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 46 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.4745793514216882176.1	x^16 - 6x^15 + 22x^14 - 64x^13 + 152x^12 - 308x^11 + 554x^10 - 876x^9 + 1200x^8 - 1412x^7 + 1384x^6 - 1086x^5 + 660x^4 - 290x^3 + 84x^2 - 14x + 1	\( 2^{22}\cdot 3^{2}\cdot 7^{2}\cdot 37^{6} \)	16T1683	Trivial
16.4.29197152583639003681.1	x^16 - 7x^15 + 26x^14 - 57x^13 + 60x^12 + 37x^11 - 238x^10 + 409x^9 - 397x^8 + 202x^7 + 47x^6 - 190x^5 + 174x^4 - 103x^3 + 38x^2 - 4x + 1	\( 149^{2}\cdot 331^{6} \)	16T1683	Trivial (GRH)
16.4.29197152583639003681.2	x^16 - 4x^15 + 2x^14 + 10x^13 - 23x^12 + 42x^11 - 65x^10 + 64x^9 - 32x^8 - 41x^7 + 121x^6 - 102x^5 + 5x^4 + 43x^3 - 32x^2 + 11x - 1	\( 149^{2}\cdot 331^{6} \)	16T1683	Trivial (GRH)
16.4.505577180252520423441.1	x^16 - 4x^15 + 24x^13 - 33x^12 - 71x^11 + 177x^10 + 157x^9 - 504x^8 - 235x^7 + 949x^6 + 60x^5 - 1327x^4 + 244x^3 + 1217x^2 - 133x - 439	\( 3^{2}\cdot 19^{6}\cdot 103^{6} \)	16T1683	Trivial (GRH)
16.0.505577180252520423441.2	x^16 - 9x^14 - 4x^13 + 48x^12 + 12x^11 - 168x^10 + 54x^9 + 354x^8 - 381x^7 - 274x^6 + 822x^5 - 441x^4 - 384x^3 + 749x^2 - 477x + 129	\( 3^{2}\cdot 19^{6}\cdot 103^{6} \)	16T1683	Trivial (GRH)
16.0.6347353545871787556864.1	x^16 - 4x^12 - 12x^10 + 14x^8 - 88x^6 + 1024x^4 - 2220x^2 + 1369	\( 2^{38}\cdot 3^{2}\cdot 37^{6} \)	16T1683	Trivial (GRH)
16.0.7337958667162225175824.2	x^16 - 3x^15 + x^14 - 2x^13 + 27x^12 - 37x^11 + 15x^10 - 39x^9 + 120x^8 - 274x^7 + 480x^6 - 469x^5 + 695x^4 - 1580x^3 + 2701x^2 - 2566x + 1186	\( 2^{4}\cdot 2777^{6} \)	16T1683	Trivial (GRH)
16.8.40951751600454154298721.2	x^16 - 5x^15 + 5x^14 - 2x^13 - 16x^12 + 79x^11 + 39x^10 - 254x^9 - 250x^8 + 474x^7 + 657x^6 - 352x^5 - 725x^4 - 61x^3 + 307x^2 + 95x - 1	\( 3^{6}\cdot 19^{6}\cdot 103^{6} \)	16T1683	Trivial (GRH)
16.4.40951751600454154298721.3	x^16 - 4x^15 + 20x^14 - 78x^13 + 217x^12 - 533x^11 + 1086x^10 - 1722x^9 + 1872x^8 - 1362x^7 - 637x^6 + 2981x^5 - 4566x^4 + 4063x^3 - 2512x^2 + 786x - 89	\( 3^{6}\cdot 19^{6}\cdot 103^{6} \)	16T1683	Trivial (GRH)
16.4.117407338674595602813184.1	x^16 - 25x^14 - 4x^13 + 221x^12 + 44x^11 - 753x^10 - 142x^9 - 641x^8 - 1566x^7 + 9355x^6 + 11302x^5 - 14325x^4 - 23220x^3 - 9796x^2 - 1888x - 142	\( 2^{8}\cdot 2777^{6} \)	16T1683	Trivial (GRH)
