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 116)

Label	Polynomial	Discriminant	Galois group	Class group
16.16.9573589958277615058944.1	x^16 - 24x^14 - 8x^13 + 200x^12 + 96x^11 - 744x^10 - 360x^9 + 1350x^8 + 544x^7 - 1176x^6 - 312x^5 + 456x^4 + 32x^3 - 72x^2 + 8x + 1	\( 2^{54}\cdot 3^{12} \)	$C_4:C_4$ (as 16T8)	Trivial (GRH)
16.0.9573589958277615058944.1	x^16 + 16x^14 - 8x^13 + 100x^12 - 48x^11 + 280x^10 - 144x^9 + 388x^8 + 32x^7 + 160x^6 - 224x^5 + 272x^4 - 32x^3 - 320x^2 - 128x + 184	\( 2^{54}\cdot 3^{12} \)	$C_4:C_4$ (as 16T8)	$[2]$
16.0.9573589958277615058944.2	x^16 - 8x^13 + 20x^12 + 48x^11 + 72x^10 - 144x^9 - 540x^8 - 608x^7 + 576x^6 + 3168x^5 + 6000x^4 + 5984x^3 + 3840x^2 + 1472x + 376	\( 2^{54}\cdot 3^{12} \)	$C_4:C_4$ (as 16T8)	$[2]$
16.0.9573589958277615058944.3	x^16 - 8x^14 - 8x^13 + 40x^12 - 8x^10 - 72x^9 + 310x^8 - 160x^7 + 280x^6 - 440x^5 - 184x^4 + 448x^3 + 1048x^2 - 344x + 433	\( 2^{54}\cdot 3^{12} \)	$C_4:C_4$ (as 16T8)	$[2]$ (GRH)
16.16.1795856326022129150390625.1	x^16 - 5x^15 - 23x^14 + 142x^13 + 122x^12 - 1367x^11 + 169x^10 + 6206x^9 - 3110x^8 - 14796x^7 + 9442x^6 + 19146x^5 - 12353x^4 - 12782x^3 + 7192x^2 + 3456x - 1424	\( 3^{12}\cdot 5^{12}\cdot 7^{12} \)	$C_4:C_4$ (as 16T8)	Trivial (GRH)
16.0.1795856326022129150390625.2	x^16 - 5x^15 + 21x^14 - 30x^13 + 50x^12 + 75x^11 + 674x^10 + 700x^9 + 1239x^8 - 700x^7 + 674x^6 - 75x^5 + 50x^4 + 30x^3 + 21x^2 + 5x + 1	\( 3^{12}\cdot 5^{12}\cdot 7^{12} \)	$C_4:C_4$ (as 16T8)	$[2, 2, 2]$ (GRH)
16.0.1795856326022129150390625.3	x^16 - 5x^15 + 27x^14 - 114x^13 + 254x^12 - 531x^11 + 1034x^10 - 878x^9 + 2007x^8 - 1492x^7 + 944x^6 - 3627x^5 + 1796x^4 - 4920x^3 + 10695x^2 - 8425x + 7795	\( 3^{12}\cdot 5^{12}\cdot 7^{12} \)	$C_4:C_4$ (as 16T8)	$[4, 8]$ (GRH)
16.0.1795856326022129150390625.4	x^16 - x^15 - 2x^14 + x^13 - 7x^12 - 61x^11 + 110x^10 + 85x^9 - 59x^8 + 340x^7 + 1760x^6 - 3904x^5 - 1792x^4 + 1024x^3 - 8192x^2 - 16384x + 65536	\( 3^{12}\cdot 5^{12}\cdot 7^{12} \)	$C_4:C_4$ (as 16T8)	$[4, 8]$ (GRH)
16.16.86380562306022715087890625.1	x^16 - 5x^15 - 36x^14 + 145x^13 + 560x^12 - 1610x^11 - 4769x^10 + 8490x^9 + 23394x^8 - 20855x^7 - 64854x^6 + 15240x^5 + 92315x^4 + 21110x^3 - 50036x^2 - 29130x - 3299	\( 5^{12}\cdot 29^{12} \)	$C_4:C_4$ (as 16T8)	Trivial (GRH)
