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 1909)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.781250000000000000000.1	x^20 - 5x^19 + 5x^18 + 15x^17 - 30x^16 - 21x^15 + 75x^14 + 15x^13 - 120x^12 - 5x^11 + 141x^10 - 5x^9 - 120x^8 + 15x^7 + 75x^6 - 21x^5 - 30x^4 + 15x^3 + 5x^2 - 5x + 1	\( 2^{16}\cdot 5^{23} \)	$F_5$ (as 20T5)	Trivial
20.0.3354518684571451850752.1	x^20 - 2x^19 + 10x^17 - 15x^16 + 40x^14 - 64x^13 + 46x^12 + 8x^11 - 32x^10 + 8x^9 + 46x^8 - 64x^7 + 40x^6 - 15x^4 + 10x^3 - 2x + 1	\( 2^{16}\cdot 13^{15} \)	$F_5$ (as 20T5)	Trivial
20.0.4656612873077392578125.1	x^20 - 10x^19 + 50x^18 - 165x^17 + 375x^16 - 552x^15 + 445x^14 - 85x^13 - 35x^12 - 375x^11 + 879x^10 - 925x^9 + 585x^8 - 285x^7 + 175x^6 - 128x^5 + 65x^4 - 15x^3 + 1	\( 5^{31} \)	$F_5$ (as 20T5)	Trivial
20.0.86093442000000000000000.1	x^20 - x^19 + 4x^18 - 4x^17 + 2x^16 + 9x^15 + 2x^14 + 46x^13 + 69x^12 + 84x^11 + 62x^10 - 6x^9 - 6x^8 + 26x^7 + 62x^6 + 54x^5 + 17x^4 + x^3 + 4x^2 + 4x + 1	\( 2^{16}\cdot 3^{16}\cdot 5^{15} \)	$F_5$ (as 20T5)	Trivial
20.0.169023218768603112760857.1	x^20 - x^19 + 2x^18 + 3x^17 - 6x^16 + 23x^15 - 13x^14 + 7x^13 + 34x^12 - 50x^11 + 81x^10 - 50x^9 + 34x^8 + 7x^7 - 13x^6 + 23x^5 - 6x^4 + 3x^3 + 2x^2 - x + 1	\( 3^{10}\cdot 17^{15} \)	$F_5$ (as 20T5)	$[2]$
20.0.513156902790069580078125.1	x^20 - 5x^19 + 20x^18 - 60x^17 + 140x^16 - 281x^15 + 460x^14 - 645x^13 + 770x^12 - 780x^11 + 711x^10 - 560x^9 + 420x^8 - 155x^7 + 60x^6 - x^5 - 20x^4 - 20x^3 - 30x^2 - 25x + 41	\( 3^{16}\cdot 5^{23} \)	$F_5$ (as 20T5)	Trivial
20.0.1014188554980499267578125.1	x^20 - 5x^19 + 13x^18 - 30x^17 + 63x^16 - 110x^15 + 181x^14 - 275x^13 + 355x^12 - 445x^11 + 561x^10 - 635x^9 + 703x^8 - 775x^7 + 773x^6 - 690x^5 + 546x^4 - 370x^3 + 215x^2 - 100x + 25	\( 5^{15}\cdot 7^{16} \)	$F_5$ (as 20T5)	Trivial
20.0.1550921573240973639548928.1	x^20 + 4x^18 + 14x^16 + 28x^14 + 45x^12 + 64x^10 + 132x^8 + 256x^6 + 292x^4 + 160x^2 + 32	\( 2^{55}\cdot 3^{16} \)	$F_5$ (as 20T5)	Trivial
20.0.12800000000000000000000000.1	x^20 + 5x^16 - 4x^15 + 30x^14 + 20x^13 + 25x^12 + 60x^11 + 46x^10 + 60x^9 + 25x^8 + 20x^7 + 30x^6 - 4x^5 + 5x^4 + 1	\( 2^{30}\cdot 5^{23} \)	$F_5$ (as 20T5)	$[2]$