16.4.117407338674595602813184.2	x^16 + 3x^14 - 2x^13 - 26x^12 + 68x^11 - 525x^10 + 260x^9 - 1833x^8 + 966x^7 - 6630x^6 + 2860x^5 - 6375x^4 + 4076x^3 - 12946x^2 + 3548x + 506	\( 2^{8}\cdot 2777^{6} \)	16T1683	Trivial (GRH)
16.0.182513362071159872862201.1	x^16 - 3x^15 + 22x^14 - 29x^13 + 148x^12 - 76x^11 + 588x^10 - 193x^9 + 1125x^8 - 148x^7 - 1120x^6 - 1286x^5 - 6707x^4 + 7172x^3 - 101x^2 + 17685x + 51999	\( 3^{2}\cdot 19^{8}\cdot 103^{6} \)	16T1683	$[2]$ (GRH)
16.4.368565764404087388688489.1	x^16 - 6x^15 + 6x^14 + 5x^13 - 15x^12 + 201x^11 + 116x^10 - 1245x^9 - 2256x^8 + 1135x^7 + 6822x^6 + 7872x^5 + 4936x^4 + 1323x^3 + 1158x^2 + 1539x + 9	\( 3^{8}\cdot 19^{6}\cdot 103^{6} \)	16T1683	Trivial (GRH)
16.4.368565764404087388688489.2	x^16 - 4x^15 - 18x^14 + 85x^13 + 123x^12 - 777x^11 - 486x^10 + 4418x^9 + 1959x^8 - 18547x^7 - 8842x^6 + 58035x^5 + 30520x^4 - 123250x^3 - 74203x^2 + 133770x + 110887	\( 3^{8}\cdot 19^{6}\cdot 103^{6} \)	16T1683	Trivial (GRH)
16.8.368565764404087388688489.2	x^16 - x^15 - 2x^14 + 2x^13 - 126x^12 + 308x^11 - 418x^10 + 1532x^9 - 1511x^8 - 219x^7 - 1447x^6 - 1800x^5 + 5614x^4 + 1499x^3 - 2960x^2 - 202x + 487	\( 3^{8}\cdot 19^{6}\cdot 103^{6} \)	16T1683	Trivial (GRH)
16.0.672728412096904653209889.1	x^16 - x^15 + 6x^14 - 10x^13 + 68x^12 + 161x^11 + 652x^10 + 1084x^9 + 1207x^8 + 77x^7 - 2185x^6 - 3441x^5 - 1214x^4 + 1828x^3 + 2321x^2 + 992x + 151	\( 3^{6}\cdot 13^{2}\cdot 1327^{6} \)	16T1683	Trivial (GRH)
16.8.672728412096904653209889.1	x^16 - 6x^15 - 3x^14 + 65x^13 - 76x^12 - 129x^11 + 141x^10 + 313x^9 + 292x^8 - 1706x^7 + 104x^6 + 1308x^5 + 2238x^4 - 426x^3 - 811x^2 + 57x + 67	\( 3^{6}\cdot 13^{2}\cdot 1327^{6} \)	16T1683	Trivial (GRH)
16.0.2795948938295250036719616.1	x^16 - 4x^15 + 8x^14 - 13x^12 - 20x^11 + 68x^10 - 4x^9 - 173x^8 - 24x^7 + 416x^6 + 188x^5 - 463x^4 - 344x^3 + 140x^2 + 192x + 48	\( 2^{20}\cdot 3^{2}\cdot 7^{6}\cdot 17^{8}\cdot 19^{2} \)	16T1683	$[2]$ (GRH)
16.4.2795948938295250036719616.1	x^16 - 4x^15 + 4x^14 + 14x^13 - 63x^12 + 110x^11 - 149x^10 + 258x^9 - 378x^8 + 464x^7 - 567x^6 + 638x^5 - 777x^4 + 846x^3 - 665x^2 + 390x - 121	\( 2^{20}\cdot 3^{2}\cdot 7^{6}\cdot 17^{8}\cdot 19^{2} \)	16T1683	$[2]$ (GRH)
