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 90)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.4099733414648735703133184.1	x^20 + 7x^18 + 24x^16 + 60x^14 + 108x^12 + 142x^10 + 143x^8 + 99x^6 + 44x^4 + 22x^2 + 11	\( 2^{10}\cdot 11^{17}\cdot 89^{2} \)	20T427	Trivial
20.4.4099733414648735703133184.1	x^20 - 7x^18 + 24x^16 - 60x^14 + 108x^12 - 142x^10 + 143x^8 - 99x^6 + 44x^4 - 22x^2 + 11	\( 2^{10}\cdot 11^{17}\cdot 89^{2} \)	20T427	Trivial (GRH)
20.0.1296992408370244370961837056.1	x^20 + 5x^18 + 21x^16 + 21x^14 + 49x^12 - 54x^10 + 121x^8 - 99x^6 + 99x^4 - 44x^2 + 11	\( 2^{10}\cdot 11^{17}\cdot 1583^{2} \)	20T427	Trivial (GRH)
20.0.1296992408370244370961837056.2	x^20 - 5x^18 + 21x^16 - 21x^14 + 49x^12 + 54x^10 + 121x^8 + 99x^6 + 99x^4 + 44x^2 + 11	\( 2^{10}\cdot 11^{17}\cdot 1583^{2} \)	20T427	Trivial (GRH)
20.0.4198127016600305360008380416.1	x^20 - x^18 - 4x^16 + 14x^14 + 3x^12 - 23x^10 + 11x^8 + 44x^6 + 11x^4 + 11	\( 2^{20}\cdot 11^{17}\cdot 89^{2} \)	20T427	Trivial (GRH)
20.4.4198127016600305360008380416.1	x^20 + x^18 - 4x^16 - 14x^14 + 3x^12 + 23x^10 + 11x^8 - 44x^6 + 11x^4 + 11	\( 2^{20}\cdot 11^{17}\cdot 89^{2} \)	20T427	Trivial (GRH)
20.10.9297543283501805026208859136.1	x^20 - 10x^18 + 17x^16 + 49x^14 - 80x^12 - 119x^10 + 60x^8 + 97x^6 + 15x^4 - 6x^2 - 1	\( -\,2^{10}\cdot 11^{16}\cdot 14057^{2} \)	20T427	Trivial (GRH)
20.8.15583578925526925703866482688.1	x^20 - 2x^19 + 3x^18 + 18x^17 - 6x^16 + 82x^15 + 106x^14 - 52x^13 + 262x^12 + 144x^11 - 286x^10 - 76x^9 - 1069x^8 - 2428x^7 - 2809x^6 - 1898x^5 + 1226x^4 + 3274x^3 + 2214x^2 + 636x + 67	\( 2^{20}\cdot 3^{5}\cdot 11^{19} \)	20T427	Trivial (GRH)
20.0.15583578925526925703866482688.2	x^20 - 2x^19 + 3x^18 - 4x^17 + 5x^16 - 6x^15 - 15x^14 + 80x^13 - 13x^12 - 296x^11 - 55x^10 + 408x^9 + 207x^8 - 162x^7 + 1041x^6 + 1490x^5 - 721x^4 - 1104x^3 + 4997x^2 - 4050x + 2047	\( 2^{20}\cdot 3^{5}\cdot 11^{19} \)	20T427	$[2]$ (GRH)
20.8.15583578925526925703866482688.2	x^20 - 2x^19 - 8x^18 + 18x^17 + 49x^16 - 116x^15 - 334x^14 + 278x^13 + 1197x^12 + 342x^11 - 1276x^10 - 868x^9 + 658x^8 + 564x^7 - 488x^6 - 226x^5 + 247x^4 + 18x^3 - 30x^2 - 2x + 1	\( 2^{20}\cdot 3^{5}\cdot 11^{19} \)	20T427	Trivial (GRH)
20.0.15583578925526925703866482688.3	x^20 - 8x^19 + 26x^18 - 36x^17 + 15x^16 - 72x^15 + 435x^14 - 1074x^13 + 1720x^12 - 2450x^11 + 3553x^10 - 4660x^9 + 5094x^8 - 5176x^7 + 5675x^6 - 5858x^5 + 4409x^4 - 1956x^3 + 346x^2 + 38x + 1	\( 2^{20}\cdot 3^{5}\cdot 11^{19} \)	20T427	$[2]$ (GRH)