20.0.146746349255915802001953125.1	x^20 - 4x^19 + 11x^18 - 14x^17 + 27x^16 - 4x^15 + 76x^14 + 26x^13 + 242x^12 + 186x^11 + 1176x^10 + 1496x^9 + 3207x^8 + 3946x^7 + 4941x^6 + 3726x^5 + 4572x^4 + 2746x^3 + 2191x^2 + 686x + 641	\( 5^{15}\cdot 37^{10} \)	$F_5$ (as 20T5)	$[2]$
20.0.275716983698000000000000000.1	x^20 - 3x^19 + 16x^18 - 32x^17 + 110x^16 - 153x^15 + 358x^14 - 206x^13 + 553x^12 + 106x^11 + 758x^10 + 946x^9 + 724x^8 + 664x^7 - 58x^6 + 66x^5 + 161x^4 + 205x^3 + 190x^2 + 50x + 25	\( 2^{16}\cdot 5^{15}\cdot 13^{10} \)	$F_5$ (as 20T5)	$[2]$
20.0.565522513762594615522033664.1	x^20 - 6x^19 + 22x^18 - 61x^17 + 147x^16 - 338x^15 + 780x^14 - 1782x^13 + 3658x^12 - 6414x^11 + 10114x^10 - 15538x^9 + 23243x^8 - 31374x^7 + 35592x^6 - 32603x^5 + 23544x^4 - 13072x^3 + 5366x^2 - 1501x + 223	\( 2^{16}\cdot 29^{15} \)	$F_5$ (as 20T5)	Trivial
20.0.738112500000000000000000000.1	x^20 + 5x^18 - 10x^17 + 20x^16 - 18x^15 - 25x^14 + 30x^13 + 20x^12 + 350x^11 - 261x^10 - 950x^9 + 155x^8 + 1010x^7 + 730x^6 - 172x^5 - 980x^4 - 880x^3 + 160x^2 + 640x + 256	\( 2^{20}\cdot 3^{10}\cdot 5^{23} \)	$F_5$ (as 20T5)	$[2, 2]$
20.0.934494206144111487135776768.1	x^20 - 4x^18 + 14x^16 + 32x^14 - 258x^12 + 1432x^10 - 824x^8 + 384x^6 + 313x^4 - 308x^2 + 242	\( 2^{55}\cdot 11^{10} \)	$F_5$ (as 20T5)	$[2]$
20.0.1099511627776000000000000000.1	x^20 - 8x^19 + 40x^18 - 136x^17 + 352x^16 - 728x^15 + 1256x^14 - 1912x^13 + 3125x^12 - 6608x^11 + 16456x^10 - 37920x^9 + 71958x^8 - 107952x^7 + 126216x^6 - 112960x^5 + 75672x^4 - 36736x^3 + 12288x^2 - 2560x + 256	\( 2^{55}\cdot 5^{15} \)	$F_5$ (as 20T5)	$[4]$
20.0.1402274470934209014892578125.2	x^20 - 2x^19 - 2x^18 + 18x^17 - 32x^16 + 88x^15 + 58x^14 - 782x^13 + 1538x^12 + 1348x^11 - 466x^10 - 894x^9 + 346x^8 - 114x^7 - 424x^6 - 88x^5 + 214x^4 + 54x^3 + 14x^2 + 4x + 1	\( 5^{15}\cdot 11^{16} \)	$F_5$ (as 20T5)	$[5]$
20.0.1410554953728000000000000000.1	x^20 - 2x^19 + 13x^18 - 22x^17 + 99x^16 - 152x^15 + 492x^14 - 688x^13 + 1763x^12 - 2238x^11 + 4497x^10 - 5026x^9 + 8525x^8 - 7336x^7 + 10214x^6 - 7176x^5 + 6476x^4 - 2960x^3 + 2160x^2 - 960x + 320	\( 2^{30}\cdot 3^{16}\cdot 5^{15} \)	$F_5$ (as 20T5)	$[2]$
20.0.1643401287186145782470703125.1	x^20 - 5x^19 + 15x^18 - 30x^17 + 45x^16 - 70x^15 + 145x^14 - 360x^13 + 755x^12 - 1115x^11 + 930x^10 - 305x^9 + 705x^8 - 3530x^7 + 8095x^6 - 11300x^5 + 11445x^4 - 9200x^3 + 5425x^2 - 1925x + 295	\( 5^{23}\cdot 13^{10} \)	$F_5$ (as 20T5)	$[2]$
