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 )

Label	Polynomial	Discriminant	Galois group	Class group
16.0.10564402173046133902941889.2	x^16 - 3x^15 + 34x^14 - 31x^13 + 473x^12 + 101x^11 + 3660x^10 + 2113x^9 + 15141x^8 + 6850x^7 + 32800x^6 + 14640x^5 + 41808x^4 + 19840x^3 + 26112x^2 + 9216x + 4096	\( 17^{14}\cdot 89^{4} \)	$C_2^2 : C_8$ (as 16T24)	$[140]$ (GRH)
16.0.10646188457767892278050816.2	x^16 + 24x^14 + 276x^12 + 1776x^10 + 6881x^8 + 15072x^6 + 16704x^4 + 3072x^2 + 256	\( 2^{48}\cdot 3^{8}\cdot 7^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[4, 4, 8]$ (GRH)
16.0.12050735989665305600000000.1	x^16 + 33x^14 + 422x^12 + 2723x^10 + 9543x^8 + 18119x^6 + 17608x^4 + 7531x^2 + 941	\( 2^{16}\cdot 5^{8}\cdot 29^{8}\cdot 941 \)	16T1461	$[2, 76]$ (GRH)
16.0.12260383203665853750390625.1	x^16 - 6x^15 + 27x^14 - 92x^13 + 309x^12 - 824x^11 + 2046x^10 - 4678x^9 + 10025x^8 - 16676x^7 + 32508x^6 - 37970x^5 + 63804x^4 - 45560x^3 + 68140x^2 - 20900x + 28775	\( 5^{8}\cdot 29^{8}\cdot 89^{4} \)	$C_2\wr C_2^2$ (as 16T150)	$[182]$ (GRH)
16.0.12796960816656000000000000.1	x^16 - 8x^15 + 62x^14 - 294x^13 + 1232x^12 - 3774x^11 + 10008x^10 - 19892x^9 + 34425x^8 - 44976x^7 + 56189x^6 - 53874x^5 + 61418x^4 - 48694x^3 + 51225x^2 - 22708x + 13921	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 61^{2}\cdot 181^{2} \)	16T797	$[2, 2, 40]$ (GRH)
16.0.13483641577021465600000000.1	x^16 + 37x^14 + 427x^12 + 2397x^10 + 7503x^8 + 13536x^6 + 13518x^4 + 6409x^2 + 841	\( 2^{16}\cdot 5^{8}\cdot 29^{6}\cdot 941^{2} \)	16T1445	$[152]$ (GRH)
16.0.13567885575582954350098576.1	x^16 - 8x^15 + 44x^14 - 168x^13 + 587x^12 - 1702x^11 + 4239x^10 - 8644x^9 + 15457x^8 - 23538x^7 + 30978x^6 - 33521x^5 + 31435x^4 - 23817x^3 + 13277x^2 - 4620x + 6466	\( 2^{4}\cdot 43^{2}\cdot 2777^{6} \)	16T1537	$[2, 90]$
16.0.13804460977881721884765625.1	x^16 - 4x^15 + 45x^14 - 160x^13 + 846x^12 - 2460x^11 + 8219x^10 - 18505x^9 + 42209x^8 - 70521x^7 + 109939x^6 - 126586x^5 + 122135x^4 - 81341x^3 + 42543x^2 - 26360x + 15151	\( 5^{10}\cdot 29^{8}\cdot 41^{4} \)	$D_4.D_4$ (as 16T175)	$[2, 52]$ (GRH)
16.0.15086928328153625600000000.1	x^16 + 23x^14 + 216x^12 + 1089x^10 + 3243x^8 + 5873x^6 + 6349x^4 + 3764x^2 + 941	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 941^{3} \)	16T1432	$[130]$ (GRH)