16.8.2795948938295250036719616.1	x^16 - 2x^15 - 13x^14 + 12x^13 + 47x^12 + 40x^11 + 32x^10 - 96x^9 - 600x^8 + 192x^7 + 128x^6 - 320x^5 + 752x^4 - 384x^3 - 832x^2 + 256x + 256	\( 2^{20}\cdot 3^{2}\cdot 7^{6}\cdot 17^{8}\cdot 19^{2} \)	16T1683	Trivial (GRH)
16.4.2795948938295250036719616.2	x^16 - 2x^15 + 3x^14 + 22x^13 - 102x^12 - 110x^11 + 542x^10 + 122x^9 - 1213x^8 - 94x^7 + 1422x^6 + 1412x^5 - 136x^4 - 1082x^3 - 227x^2 - 38x + 209	\( 2^{20}\cdot 3^{2}\cdot 7^{6}\cdot 17^{8}\cdot 19^{2} \)	16T1683	Trivial (GRH)
16.0.9129646748653218725625856.1	x^16 - 2x^15 + 13x^14 + 69x^12 + 82x^11 + 380x^10 + 538x^9 + 1041x^8 + 2412x^7 + 2317x^6 + 3498x^5 + 4505x^4 + 1676x^3 + 5114x^2 - 6204x + 1548	\( 2^{20}\cdot 7^{6}\cdot 17^{8}\cdot 103^{2} \)	16T1683	$[6]$ (GRH)
16.4.13567885575582954350098576.1	x^16 - x^15 + 16x^14 - 8x^13 + 109x^12 + 36x^11 + 382x^10 + 651x^9 + 1605x^8 + 3767x^7 + 3088x^6 + 5827x^5 + 836x^4 - 10392x^3 - 13077x^2 - 1914x - 2	\( 2^{4}\cdot 43^{2}\cdot 2777^{6} \)	16T1683	Trivial (GRH)
16.8.13567885575582954350098576.1	x^16 - 8x^14 - 8x^13 - 24x^12 - 122x^11 - 265x^10 + 197x^9 + 1923x^8 + 4338x^7 + 10472x^6 + 27636x^5 + 50000x^4 + 48781x^3 + 18937x^2 - 1148x - 1468	\( 2^{4}\cdot 43^{2}\cdot 2777^{6} \)	16T1683	Trivial (GRH)
16.4.13567885575582954350098576.2	x^16 - 3x^15 - x^14 + 28x^13 - 75x^12 - 5x^11 + 302x^10 - 284x^9 - 479x^8 + 1660x^7 - x^6 - 7627x^5 + 9914x^4 + 12057x^3 - 23175x^2 - 26034x + 33823	\( 2^{4}\cdot 43^{2}\cdot 2777^{6} \)	16T1683	Trivial (GRH)
16.8.13567885575582954350098576.2	x^16 - 2x^15 - 4x^14 + 3x^13 - 8x^12 + 98x^11 - 123x^10 - 276x^9 - 542x^8 + 234x^7 + 4061x^6 + 6065x^5 + 6542x^4 - 127x^3 - 6552x^2 - 820x + 1433	\( 2^{4}\cdot 43^{2}\cdot 2777^{6} \)	16T1683	Trivial (GRH)
16.0.14783582327763949701838281.1	x^16 - 7x^15 + 58x^14 - 248x^13 + 1097x^12 - 3241x^11 + 9561x^10 - 20458x^9 + 43455x^8 - 67912x^7 + 107798x^6 - 120579x^5 + 147358x^4 - 111106x^3 + 109469x^2 - 44856x + 37197	\( 3^{6}\cdot 19^{8}\cdot 103^{6} \)	16T1683	$[2]$ (GRH)
16.12.14783582327763949701838281.1	x^16 - 4x^15 - 21x^14 + 98x^13 + 123x^12 - 1016x^11 + 223x^10 + 7011x^9 - 4373x^8 - 37765x^7 + 2415x^6 + 128210x^5 + 92402x^4 - 167478x^3 - 255674x^2 - 68672x + 27799	\( 3^{6}\cdot 19^{8}\cdot 103^{6} \)	16T1683	Trivial (GRH)