16.0.86380562306022715087890625.2	x^16 - 4x^15 + 49x^14 - 154x^13 + 861x^12 - 1822x^11 + 6096x^10 - 7367x^9 + 18077x^8 - 8493x^7 + 27841x^6 + 3012x^5 + 28871x^4 + 19024x^3 + 19169x^2 + 9889x + 1711	\( 5^{12}\cdot 29^{12} \)	$C_4:C_4$ (as 16T8)	$[2, 4]$ (GRH)
16.0.86380562306022715087890625.3	x^16 - x^15 - 3x^14 + 16x^13 - 36x^12 + 49x^11 + 308x^10 - 1196x^9 + 1233x^8 + 5196x^7 + 9868x^6 + 7953x^5 - 29020x^4 - 33488x^3 - 5819x^2 + 109503x + 279841	\( 5^{12}\cdot 29^{12} \)	$C_4:C_4$ (as 16T8)	$[6, 12]$ (GRH)
16.16.5508664624112838398681640625.1	x^16 - 4x^15 - 51x^14 + 196x^13 + 906x^12 - 2982x^11 - 8509x^10 + 19533x^9 + 44732x^8 - 56263x^7 - 114529x^6 + 75917x^5 + 127991x^4 - 55591x^3 - 51826x^2 + 20159x + 1021	\( 5^{12}\cdot 41^{12} \)	$C_4:C_4$ (as 16T8)	Trivial (GRH)
16.0.5508664624112838398681640625.9	x^16 - 5x^15 + 8x^14 + 15x^13 - 115x^12 + 265x^11 - 72x^10 - 675x^9 + 649x^8 - 5400x^7 - 4608x^6 + 135680x^5 - 471040x^4 + 491520x^3 + 2097152x^2 - 10485760x + 16777216	\( 5^{12}\cdot 41^{12} \)	$C_4:C_4$ (as 16T8)	$[12, 12]$ (GRH)
16.0.5508664624112838398681640625.10	x^16 - 95x^14 + 3851x^12 - 88710x^10 + 1286011x^8 - 11934110x^6 + 69284846x^4 - 237776760x^2 + 395254161	\( 5^{12}\cdot 41^{12} \)	$C_4:C_4$ (as 16T8)	$[2, 2, 10]$ (GRH)
16.16.13573982477229290545823357041.1	x^16 - 4x^15 - 55x^14 + 210x^13 + 1089x^12 - 3878x^11 - 9962x^10 + 32075x^9 + 44659x^8 - 124859x^7 - 93555x^6 + 214708x^5 + 73203x^4 - 133892x^3 - 11509x^2 + 9255x + 1223	\( 13^{12}\cdot 17^{12} \)	$C_4:C_4$ (as 16T8)	Trivial (GRH)
16.0.13573982477229290545823357041.3	x^16 - 4x^15 + 29x^14 - 84x^13 + 319x^12 - 944x^11 + 2090x^10 - 4899x^9 + 10309x^8 - 16629x^7 + 25877x^6 - 42862x^5 + 53241x^4 - 50012x^3 + 59905x^2 - 62675x + 26711	\( 13^{12}\cdot 17^{12} \)	$C_4:C_4$ (as 16T8)	$[4, 8]$ (GRH)
16.0.13573982477229290545823357041.5	x^16 + 119x^14 + 5456x^12 + 121006x^10 + 1343266x^8 + 7090207x^6 + 14841596x^4 + 9180884x^2 + 139129	\( 13^{12}\cdot 17^{12} \)	$C_4:C_4$ (as 16T8)	$[2, 2, 10]$ (GRH)
16.0.648034417553121620683837890625.3	x^16 - 5x^15 + 36x^14 - 195x^13 + 1105x^12 - 5065x^11 + 27324x^10 - 149175x^9 + 771979x^8 - 3163050x^7 + 10091364x^6 - 24600040x^5 + 46030480x^4 - 64197120x^3 + 65519616x^2 - 44564480x + 16777216	\( 5^{12}\cdot 61^{12} \)	$C_4:C_4$ (as 16T8)	$[12, 12]$ (GRH)
16.0.648034417553121620683837890625.6	x^16 - 4x^15 + 41x^14 - 126x^13 + 978x^12 - 1964x^11 + 12609x^10 - 20673x^9 + 112208x^8 - 207249x^7 + 983391x^6 - 1876433x^5 + 8645703x^4 - 17027763x^3 + 37293974x^2 - 33563693x + 63101531	\( 5^{12}\cdot 61^{12} \)	$C_4:C_4$ (as 16T8)	$[2, 6, 30]$ (GRH)