16.0.15686332680774922119140625.1	x^16 - 4x^15 + 62x^14 - 162x^13 + 1357x^12 - 2204x^11 + 13752x^10 - 12451x^9 + 72905x^8 - 32084x^7 + 221779x^6 - 14352x^5 + 393392x^4 + 80477x^3 + 366837x^2 + 106495x + 130321	\( 3^{8}\cdot 5^{12}\cdot 29^{4}\cdot 61^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T542)	$[2, 4, 16]$ (GRH)
16.0.18727984661882905600000000.1	x^16 + 27x^14 + 293x^12 + 1661x^10 + 5333x^8 + 9812x^6 + 9932x^4 + 4901x^2 + 841	\( 2^{16}\cdot 5^{8}\cdot 29^{6}\cdot 1109^{2} \)	16T1445	$[136]$ (GRH)
16.0.20928938182187993309151488.1	x^16 - 3x^15 + 26x^14 - 61x^13 + 302x^12 - 481x^11 + 1800x^10 - 1694x^9 + 6221x^8 - 1408x^7 + 12724x^6 + 4447x^5 + 29261x^4 + 14047x^3 + 63157x^2 + 36221x + 38659	\( 2^{8}\cdot 13^{4}\cdot 17^{15} \)	$C_2^3.C_8$ (as 16T104)	$[2, 2, 50]$ (GRH)
16.0.22502537891856000000000000.9	x^16 - 8x^15 + 38x^14 - 126x^13 + 392x^12 - 1078x^11 + 2868x^10 - 6508x^9 + 14535x^8 - 27518x^7 + 52626x^6 - 80626x^5 + 131167x^4 - 151166x^3 + 199323x^2 - 133920x + 139681	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 11^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[2, 4, 4, 8]$ (GRH)
16.0.22585894701900222828166433.1	x^16 - x^15 + 35x^14 - 52x^13 + 426x^12 - 834x^11 + 2908x^10 - 5441x^9 + 12734x^8 - 20894x^7 + 36823x^6 - 49114x^5 + 65638x^4 - 66318x^3 + 63428x^2 - 39339x + 19211	\( 17^{15}\cdot 53^{4} \)	$C_{16} : C_2$ (as 16T22)	$[9, 18]$ (GRH)
16.0.23948260540416000000000000.1	x^16 + 32x^14 + 390x^12 + 2472x^10 + 9054x^8 + 19658x^6 + 24455x^4 + 15458x^2 + 3481	\( 2^{32}\cdot 3^{8}\cdot 5^{12}\cdot 59^{2} \)	16T1102	$[2, 122]$ (GRH)
16.0.23948260540416000000000000.2	x^16 + 36x^14 + 527x^12 + 4038x^10 + 17390x^8 + 42102x^6 + 53962x^4 + 30444x^2 + 3481	\( 2^{32}\cdot 3^{8}\cdot 5^{12}\cdot 59^{2} \)	16T1102	$[2, 106]$ (GRH)
16.0.23948260540416000000000000.3	x^16 + 32x^14 + 418x^12 + 2884x^10 + 11340x^8 + 25514x^6 + 31183x^4 + 18172x^2 + 3481	\( 2^{32}\cdot 3^{8}\cdot 5^{12}\cdot 59^{2} \)	$C_2^4.C_2^4$ (as 16T464)	$[2, 112]$ (GRH)
16.0.24695998799082214400000000.1	x^16 + 24x^14 + 234x^12 + 1217x^10 + 3710x^8 + 6827x^6 + 7451x^4 + 4436x^2 + 1109	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 1109^{3} \)	16T1432	$[146]$ (GRH)
16.0.24695998799082214400000000.2	x^16 + 35x^14 + 391x^12 + 2107x^10 + 6265x^8 + 10736x^6 + 10474x^4 + 5361x^2 + 1109	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 1109^{3} \)	16T1741	$[186]$ (GRH)