16.4.16151789973180531837239296.1	x^16 - 4x^15 + 16x^14 - 38x^13 + 26x^12 + 64x^11 - 495x^10 + 1222x^9 - 2187x^8 + 3284x^7 - 3124x^6 + 1888x^5 - 1012x^4 + 464x^3 - 80x^2 - 32x + 16	\( 2^{20}\cdot 7^{6}\cdot 17^{8}\cdot 137^{2} \)	16T1683	$[2]$ (GRH)
16.4.16151789973180531837239296.2	x^16 + 14x^14 + 17x^12 + 170x^10 - 780x^8 + 514x^6 - 1623x^4 + 854x^2 + 49	\( 2^{20}\cdot 7^{6}\cdot 17^{8}\cdot 137^{2} \)	16T1683	$[2]$ (GRH)
16.0.21755735644518995438075904.1	x^16 - 2x^15 + 3x^14 - 12x^13 + 38x^12 - 28x^11 - x^10 - 200x^9 + 855x^8 - 2074x^7 + 4058x^6 - 6436x^5 + 7586x^4 - 6024x^3 + 2972x^2 - 832x + 124	\( 2^{20}\cdot 3^{2}\cdot 7^{6}\cdot 17^{8}\cdot 53^{2} \)	16T1683	$[2, 2]$ (GRH)
16.12.21755735644518995438075904.1	x^16 - 4x^15 - 18x^14 + 78x^13 + 73x^12 - 442x^11 + 120x^10 + 788x^9 - 948x^8 - 1208x^7 + 1376x^6 + 2904x^5 + 1828x^4 + 88x^3 - 320x^2 - 48x + 16	\( 2^{20}\cdot 3^{2}\cdot 7^{6}\cdot 17^{8}\cdot 53^{2} \)	16T1683	Trivial (GRH)
16.0.26960382975639239273742336.1	x^16 - 6x^15 + 27x^14 - 82x^13 + 226x^12 - 526x^11 + 1158x^10 - 2208x^9 + 3868x^8 - 5870x^7 + 8599x^6 - 10966x^5 + 11434x^4 - 9710x^3 + 6392x^2 - 2312x + 1207	\( 2^{20}\cdot 3^{2}\cdot 7^{6}\cdot 17^{8}\cdot 59^{2} \)	16T1683	$[2]$ (GRH)
16.8.26960382975639239273742336.1	x^16 - 4x^15 + 9x^14 - 34x^12 + 48x^11 - 230x^10 - 72x^9 + 7x^8 - 20x^7 + 1102x^6 + 110x^5 + 936x^4 - 1566x^3 - 1285x^2 + 798x + 321	\( 2^{20}\cdot 3^{2}\cdot 7^{6}\cdot 17^{8}\cdot 59^{2} \)	16T1683	Trivial (GRH)
16.0.32054879040492388001775616.1	x^16 - 2x^15 - 7x^14 + 20x^13 - 6x^12 + 16x^11 - 225x^10 + 464x^9 + 356x^8 - 3676x^7 + 9691x^6 - 19112x^5 + 36241x^4 - 51842x^3 + 56840x^2 - 66252x + 46876	\( 2^{20}\cdot 7^{6}\cdot 17^{8}\cdot 193^{2} \)	16T1683	$[2]$ (GRH)
16.8.32054879040492388001775616.1	x^16 - 29x^14 - 18x^13 + 179x^12 + 172x^11 - 476x^10 - 648x^9 + 667x^8 + 1172x^7 - 365x^6 - 1082x^5 - 179x^4 + 384x^3 + 226x^2 + 36x - 4	\( 2^{20}\cdot 7^{6}\cdot 17^{8}\cdot 193^{2} \)	16T1683	Trivial (GRH)
16.12.217086169209327269601577216.1	x^16 - 4x^15 - 26x^14 + 154x^13 + 69x^12 - 1929x^11 + 3058x^10 + 6878x^9 - 26734x^8 + 25233x^7 + 45693x^6 - 179935x^5 + 100995x^4 + 260522x^3 - 260527x^2 - 35863x + 65669	\( 2^{8}\cdot 43^{2}\cdot 2777^{6} \)	16T1683	Trivial (GRH)