16.0.648034417553121620683837890625.8	x^16 - 2x^15 + 10x^14 + 135x^13 + 2136x^12 - 4780x^11 + 46571x^10 + 216170x^9 + 341046x^8 + 2060735x^7 + 17453050x^6 + 35047982x^5 + 39593521x^4 + 107817400x^3 + 365353240x^2 + 691165560x + 791267920	\( 5^{12}\cdot 61^{12} \)	$C_4:C_4$ (as 16T8)	$[2, 6, 6]$ (GRH)
16.0.8243206936713178643875538610721.1	x^16 - 4x^15 - 23x^14 + 98x^13 + 246x^12 - 1492x^11 + 537x^10 + 7567x^9 - 13310x^8 - 1665x^7 + 62333x^6 - 30189x^5 + 55705x^4 + 235277x^3 + 226780x^2 + 67135x + 58841	\( 13^{12}\cdot 29^{12} \)	$C_4:C_4$ (as 16T8)	$[12, 12]$ (GRH)
16.0.8243206936713178643875538610721.4	x^16 - 31x^14 - 66x^13 + 581x^12 - 162x^11 - 940x^10 - 2149x^9 + 59327x^8 - 155387x^7 + 87135x^6 - 9376x^5 - 3004289x^4 + 3617292x^3 + 12664385x^2 - 3357557x + 4004113	\( 13^{12}\cdot 29^{12} \)	$C_4:C_4$ (as 16T8)	$[2, 6, 30]$ (GRH)
16.0.8243206936713178643875538610721.8	x^16 - 2x^15 + 10x^14 + 369x^13 + 820x^12 - 18754x^11 - 64949x^10 + 378230x^9 + 3768300x^8 + 8212415x^7 + 13124314x^6 + 37922114x^5 + 106741005x^4 + 159631694x^3 + 91351640x^2 + 478872560x + 849081392	\( 13^{12}\cdot 29^{12} \)	$C_4:C_4$ (as 16T8)	$[2, 6, 6]$ (GRH)
16.0.60300391495425327222539306640625.5	x^16 - x^15 + 34x^14 - 17x^13 + 1081x^12 - 2863x^11 + 37414x^10 - 77707x^9 + 1160571x^8 - 1831298x^7 + 3157636x^6 - 4940264x^5 + 8292784x^4 + 1210688x^3 + 176896x^2 + 25600x + 4096	\( 5^{12}\cdot 89^{12} \)	$C_4:C_4$ (as 16T8)	$[2, 6, 60]$ (GRH)
16.0.60300391495425327222539306640625.20	x^16 - 5x^15 + 97x^14 - 450x^13 + 3620x^12 - 15095x^11 + 81672x^10 - 331650x^9 + 1434649x^8 - 5203580x^7 + 13030788x^6 - 13507995x^5 + 18270660x^4 - 19110520x^3 + 29677943x^2 - 30739535x + 41700391	\( 5^{12}\cdot 89^{12} \)	$C_4:C_4$ (as 16T8)	$[2, 24, 240]$ (GRH)
16.0.60300391495425327222539306640625.23	x^16 - 4x^15 - 59x^14 + 224x^13 + 1913x^12 - 5644x^11 - 40746x^10 + 93377x^9 + 564003x^8 - 1189269x^7 - 5269299x^6 + 11501862x^5 + 40514783x^4 - 92662748x^3 - 168241441x^2 + 248573337x + 498229211	\( 5^{12}\cdot 89^{12} \)	$C_4:C_4$ (as 16T8)	$[2, 6, 12]$ (GRH)
16.16.275103767122062920083301025390625.1	x^16 - x^15 - 149x^14 + 129x^13 + 7381x^12 - 8750x^11 - 146355x^10 + 254535x^9 + 1101440x^8 - 2333750x^7 - 3101025x^6 + 7870550x^5 + 2368075x^4 - 8288250x^3 - 1506750x^2 + 2731125x + 822625	\( 5^{12}\cdot 101^{12} \)	$C_4:C_4$ (as 16T8)	$[2]$ (GRH)