16.0.25221297570561000000000000.1	x^16 + 35x^14 + 475x^12 + 3225x^10 + 11775x^8 + 22875x^6 + 21250x^4 + 6875x^2 + 625	\( 2^{12}\cdot 3^{12}\cdot 5^{12}\cdot 83^{4} \)	$C_2\times C_2^3:S_4$ (as 16T747)	$[2, 2, 30]$ (GRH)
16.0.26372940026256000000000000.1	x^16 + 20x^14 + 167x^12 + 755x^10 + 2004x^8 + 3165x^6 + 2868x^4 + 1340x^2 + 241	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 241\cdot 1021^{2} \)	16T1771	$[2, 52]$ (GRH)
16.0.26585452170716224216367104.1	x^16 + 24x^14 + 276x^12 + 1776x^10 + 6850x^8 + 14784x^6 + 17024x^4 + 6144x^2 + 1024	\( 2^{62}\cdot 7^{8} \)	$C_8\times C_2$ (as 16T5)	$[136]$ (GRH)
16.0.31703006950533291639898112.1	x^16 + 34x^14 + 425x^12 + 2584x^10 + 8670x^8 + 16898x^6 + 19040x^4 + 11492x^2 + 2873	\( 2^{16}\cdot 13^{2}\cdot 17^{15} \)	$(C_2\times C_8).D_4$ (as 16T306)	$[2, 2, 50]$ (GRH)
16.0.33133506085029178470629376.2	x^16 + 27x^14 + 295x^12 + 1688x^10 + 5432x^8 + 9729x^6 + 8855x^4 + 3249x^2 + 361	\( 2^{16}\cdot 3^{2}\cdot 19^{6}\cdot 103^{6} \)	16T1757	$[196]$ (GRH)
16.0.35074927889488281600000000.1	x^16 - 4x^15 + 34x^14 - 64x^13 + 539x^12 - 1000x^11 + 4842x^10 - 4648x^9 + 19562x^8 - 22604x^7 + 45816x^6 - 21740x^5 + 19433x^4 + 3616x^3 + 4684x^2 - 68x + 1	\( 2^{24}\cdot 3^{8}\cdot 5^{8}\cdot 13^{8} \)	$C_2^4$ (as 16T3)	$[4, 8, 8]$ (GRH)
16.0.35279244160869606400000000.1	x^16 + 34x^14 + 443x^12 + 2832x^10 + 9661x^8 + 18056x^6 + 17887x^4 + 8278x^2 + 1249	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 1249^{3} \)	16T972	$[2, 92]$ (GRH)
16.0.35676952034653344666763264.2	x^16 + 18x^14 + 129x^12 + 478x^10 + 990x^8 + 1154x^6 + 726x^4 + 223x^2 + 25	\( 2^{14}\cdot 17^{4}\cdot 97^{4}\cdot 131^{4} \)	16T1938	$[2, 60]$
16.0.36093282486485263170800449.1	x^16 - 6x^15 + 24x^14 - 68x^13 + 229x^12 - 610x^11 + 1652x^10 - 3427x^9 + 8268x^8 - 14574x^7 + 31149x^6 - 43150x^5 + 84686x^4 - 84235x^3 + 155680x^2 - 83057x + 153851	\( 11^{8}\cdot 17^{14} \)	$C_8\times C_2$ (as 16T5)	$[17, 17]$ (GRH)
16.0.37319027463036582275390625.1	x^16 - x^15 + 22x^14 - 15x^13 + 370x^12 - 219x^11 + 1996x^10 + 855x^9 + 6474x^8 + 2315x^7 + 9134x^6 + 8383x^5 + 7555x^4 + 3230x^3 + 1088x^2 + 152x + 16	\( 3^{8}\cdot 5^{12}\cdot 13^{12} \)	$C_4\times C_2^2$ (as 16T2)	$[2, 104]$ (GRH)
16.0.39615410820716953600000000.1	x^16 - 8x^15 + 20x^14 - 34x^12 - 160x^11 + 988x^10 - 2520x^9 + 6291x^8 - 13520x^7 + 25876x^6 - 37312x^5 + 55602x^4 - 61552x^3 + 73496x^2 - 47168x + 55036	\( 2^{44}\cdot 5^{8}\cdot 7^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[2, 8, 8]$ (GRH)