16.12.217086169209327269601577216.2	x^16 - 3x^15 - 38x^14 + 122x^13 + 416x^12 - 1570x^11 - 1120x^10 + 9807x^9 - 9105x^8 - 36275x^7 + 74048x^6 + 92579x^5 - 193421x^4 - 166344x^3 + 166348x^2 + 152668x + 21404	\( 2^{8}\cdot 43^{2}\cdot 2777^{6} \)	16T1683	Trivial (GRH)
16.0.55574059317587781018003767296.1	x^16 - 2x^15 + 63x^14 - 98x^13 + 1293x^12 - 2424x^11 + 14718x^10 - 27452x^9 + 111742x^8 - 178046x^7 + 541767x^6 - 754052x^5 + 1837140x^4 - 1943072x^3 + 3767542x^2 - 2328330x + 4049131	\( 2^{16}\cdot 43^{2}\cdot 2777^{6} \)	16T1683	$[4, 972]$ (GRH)
16.16.55574059317587781018003767296.1	x^16 - 2x^15 - 82x^14 + 92x^13 + 2355x^12 - 1040x^11 - 28620x^10 + 2070x^9 + 165983x^8 + 30748x^7 - 472309x^6 - 195268x^5 + 608750x^4 + 394204x^3 - 242294x^2 - 257328x - 55969	\( 2^{16}\cdot 43^{2}\cdot 2777^{6} \)	16T1683	Trivial (GRH)
16.0.55574059317587781018003767296.2	x^16 - 2x^15 + 56x^14 - 36x^13 + 1298x^12 + 246x^11 + 17477x^10 + 11672x^9 + 149104x^8 + 117458x^7 + 784597x^6 + 588454x^5 + 2445840x^4 + 1448666x^3 + 3937755x^2 + 2216914x + 1884046	\( 2^{16}\cdot 43^{2}\cdot 2777^{6} \)	16T1683	$[4, 2936]$ (GRH)
16.16.55574059317587781018003767296.2	x^16 - 2x^15 - 75x^14 + 164x^13 + 1932x^12 - 4552x^11 - 22352x^10 + 56970x^9 + 120407x^8 - 337842x^7 - 275711x^6 + 895866x^5 + 231861x^4 - 945272x^3 - 60485x^2 + 279420x - 53384	\( 2^{16}\cdot 43^{2}\cdot 2777^{6} \)	16T1683	Trivial (GRH)
16.0.411071299803720668601961257369600.1	x^16 + 4x^14 + 162x^12 + 472x^10 + 7011x^8 + 13240x^6 + 56922x^4 + 50380x^2 + 52441	\( 2^{24}\cdot 3^{2}\cdot 5^{2}\cdot 229^{6}\cdot 27479^{2} \)	16T1683	$[2, 42]$ (GRH)
16.0.67801478158550400798933242931302656.1	x^16 - 4x^15 + 35x^14 - 79x^13 + 387x^12 - 438x^11 + 1989x^10 - 610x^9 + 6898x^8 + 1830x^7 + 17901x^6 + 11826x^5 + 31347x^4 + 19197x^3 + 25515x^2 + 8748x + 6561	\( 2^{8}\cdot 7^{8}\cdot 101^{6}\cdot 6578749^{2} \)	16T1683	$[752]$ (GRH)
16.0.75533137975838300208821896262713344.1	x^16 - 4x^14 + 102x^12 - 292x^10 + 2097x^8 - 3712x^6 + 9488x^4 - 7680x^2 + 4096	\( 2^{26}\cdot 3^{8}\cdot 29^{8}\cdot 585601^{2} \)	16T1683	$[2, 2, 800]$ (GRH)
16.0.127002546850722315433493970504954877491242379898127259138662656.1	x^16 + 506x^14 + 153141x^12 + 40817027x^10 + 13041310242x^8 + 2486417463503x^6 + 576348918922940x^4 + 51604660127115744x^2 + 8441290099132106896	\( 2^{8}\cdot 7^{8}\cdot 101^{6}\cdot 6578749^{6} \)	16T1683	$[2, 2, 1411001944]$ (GRH)