16.0.275103767122062920083301025390625.40	x^16 - x^15 - 37x^14 + 31x^13 + 563x^12 - 3976x^11 + 4075x^10 + 76105x^9 - 156054x^8 - 48180x^7 + 3496685x^6 - 7936374x^5 + 9489133x^4 + 64628944x^3 - 3939082x^2 + 368350701x + 906892741	\( 5^{12}\cdot 101^{12} \)	$C_4:C_4$ (as 16T8)	$[2, 2, 4, 4, 40]$ (GRH)
16.0.275103767122062920083301025390625.44	x^16 - x^15 - 12x^14 - 95x^13 + 111x^12 - 4895x^11 + 17972x^10 + 57043x^9 + 267861x^8 - 1893360x^7 + 9041980x^6 - 31402800x^5 + 71416400x^4 - 255944000x^3 + 744952000x^2 - 2109120000x + 4569760000	\( 5^{12}\cdot 101^{12} \)	$C_4:C_4$ (as 16T8)	$[2, 2, 2, 20, 40]$ (GRH)
16.0.686685737739964474054511962890625.1	x^16 - 5x^15 + 54x^14 - 330x^13 + 2665x^12 - 14440x^11 + 113001x^10 - 765600x^9 + 5410069x^8 - 26546400x^7 + 94786356x^6 - 239767135x^5 + 439402015x^4 - 537558270x^3 + 460788564x^2 - 253328120x + 78074896	\( 5^{12}\cdot 109^{12} \)	$C_4:C_4$ (as 16T8)	$[10, 10, 10]$ (GRH)
16.0.686685737739964474054511962890625.6	x^16 - 4x^15 + 89x^14 - 294x^13 + 4015x^12 - 11714x^11 + 118502x^10 - 287877x^9 + 2380153x^8 - 4384707x^7 + 33049817x^6 - 40610728x^5 + 311208069x^4 - 202336688x^3 + 1801687213x^2 - 398902253x + 4791131651	\( 5^{12}\cdot 109^{12} \)	$C_4:C_4$ (as 16T8)	$[20, 340]$ (GRH)
16.0.686685737739964474054511962890625.8	x^16 + 285x^14 + 32109x^12 + 1840490x^10 + 57640466x^8 + 976886210x^6 + 8211857189x^4 + 27886579105x^2 + 27982932961	\( 5^{12}\cdot 109^{12} \)	$C_4:C_4$ (as 16T8)	$[2, 10, 10]$ (GRH)
16.16.11445391768549949624817238631584321.1	x^16 - x^15 - 212x^14 + 188x^13 + 14729x^12 - 23010x^11 - 425769x^10 + 1107152x^9 + 4184332x^8 - 18037073x^7 + 11515707x^6 + 33312812x^5 - 58857565x^4 + 30604631x^3 - 1439221x^2 - 1963061x - 8161	\( 13^{12}\cdot 53^{12} \)	$C_4:C_4$ (as 16T8)	$[2]$ (GRH)
16.0.11445391768549949624817238631584321.18	x^16 - 4x^15 + 93x^14 - 308x^13 + 3119x^12 - 10176x^11 + 51702x^10 - 162303x^9 + 522505x^8 - 1351737x^7 + 3249693x^6 - 6525662x^5 + 11390353x^4 - 16782028x^3 + 20319485x^2 - 16382503x + 6828071	\( 13^{12}\cdot 53^{12} \)	$C_4:C_4$ (as 16T8)	$[2, 4, 4, 8, 8]$ (GRH)
16.0.11445391768549949624817238631584321.35	x^16 + 33x^14 - 46x^13 + 795x^12 - 794x^11 + 9142x^10 + 8403x^9 + 54723x^8 + 128673x^7 + 210951x^6 + 849452x^5 + 8132377x^4 + 935100x^3 + 27985873x^2 - 64315489x + 61062797	\( 13^{12}\cdot 53^{12} \)	$C_4:C_4$ (as 16T8)	$[2, 2, 4, 16, 16]$ (GRH)