20.8.15583578925526925703866482688.3	x^20 - 8x^19 + 26x^18 - 36x^17 + 4x^16 + 38x^15 + 6x^14 - 172x^13 + 246x^12 + 234x^11 - 924x^10 + 840x^9 - 241x^8 - 798x^7 + 1099x^6 - 534x^5 + 218x^4 + 112x^3 - 193x^2 + 38x + 1	\( 2^{20}\cdot 3^{5}\cdot 11^{19} \)	20T427	Trivial (GRH)
20.8.15583578925526925703866482688.4	x^20 - 10x^19 + 42x^18 - 82x^17 - 32x^16 + 698x^15 - 2330x^14 + 4750x^13 - 6674x^12 + 6048x^11 - 1353x^10 - 6804x^9 + 15328x^8 - 20492x^7 + 20369x^6 - 15956x^5 + 10123x^4 - 5226x^3 + 2080x^2 - 546x + 67	\( 2^{20}\cdot 3^{5}\cdot 11^{19} \)	20T427	Trivial (GRH)
20.0.32473988377432635504517950464.1	x^20 - 7x^19 + 19x^18 - 26x^17 + 38x^16 - 119x^15 + 279x^14 - 503x^13 + 1101x^12 - 2131x^11 + 2762x^10 - 3047x^9 + 4289x^8 - 4711x^7 + 3842x^6 - 4727x^5 + 4805x^4 - 3077x^3 + 2687x^2 - 2421x + 989	\( 2^{10}\cdot 11^{17}\cdot 89^{4} \)	20T427	$[2]$ (GRH)
20.0.32473988377432635504517950464.2	x^20 - x^18 - 5x^17 + 14x^16 + 59x^15 + 58x^14 - 159x^13 - 361x^12 + 718x^11 + 1827x^10 - 1925x^9 - 3731x^8 + 4260x^7 + 6050x^6 - 4139x^5 - 8191x^4 + 6864x^3 + 5820x^2 - 8017x + 3761	\( 2^{10}\cdot 11^{17}\cdot 89^{4} \)	20T427	$[2]$ (GRH)
20.4.32473988377432635504517950464.2	x^20 - 5x^19 - 6x^18 + 56x^17 + 24x^16 - 360x^15 + 10x^14 + 1201x^13 + 270x^12 - 3420x^11 - 1079x^10 + 7462x^9 + 1339x^8 - 10080x^7 - 3468x^6 + 14292x^5 - 1455x^4 - 8443x^3 + 1761x^2 + 3362x - 1451	\( 2^{10}\cdot 11^{17}\cdot 89^{4} \)	20T427	Trivial (GRH)
20.0.32473988377432635504517950464.3	x^20 - 3x^19 + 15x^17 - 23x^16 - 39x^15 + 278x^14 - 164x^13 - 842x^12 + 480x^11 + 1737x^10 - 584x^9 + 1775x^8 - 6244x^7 - 2167x^6 + 3978x^5 + 13836x^4 - 5691x^3 - 6236x^2 + 1453x + 7019	\( 2^{10}\cdot 11^{17}\cdot 89^{4} \)	20T427	$[2]$ (GRH)
20.4.32473988377432635504517950464.3	x^20 - x^19 - 9x^18 + 11x^17 - x^16 + 21x^15 - 29x^14 - 79x^13 - 124x^12 + 760x^11 - 550x^10 + 1099x^9 - 3277x^8 + 1637x^7 + 2365x^6 - 1220x^5 - 1660x^4 + 194x^3 + 662x^2 + 278x + 43	\( 2^{10}\cdot 11^{17}\cdot 89^{4} \)	20T427	Trivial (GRH)
20.0.32473988377432635504517950464.4	x^20 - 6x^19 + 10x^18 + 23x^17 - 68x^16 - 102x^15 + 694x^14 - 1307x^13 + 1462x^12 - 1657x^11 + 1673x^10 - 198x^9 - 1072x^8 + 464x^7 - 503x^6 + 1441x^5 - 428x^4 - 1032x^3 + 872x^2 - 256x + 32	\( 2^{10}\cdot 11^{17}\cdot 89^{4} \)	20T427	$[2]$ (GRH)