20.0.1818989403545856475830078125.2	x^20 + 25x^10 + 5	\( 5^{39} \)	$F_5$ (as 20T5)	Trivial
20.0.4031987800898000000000000000.1	x^20 - 5x^19 - 3x^18 + 51x^17 - 36x^16 - 221x^15 + 399x^14 - 153x^13 + 262x^12 - 677x^11 + 169x^10 + 203x^9 + 236x^8 - 335x^7 - 335x^6 + 325x^5 + 990x^4 + 1025x^3 + 575x^2 + 175x + 25	\( 2^{16}\cdot 5^{15}\cdot 17^{10} \)	$F_5$ (as 20T5)	$[2]$
20.0.4966875620168119680952696832.1	x^20 - 8x^19 + 40x^18 - 112x^17 + 194x^16 - 88x^15 - 380x^14 + 1128x^13 - 1232x^12 - 32x^11 + 2600x^10 - 4352x^9 + 4326x^8 - 2744x^7 + 1924x^6 - 1304x^5 + 1047x^4 - 72x^3 + 168x^2 - 96x + 16	\( 2^{55}\cdot 13^{10} \)	$F_5$ (as 20T5)	$[2]$
20.0.5337142039963166778564453125.1	x^20 - 4x^19 + 10x^18 - 5x^17 - 19x^16 + 50x^15 + 54x^14 - 40x^13 - 199x^12 + 840x^11 + 620x^10 - 1279x^9 + 1556x^8 + 5430x^7 + 3925x^6 - 1385x^5 + 2240x^4 + 2325x^3 + 1225x^2 + 25x + 25	\( 5^{15}\cdot 53^{10} \)	$F_5$ (as 20T5)	$[2]$
20.0.9256148959232000000000000000.1	x^20 - 6x^19 + 21x^18 - 54x^17 + 162x^16 - 494x^15 + 1081x^14 - 1382x^13 + 1059x^12 - 1812x^11 + 5568x^10 - 7980x^9 + 1291x^8 + 3950x^7 + 6055x^6 - 2470x^5 - 890x^4 + 850x^3 + 1275x^2 + 150x + 25	\( 2^{30}\cdot 5^{15}\cdot 7^{10} \)	$F_5$ (as 20T5)	$[2, 2]$ (GRH)
20.0.20776019874734407680000000000.1	x^20 - 8x^19 + 24x^18 - 48x^17 + 134x^16 - 296x^15 + 584x^14 - 1304x^13 + 1717x^12 - 2032x^11 + 3016x^10 - 1352x^9 + 4276x^8 + 3008x^7 - 6232x^6 + 9872x^5 + 2300x^4 - 4992x^3 + 1872x^2 - 256x + 16	\( 2^{55}\cdot 3^{10}\cdot 5^{10} \)	$F_5$ (as 20T5)	$[2, 2]$
20.0.21852734616490167965351477248.1	x^20 - 10x^19 + 60x^18 - 255x^17 + 833x^16 - 2176x^15 + 4622x^14 - 8044x^13 + 11428x^12 - 13058x^11 + 11680x^10 - 7762x^9 + 3457x^8 - 830x^7 + 1310x^6 - 3773x^5 + 4070x^4 - 1854x^3 - 876x^2 + 1177x + 1381	\( 2^{16}\cdot 37^{15} \)	$F_5$ (as 20T5)	Trivial
20.0.24032520061123371124267578125.1	x^20 - 5x^19 + 20x^18 - 65x^17 + 200x^16 - 482x^15 + 1015x^14 - 2005x^13 + 3375x^12 - 5715x^11 + 8584x^10 - 12320x^9 + 16915x^8 - 25850x^7 + 28430x^6 - 32983x^5 + 54230x^4 + 1020x^3 + 71185x^2 + 31085x + 14741	\( 5^{23}\cdot 17^{10} \)	$F_5$ (as 20T5)	$[2]$