16.0.29233126977165462000179004150390625.1	x^16 - 5x^15 + 69x^14 - 70x^13 + 2770x^12 - 1125x^11 + 184986x^10 + 510300x^9 + 7821279x^8 - 4592700x^7 + 14983866x^6 + 820125x^5 + 18173970x^4 + 4133430x^3 + 36669429x^2 + 23914845x + 43046721	\( 5^{12}\cdot 149^{12} \)	$C_4:C_4$ (as 16T8)	$[10, 10, 10]$ (GRH)
16.0.29233126977165462000179004150390625.6	x^16 - 4x^15 + 109x^14 - 364x^13 + 6330x^12 - 19774x^11 + 227457x^10 - 596057x^9 + 5325668x^8 - 9941937x^7 + 86452747x^6 - 92670513x^5 + 1175303819x^4 - 209534153x^3 + 9069376118x^2 + 174773137x + 45464483611	\( 5^{12}\cdot 149^{12} \)	$C_4:C_4$ (as 16T8)	$[5, 60, 60]$ (GRH)
16.0.29233126977165462000179004150390625.8	x^16 - 2x^15 + 15x^14 + 345x^13 - 8761x^12 - 21267x^11 - 3437x^10 + 998855x^9 + 18367581x^8 - 37933807x^7 + 155539363x^6 - 563384901x^5 - 11591574241x^4 + 9061447011x^3 - 118330534131x^2 + 1006440846256x + 9114300768451	\( 5^{12}\cdot 149^{12} \)	$C_4:C_4$ (as 16T8)	$[2, 10, 10]$ (GRH)
16.16.61841248347955294332328765542314401.1	x^16 - 5x^15 - 221x^14 + 1528x^13 + 11835x^12 - 107804x^11 - 119494x^10 + 2467270x^9 - 2022752x^8 - 20231211x^7 + 28230493x^6 + 62582502x^5 - 87126427x^4 - 66676452x^3 + 55262142x^2 - 6612084x + 105543	\( 13^{12}\cdot 61^{12} \)	$C_4:C_4$ (as 16T8)	$[2]$ (GRH)
16.0.61841248347955294332328765542314401.15	x^16 - 4x^15 + 153x^14 - 518x^13 + 8811x^12 - 23274x^11 + 227730x^10 - 437329x^9 + 2534757x^8 - 3186879x^7 + 8460029x^6 - 126984x^5 + 6144281x^4 - 9463368x^3 + 5579973x^2 + 24448631x + 15614639	\( 13^{12}\cdot 61^{12} \)	$C_4:C_4$ (as 16T8)	$[2, 2, 4, 4, 8]$ (GRH)
16.0.61841248347955294332328765542314401.29	x^16 + 37x^14 - 72x^13 + 994x^12 - 1998x^11 + 18125x^10 - 71199x^9 + 167858x^8 - 831663x^7 + 2597153x^6 - 9535563x^5 + 21565485x^4 - 26219943x^3 + 63196200x^2 - 79315929x + 190380537	\( 13^{12}\cdot 61^{12} \)	$C_4:C_4$ (as 16T8)	$[2, 2, 2, 36, 360]$ (GRH)
16.0.286218361857094751614277009933470801.7	x^16 - 4x^15 + x^14 + 14x^13 + 450x^12 - 3772x^11 + 4773x^10 + 5215x^9 - 100624x^8 + 363819x^7 - 510377x^6 - 1201029x^5 + 25631015x^4 + 40577113x^3 - 42465958x^2 - 41607389x + 68049763	\( 17^{12}\cdot 53^{12} \)	$C_4:C_4$ (as 16T8)	$[2, 14, 476]$ (GRH)
16.0.286218361857094751614277009933470801.9	x^16 - 4x^15 + 17x^14 - 42x^13 + 507x^12 - 1058x^11 + 7486x^10 - 15529x^9 + 51943x^8 - 103927x^7 + 1100675x^6 - 1990836x^5 + 15449301x^4 - 21086696x^3 + 68885217x^2 - 46191701x + 90915613	\( 17^{12}\cdot 53^{12} \)	$C_4:C_4$ (as 16T8)	$[2, 70, 140]$ (GRH)