16.0.41107867812353742431640625.1	x^16 - x^15 + 12x^14 - 17x^13 + 2x^12 - 75x^11 - 142x^10 - 399x^9 + 470x^8 - 121x^7 + 3168x^6 + 5225x^5 + 8927x^4 + 11662x^3 + 12432x^2 + 7816x + 4336	\( 5^{12}\cdot 17^{14} \)	$C_8\times C_2$ (as 16T5)	$[146]$ (GRH)
16.0.44125479974206216421244928.1	x^16 + 32x^14 + 392x^12 + 2352x^10 + 7418x^8 + 12240x^6 + 9800x^4 + 3136x^2 + 337	\( 2^{60}\cdot 337^{3} \)	16T1251	$[5, 30]$ (GRH)
16.0.44125479974206216421244928.2	x^16 + 28x^14 + 322x^12 + 1968x^10 + 6901x^8 + 13920x^6 + 15086x^4 + 7020x^2 + 337	\( 2^{60}\cdot 337^{3} \)	16T1251	$[5, 30]$ (GRH)
16.0.48023489818559305679372288.1	x^16 + 34x^14 + 476x^12 + 3536x^10 + 14960x^8 + 35904x^6 + 45696x^4 + 26112x^2 + 4352	\( 2^{24}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2, 194]$ (GRH)
16.0.49497384532993638400000000.1	x^16 + 20x^14 + 164x^12 + 718x^10 + 1828x^8 + 2756x^6 + 2389x^4 + 1086x^2 + 199	\( 2^{40}\cdot 5^{8}\cdot 199\cdot 761^{2} \)	16T1769	$[126]$ (GRH)
16.0.49535258684630680881135616.1	x^16 + 35x^14 + 486x^12 + 3428x^10 + 13207x^8 + 28366x^6 + 33276x^4 + 19631x^2 + 4489	\( 2^{16}\cdot 17^{14}\cdot 67^{2} \)	16T1194	$[2, 2, 78]$ (GRH)
16.0.49535258684630680881135616.2	x^16 + 33x^14 + 435x^12 + 2981x^10 + 11592x^8 + 26051x^6 + 32613x^4 + 20234x^2 + 4489	\( 2^{16}\cdot 17^{14}\cdot 67^{2} \)	16T1194	$[2, 2, 72]$ (GRH)
16.0.54660589158400000000000000.3	x^16 + 24x^14 + 292x^12 + 2192x^10 + 10940x^8 + 36848x^6 + 80512x^4 + 95776x^2 + 55696	\( 2^{36}\cdot 5^{14}\cdot 19^{4} \)	$C_2\times C_2^3.C_4$ (as 16T99)	$[2, 4, 24]$ (GRH)
16.0.56118626684141976944640000.1	x^16 - 8x^15 + 36x^14 - 104x^13 + 228x^12 - 288x^11 + 180x^10 + 848x^9 - 1002x^8 + 888x^7 + 12924x^6 - 35352x^5 + 95420x^4 - 146992x^3 + 193260x^2 - 175344x + 117889	\( 2^{46}\cdot 3^{12}\cdot 5^{4}\cdot 7^{4} \)	$C_2^4:C_2^2$ (as 16T119)	$[2, 2, 28]$ (GRH)
16.0.58432555897690521600000000.3	x^16 - 20x^14 - 24x^13 + 178x^12 + 408x^11 - 200x^10 - 1320x^9 - 113x^8 + 3840x^7 + 11128x^6 + 20184x^5 + 32086x^4 + 39336x^3 + 53260x^2 + 32616x + 27646	\( 2^{48}\cdot 3^{12}\cdot 5^{8} \)	$D_8$ (as 16T7)	$[6, 24]$ (GRH)
16.0.62994975926473753600000000.1	x^16 + 27x^14 + 270x^12 + 1392x^10 + 4145x^8 + 7369x^6 + 7657x^4 + 4247x^2 + 961	\( 2^{16}\cdot 5^{8}\cdot 31^{4}\cdot 41^{2}\cdot 1259^{2} \)	16T1884	$[2, 116]$ (GRH)