20.0.32758971529018084480000000000.1	x^20 + 12x^18 - 7x^17 + 41x^16 - 58x^15 + 102x^14 + 272x^13 + 568x^12 + 538x^11 + 664x^10 + 362x^9 + 3461x^8 + 14x^7 + 8626x^6 + 3161x^5 + 5774x^4 + 3726x^3 + 1980x^2 + 351x + 81	\( 2^{16}\cdot 5^{10}\cdot 13^{15} \)	$F_5$ (as 20T5)	$[2]$
20.0.33359761956402000000000000000.1	x^20 - 5x^19 + 27x^18 - 81x^17 + 204x^16 - 379x^15 + 509x^14 - 707x^13 + 1062x^12 - 1983x^11 + 3759x^10 - 2473x^9 + 2326x^8 - 1065x^7 + 6885x^6 + 765x^5 - 540x^4 + 6075x^3 + 2025x^2 + 2025x + 2025	\( 2^{16}\cdot 3^{10}\cdot 5^{15}\cdot 7^{10} \)	$F_5$ (as 20T5)	$[2, 2]$ (GRH)
20.0.33630250781250000000000000000.1	x^20 - 5x^19 - 15x^18 + 115x^17 - 20x^16 - 841x^15 + 1115x^14 + 1785x^13 - 3880x^12 - 1055x^11 + 5601x^10 - 1055x^9 - 3880x^8 + 1785x^7 + 1115x^6 - 841x^5 - 20x^4 + 115x^3 - 15x^2 - 5x + 1	\( 2^{16}\cdot 3^{16}\cdot 5^{23} \)	$F_5$ (as 20T5)	$[5]$ (GRH)
20.0.33630250781250000000000000000.2	x^20 - 5x^19 + 10x^18 - 10x^17 + 30x^16 - 113x^15 - 30x^14 + 590x^13 + 275x^12 - 2640x^11 - 2256x^10 + 6770x^9 + 8900x^8 - 9670x^7 - 21040x^6 + 9408x^5 + 56075x^4 + 65245x^3 + 37290x^2 + 10890x + 1331	\( 2^{16}\cdot 3^{16}\cdot 5^{23} \)	$F_5$ (as 20T5)	$[5]$ (GRH)
20.0.33630250781250000000000000000.3	x^20 - 5x^19 + 15x^18 - 35x^17 + 70x^16 - 97x^15 + 95x^14 - 135x^13 + 590x^12 - 2555x^11 + 5169x^10 - 6185x^9 + 2780x^8 + 4905x^7 + 1565x^6 - 7753x^5 + 3460x^4 + 595x^3 - 2205x^2 - 1715x + 2401	\( 2^{16}\cdot 3^{16}\cdot 5^{23} \)	$F_5$ (as 20T5)	$[5]$ (GRH)
20.0.74651918354942620880126953125.1	x^20 - 2x^19 + 7x^18 - 2x^17 - 37x^16 + 28x^15 - 245x^13 + 266x^12 + 395x^11 - 660x^10 + 1358x^9 + 6413x^8 + 6698x^7 + 4837x^6 + 9188x^5 + 16636x^4 + 20385x^3 + 19110x^2 + 11925x + 3555	\( 3^{10}\cdot 5^{15}\cdot 23^{10} \)	$F_5$ (as 20T5)	$[2, 2]$ (GRH)
20.0.87354219101251702667236328125.1	x^20 - 4x^19 + 7x^18 - x^17 - 6x^16 - 119x^15 + 843x^14 - 3114x^13 + 8298x^12 - 17511x^11 + 30458x^10 - 45048x^9 + 57805x^8 - 64072x^7 + 59806x^6 - 45528x^5 + 27366x^4 - 12495x^3 + 4080x^2 - 850x + 85	\( 5^{15}\cdot 17^{15} \)	$F_5$ (as 20T5)	$[4]$
20.0.131153132009996266143798828125.1	x^20 - 2x^19 - 17x^18 + 48x^17 + 94x^16 - 402x^15 + 137x^14 + 1337x^13 - 2082x^12 - 23x^11 + 3747x^10 - 5361x^9 + 5490x^8 - 5271x^7 + 5114x^6 - 4061x^5 + 2436x^4 - 1100x^3 + 415x^2 - 125x + 25	\( 5^{15}\cdot 73^{10} \)	$F_5$ (as 20T5)	$[2]$ (GRH)
