - 1561x^9 + 156705x^8 + 53505x^7 + 1078359x^6 - 229641x^5 + 5768725x^4 - 2814377x^3 + 16674731x^2 - 6159188x + 19185895	\( 17^{15}\cdot 47^{8} \)	$D_{16}$ (as 16T56)	$[8, 16]$ (GRH)
16.2.69542802636157609642914448041743.1	x^16 - 47x^13 - 470x^12 - 705x^11 + 11186x^10 + 10951x^9 - 112706x^8 - 82203x^7 + 303620x^6 + 252484x^5 + 91368x^4 - 768591x^3 - 155335x^2 - 17625x + 52875	\( -\,7^{8}\cdot 47^{15} \)	$D_{16}$ (as 16T56)	$[3]$ (GRH)
16.2.77674857879654074046142123779211.2	x^16 - 6x^15 + 19x^14 - 29x^13 + 4x^12 + 1659x^11 - 13133x^10 + 59894x^9 - 123455x^8 + 87641x^7 + 409868x^6 + 197569x^5 - 1210880x^4 - 2883720x^3 + 1183464x^2 + 2882976x + 4820096	\( -\,17^{15}\cdot 83^{7} \)	$D_{16}$ (as 16T56)	$[4]$ (GRH)
16.2.398523756312075451372168518540991.1	x^16 - x^15 - 47x^14 - 16x^13 + 1220x^12 + 1088x^11 - 16813x^10 - 23595x^9 + 113531x^8 + 268072x^7 - 352708x^6 - 1414400x^5 + 817744x^4 + 4368256x^3 - 2448320x^2 - 27340032x - 43011072	\( -\,19^{8}\cdot 31^{15} \)	$D_{16}$ (as 16T56)	Trivial (GRH)
16.0.420290829261882123587154930841553.1	x^16 - 2x^15 - 30x^14 + 26x^13 + 1121x^12 + 4966x^11 + 9737x^10 + 8508x^9 + 22662x^8 + 99040x^7 + 236933x^6 + 297390x^5 + 680152x^4 + 933880x^3 + 1149264x^2 + 1696064x + 3890944	\( 17^{15}\cdot 59^{8} \)	$D_{16}$ (as 16T56)	$[16]$ (GRH)
16.0.1162337480711184271576898233831313.14	x^16 - 6x^15 + 2x^14 - 12x^13 + 667x^12 - 2166x^11 + 1538x^10 + 2502x^9 + 59618x^8 - 314460x^7 + 1075792x^6 - 2781018x^5 + 4768445x^4 + 1679760x^3 - 18353684x^2 + 14086248x + 30880773	\( 17^{15}\cdot 67^{8} \)	$D_{16}$ (as 16T56)	$[4, 32]$ (GRH)
16.2.1384920350642158387276644512694891.1	x^16 - 2x^15 + 14x^14 + 105x^13 - 755x^12 + 4640x^11 - 15581x^10 + 41759x^9 - 90470x^8 + 103959x^7 + 31703x^6 - 235268x^5 - 309548x^4 + 1806831x^3 - 2517036x^2 + 1299672x - 235224	\( -\,3^{7}\cdot 97^{15} \)	$D_{16}$ (as 16T56)	$[8]$ (GRH)
16.0.4154761051926475161829933538084673.2	x^16 - 7x^15 + 26x^14 - 45x^13 + 211x^12 - 1274x^11 - 4493x^10 + 20935x^9 + 11734x^8 + 264213x^7 - 667219x^6 - 3721270x^5 + 6436324x^4 + 12698880x^3 + 10833600x^2 - 76032000x + 51840000	\( 3^{8}\cdot 97^{15} \)	$D_{16}$ (as 16T56)	$[32]$ (GRH)
16.0.6447013204011288145829796273674513.1	x^16 - 8x^15 + 64x^14 - 308x^13 + 1682x^12 - 6452x^11 + 29822x^10 - 96354x^9 + 415396x^8 - 1143564x^7 + 3114838x^6 - 5687148x^5 + 10843313x^4 - 13379230x^3 - 8650820x^2 + 14558768x + 23119168	\( 17^{15}\cdot 83^{8} \)	$D_{16}$ (as 16T56)	$[16]$ (GRH)
16.0.11888044252790185643475966652687313.1	x^16 - 2x^15 - 33x^14 + 275x^13 + 1385x^12 - 5763x^11 - 36633x^10 + 2216x^9 + 409334x^8 + 872766x^7 - 1426424x^6 - 7059308x^5 - 3351926x^4 + 7815964x^3 + 9240200x^2 + 54292082x + 85351591	\( 31^{15}\cdot 47^{7} \)	$D_{16}$ (as 16T56)	$[3, 3]$ (GRH)
16.0.16630354781940843607026711048224768.1	x^16 + 64x^14 + 1616x^12 + 20736x^10 + 146496x^8 + 579520x^6 + 1254144x^4 + 1353472x^2 + 547832	\( 2^{79}\cdot 31^{7} \)	$D_{16}$ (as 16T56)	$[2, 2, 3106]$ (GRH)