16.0.63456228123711897600000000.3	x^16 + 161x^12 + 576x^8 + 161x^4 + 1	\( 2^{32}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8} \)	$C_2^4$ (as 16T3)	$[2, 2, 2, 16]$ (GRH)
16.0.63456228123711897600000000.11	x^16 - 20x^14 + 182x^12 - 468x^10 + 1859x^8 + 2652x^6 + 17954x^4 + 19168x^2 + 28561	\( 2^{32}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8} \)	$C_2^4$ (as 16T3)	$[2, 2, 4, 8]$ (GRH)
16.0.63456228123711897600000000.12	x^16 - 28x^14 - 12x^13 + 360x^12 + 72x^11 - 2630x^10 + 840x^9 + 13881x^8 - 16152x^7 - 37930x^6 + 48084x^5 + 76402x^4 - 60288x^3 + 51360x^2 + 169920x + 67104	\( 2^{32}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8} \)	$C_2^4$ (as 16T3)	$[2, 2, 4, 8]$ (GRH)
16.0.63456228123711897600000000.14	x^16 - 4x^15 + 30x^14 - 56x^13 + 383x^12 - 660x^11 + 2958x^10 - 2628x^9 + 10176x^8 - 7192x^7 + 25000x^6 - 8448x^5 + 18363x^4 - 11064x^3 + 9876x^2 - 3100x + 961	\( 2^{32}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8} \)	$C_2^4$ (as 16T3)	$[2, 2, 4, 8]$ (GRH)
16.0.63456228123711897600000000.18	x^16 - 8x^15 + 20x^14 - 48x^12 - 76x^11 + 998x^10 - 3340x^9 + 8969x^8 - 18388x^7 + 34410x^6 - 50244x^5 + 70504x^4 - 73380x^3 + 78354x^2 - 47772x + 37809	\( 2^{32}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8} \)	$C_2^4$ (as 16T3)	$[2, 4, 4, 8]$ (GRH)
16.0.63456228123711897600000000.22	x^16 - 8x^15 + 52x^14 - 224x^13 + 872x^12 - 2684x^11 + 7338x^10 - 16472x^9 + 33053x^8 - 55468x^7 + 76638x^6 - 83224x^5 + 70130x^4 - 44152x^3 - 60356x^2 + 74504x + 80644	\( 2^{32}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8} \)	$C_2^4$ (as 16T3)	$[2, 2, 2, 16]$ (GRH)
16.0.65790008098816000000000000.1	x^16 + 4x^14 - 12x^13 + 94x^12 - 216x^11 + 652x^10 - 1148x^9 + 4132x^8 - 9824x^7 + 27006x^6 - 43844x^5 + 59523x^4 - 54320x^3 + 37368x^2 - 14976x + 5351	\( 2^{32}\cdot 5^{12}\cdot 89^{4} \)	$C_2^4.C_2^3$ (as 16T210)	$[2, 56]$ (GRH)
16.0.65790008098816000000000000.2	x^16 - 4x^15 + 22x^14 - 92x^13 + 213x^12 - 532x^11 + 912x^10 - 356x^9 - 1015x^8 - 5232x^7 + 16098x^6 + 69508x^5 + 245011x^4 + 294708x^3 + 304498x^2 + 317500x + 657121	\( 2^{32}\cdot 5^{12}\cdot 89^{4} \)	$C_2^4.C_2^3$ (as 16T217)	$[2, 52]$ (GRH)
16.0.72138957898383360000000000.1	x^16 + 36x^14 + 512x^12 + 3744x^10 + 15376x^8 + 36360x^6 + 48240x^4 + 32400x^2 + 8100	\( 2^{50}\cdot 3^{8}\cdot 5^{10} \)	$C_2\times C_2^2.D_4$ (as 16T92)	$[2, 80]$ (GRH)

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