20.0.181102173953389804962158203125.1	x^20 - 3x^19 + 13x^18 - 18x^17 + 74x^16 - 63x^15 + 202x^14 + 3x^13 + 828x^12 - 357x^11 - 578x^10 - 2484x^9 - 1065x^8 - 789x^7 + 994x^6 + 1896x^5 + 2446x^4 + 2010x^3 + 700x^2 + 690x + 545	\( 3^{16}\cdot 5^{15}\cdot 13^{10} \)	$F_5$ (as 20T5)	$[2]$ (GRH)
20.0.198839676120293140411376953125.1	x^20 - 5x^19 + 10x^18 - 10x^17 + 30x^16 - 141x^15 + 340x^14 - 415x^13 + 220x^12 + 20x^11 - 99x^10 + 20x^9 + 220x^8 - 415x^7 + 340x^6 - 141x^5 + 30x^4 - 10x^3 + 10x^2 - 5x + 1	\( 3^{10}\cdot 5^{23}\cdot 7^{10} \)	$F_5$ (as 20T5)	$[2, 2]$ (GRH)
20.20.220683788281250000000000000000.1	x^20 - 10x^19 + 20x^18 + 105x^17 - 465x^16 + 48x^15 + 2450x^14 - 3200x^13 - 3700x^12 + 9850x^11 - 1396x^10 - 10230x^9 + 6315x^8 + 3270x^7 - 3620x^6 + 17x^5 + 680x^4 - 100x^3 - 40x^2 + 5x + 1	\( 2^{16}\cdot 5^{23}\cdot 7^{10} \)	$F_5$ (as 20T5)	Trivial (GRH)
20.0.220894941712131239715817914368.1	x^20 - 4x^19 + 14x^18 - 20x^17 + 63x^16 - 16x^15 + 220x^14 + 264x^13 + 1741x^12 + 1036x^11 + 6254x^10 + 11660x^9 + 22413x^8 + 29992x^7 + 50816x^6 + 74528x^5 + 80510x^4 + 81312x^3 + 52056x^2 + 25888x + 11576	\( 2^{55}\cdot 19^{10} \)	$F_5$ (as 20T5)	$[2]$ (GRH)
20.0.371458280474198465736072578229.1	x^20 - x^19 - 2x^18 - 11x^17 + 54x^16 - 28x^15 + 63x^14 - 158x^13 + 317x^12 - 264x^11 + 852x^10 - 323x^9 + 986x^8 - 413x^7 + 2414x^6 - 1452x^5 + 5813x^4 - 2026x^3 + 6579x^2 - 1020x + 2075	\( 3^{16}\cdot 29^{15} \)	$F_5$ (as 20T5)	Trivial (GRH)
20.0.755827200000000000000000000000.1	x^20 - 25x^16 + 60x^14 + 165x^12 - 270x^10 - 2680x^8 + 6120x^6 + 2080x^4 - 2400x^2 + 2880	\( 2^{30}\cdot 3^{10}\cdot 5^{23} \)	$F_5$ (as 20T5)	$[2, 2]$ (GRH)
20.0.841414466600402000000000000000.1	x^20 - 6x^19 + 15x^18 - 36x^17 + 115x^16 - 242x^15 + 466x^14 - 1176x^13 + 1851x^12 - 2716x^11 + 6539x^10 - 8834x^9 + 13461x^8 - 34154x^7 + 25816x^6 + 22302x^5 - 11105x^4 - 18754x^3 - 10375x^2 + 2366x + 18671	\( 2^{16}\cdot 5^{15}\cdot 29^{10} \)	$F_5$ (as 20T5)	$[2, 2]$ (GRH)
20.0.951590574034612536651611328125.1	x^20 - 2x^19 + 23x^18 - 52x^17 + 194x^16 - 482x^15 + 1027x^14 - 1983x^13 + 3618x^12 - 5173x^11 + 7077x^10 - 8941x^9 + 9730x^8 - 9101x^7 + 7784x^6 - 5241x^5 + 2746x^4 - 1190x^3 + 415x^2 - 75x + 25	\( 5^{15}\cdot 89^{10} \)	$F_5$ (as 20T5)	$[2, 2]$ (GRH)