16.0.286218361857094751614277009933470801.23	x^16 - 3x^15 + 183x^14 - 159x^13 + 13024x^12 + 19563x^11 + 442958x^10 + 2076975x^9 + 14494211x^8 + 72959856x^7 + 412915231x^6 + 1894750586x^5 + 6943110997x^4 + 18036657805x^3 + 32555640354x^2 + 33661076896x + 15061337953	\( 17^{12}\cdot 53^{12} \)	$C_4:C_4$ (as 16T8)	$[2, 280, 560]$ (GRH)
16.16.26252865470156848284984700456389559681.1	x^16 - x^15 - 386x^14 - 978x^13 + 33397x^12 + 90172x^11 - 1157913x^10 - 2853491x^9 + 18517725x^8 + 38672703x^7 - 135765373x^6 - 223518780x^5 + 384304713x^4 + 466800116x^3 - 276793968x^2 - 345202792x - 53337296	\( 13^{12}\cdot 101^{12} \)	$C_4:C_4$ (as 16T8)	Trivial (GRH)
16.0.26252865470156848284984700456389559681.4	x^16 - 4x^15 + 141x^14 - 476x^13 + 7718x^12 - 21126x^11 + 204969x^10 - 440625x^9 + 2836720x^8 - 4701297x^7 + 19646115x^6 - 24590405x^5 + 54351103x^4 - 58934929x^3 - 17975866x^2 - 15162339x + 71134267	\( 13^{12}\cdot 101^{12} \)	$C_4:C_4$ (as 16T8)	$[5, 5, 10, 20]$ (GRH)
16.0.26252865470156848284984700456389559681.6	x^16 + 57x^14 - 334x^13 + 2319x^12 - 13622x^11 + 104686x^10 - 518319x^9 + 2090613x^8 - 11794245x^7 + 51922689x^6 - 174630340x^5 + 510117913x^4 - 1506235284x^3 + 4103046553x^2 - 6992958031x + 6194357651	\( 13^{12}\cdot 101^{12} \)	$C_4:C_4$ (as 16T8)	$[26, 260]$ (GRH)
16.0.143902101499474565788603458614754288481.3	x^16 - 4x^15 - 39x^14 + 154x^13 + 1509x^12 - 2202x^11 - 33967x^10 + 37482x^9 + 478829x^8 - 1172884x^7 - 2897647x^6 + 13350656x^5 + 85842500x^4 - 404797504x^3 + 30548912x^2 + 646882304x + 2548078528	\( 17^{12}\cdot 89^{12} \)	$C_4:C_4$ (as 16T8)	$[28, 728]$ (GRH)
16.0.143902101499474565788603458614754288481.10	x^16 - 4x^15 + 213x^14 - 728x^13 + 23472x^12 - 67494x^11 + 1674140x^10 - 3988680x^9 + 82648724x^8 - 159005322x^7 + 2881145428x^6 - 4255788538x^5 + 68938613619x^4 - 70436280004x^3 + 1014049127255x^2 - 539518460270x + 6855061765612	\( 17^{12}\cdot 89^{12} \)	$C_4:C_4$ (as 16T8)	$[2, 602, 602]$ (GRH)
16.0.143902101499474565788603458614754288481.11	x^16 - 2x^15 + 20x^14 - 1532x^13 + 18456x^12 - 36352x^11 - 2708722x^10 + 6899572x^9 - 254586024x^8 + 2092644532x^7 + 7734173792x^6 + 40074764600x^5 + 1722809966457x^4 - 6943784680154x^3 + 59097374743052x^2 - 419116620051792x + 1373873435767232	\( 17^{12}\cdot 89^{12} \)	$C_4:C_4$ (as 16T8)	$[7, 14, 14, 14]$ (GRH)