20.0.1160968955369998535166956051501.1	x^20 - 16x^18 + 82x^16 + 13x^14 - 999x^12 + 308x^10 + 7923x^8 + 12402x^6 + 4714x^4 - 1313x^2 + 101	\( 101^{15} \)	$F_5$ (as 20T5)	Trivial (GRH)
20.0.1325648358836768000000000000000.1	x^20 - 10x^18 - 10x^17 + 11x^16 + 80x^15 + 290x^14 + 20x^13 - 1584x^12 - 3590x^11 + 5160x^10 + 15670x^9 + 1091x^8 - 43440x^7 - 32170x^6 + 77300x^5 + 49621x^4 - 55690x^3 - 36870x^2 - 17700x + 48220	\( 2^{20}\cdot 5^{15}\cdot 23^{10} \)	$F_5$ (as 20T5)	$[2, 2]$ (GRH)
20.0.1492547363720394483260280799232.1	x^20 - 8x^19 + 28x^18 - 80x^17 + 286x^16 - 896x^15 + 2080x^14 - 4136x^13 + 9133x^12 - 17560x^11 + 29132x^10 - 49080x^9 + 105208x^8 - 212512x^7 + 339544x^6 - 409424x^5 + 410364x^4 - 340128x^3 + 234400x^2 - 97920x + 18496	\( 2^{55}\cdot 23^{10} \)	$F_5$ (as 20T5)	$[2, 2]$ (GRH)
20.0.1701057228680302987747119277957.1	x^20 - 7x^19 + 29x^18 - 90x^17 + 210x^16 - 345x^15 + 260x^14 + 206x^13 - 62x^12 + 1599x^11 - 2242x^10 - 4550x^9 - 1200x^8 + 2598x^7 + 8307x^6 + 10639x^5 + 7581x^4 + 4455x^3 + 2700x^2 + 1215x + 243	\( 7^{16}\cdot 13^{15} \)	$F_5$ (as 20T5)	Trivial (GRH)
20.0.2648374236155086600616455078125.1	x^20 - 10x^19 + 50x^18 - 165x^17 + 386x^16 - 640x^15 + 880x^14 - 1590x^13 + 4691x^12 - 13170x^11 + 29250x^10 - 50875x^9 + 78876x^8 - 111880x^7 + 156405x^6 - 191825x^5 + 181936x^4 - 122455x^3 + 29985x^2 + 10150x + 43025	\( 3^{16}\cdot 5^{15}\cdot 17^{10} \)	$F_5$ (as 20T5)	$[2]$ (GRH)
20.0.3063157970528898000000000000000.1	x^20 - 10x^19 + 64x^18 - 291x^17 + 1069x^16 - 3248x^15 + 8514x^14 - 19384x^13 + 39326x^12 - 71194x^11 + 118256x^10 - 179424x^9 + 256621x^8 - 336594x^7 + 417836x^6 - 458653x^5 + 468466x^4 - 389860x^3 + 311630x^2 - 163125x + 96595	\( 2^{16}\cdot 3^{10}\cdot 5^{15}\cdot 11^{10} \)	$F_5$ (as 20T5)	$[2, 2, 2]$ (GRH)
20.0.3256311210466946358286064453125.1	x^20 - 9x^19 + 51x^18 - 231x^17 + 833x^16 - 2458x^15 + 5989x^14 - 11695x^13 + 20202x^12 - 33492x^11 + 57953x^10 - 92370x^9 + 130181x^8 - 163476x^7 + 201934x^6 - 235037x^5 + 238937x^4 - 173528x^3 + 91296x^2 - 30696x + 10256	\( 5^{10}\cdot 37^{15} \)	$F_5$ (as 20T5)	$[2]$ (GRH)
20.0.3530940612500000000000000000000.1	x^20 + 15x^18 + 75x^16 + 30x^14 - 385x^12 + 815x^10 + 1745x^8 - 2980x^6 + 5420x^4 - 8400x^2 + 3920	\( 2^{20}\cdot 5^{23}\cdot 7^{10} \)	$F_5$ (as 20T5)	$[2, 2]$ (GRH)