20.4.32473988377432635504517950464.4	x^20 - 5x^19 + 4x^18 + 43x^17 - 127x^16 + 12x^15 + 376x^14 - 348x^13 - 353x^12 + 618x^11 - 307x^10 - 253x^9 + 1051x^8 - 586x^7 - 1010x^6 + 315x^5 - 528x^4 + 153x^3 + 1163x^2 - 339x - 617	\( 2^{10}\cdot 11^{17}\cdot 89^{4} \)	20T427	Trivial (GRH)
20.4.32473988377432635504517950464.5	x^20 - 6x^19 + 7x^18 + 34x^17 - 75x^16 - 170x^15 + 474x^14 + 405x^13 - 1558x^12 - 795x^11 + 3455x^10 + 517x^9 - 4065x^8 - 324x^7 + 1497x^6 + 1788x^5 + 4605x^4 + 776x^3 - 5247x^2 - 4199x - 947	\( 2^{10}\cdot 11^{17}\cdot 89^{4} \)	20T427	Trivial (GRH)
20.0.58966631474860149560041954113.1	x^20 - 6x^19 + 21x^18 - 56x^17 + 126x^16 - 252x^15 + 429x^14 - 671x^13 + 1012x^12 - 1441x^11 + 1837x^10 - 2024x^9 + 2266x^8 - 2409x^7 + 2453x^6 - 1947x^5 + 1452x^4 - 968x^3 + 726x^2 - 363x + 121	\( 3^{5}\cdot 11^{17}\cdot 21911^{2} \)	20T427	Trivial (GRH)
20.0.154181708612560135336755200000.1	x^20 - 8x^19 + 28x^18 - 68x^17 + 170x^16 - 454x^15 + 1146x^14 - 2830x^13 + 6881x^12 - 15568x^11 + 31984x^10 - 58918x^9 + 96846x^8 - 143610x^7 + 189640x^6 - 213758x^5 + 197354x^4 - 143246x^3 + 77376x^2 - 28442x + 5543	\( 2^{30}\cdot 5^{5}\cdot 11^{16} \)	20T427	Trivial (GRH)
20.12.154181708612560135336755200000.1	x^20 - 4x^19 - 10x^18 + 66x^17 - 73x^16 - 144x^15 + 628x^14 - 1046x^13 + 1073x^12 - 1234x^11 - 106x^10 + 3264x^9 - 2159x^8 - 2136x^7 + 1884x^6 + 826x^5 - 534x^4 - 198x^3 + 20x^2 + 12x + 1	\( 2^{30}\cdot 5^{5}\cdot 11^{16} \)	20T427	Trivial (GRH)
20.16.154181708612560135336755200000.1	x^20 - 6x^19 - 8x^18 + 124x^17 - 201x^16 - 544x^15 + 2204x^14 - 1782x^13 - 3551x^12 + 8740x^11 - 5372x^10 - 3014x^9 + 5340x^8 - 2100x^7 + 654x^6 - 952x^5 + 505x^4 + 6x^3 - 46x^2 + 2x + 1	\( 2^{30}\cdot 5^{5}\cdot 11^{16} \)	20T427	Trivial (GRH)
20.8.154181708612560135336755200000.1	x^20 - 8x^19 + 28x^18 - 38x^17 - 59x^16 + 288x^15 - 216x^14 - 692x^13 + 1105x^12 + 1352x^11 - 3784x^10 - 430x^9 + 6057x^8 - 2062x^7 - 2114x^6 + 2022x^5 - 906x^4 + 72x^3 + 64x^2 - 20x + 1	\( 2^{30}\cdot 5^{5}\cdot 11^{16} \)	20T427	Trivial (GRH)
20.0.154181708612560135336755200000.2	x^20 - 6x^19 + 16x^18 - 30x^17 + 84x^16 - 248x^15 + 550x^14 - 1042x^13 + 2181x^12 - 5552x^11 + 15096x^10 - 35740x^9 + 67159x^8 - 99940x^7 + 122804x^6 - 130498x^5 + 120027x^4 - 89852x^3 + 49864x^2 - 18066x + 3323	\( 2^{30}\cdot 5^{5}\cdot 11^{16} \)	20T427	$[3]$ (GRH)
20.12.154181708612560135336755200000.2	x^20 - 4x^19 - 8x^18 + 70x^17 - 55x^16 - 454x^15 + 754x^14 + 1436x^13 - 2779x^12 - 3230x^11 + 5104x^10 + 8016x^9 - 9163x^8 - 13214x^7 + 14254x^6 + 5846x^5 - 6956x^4 - 742x^3 + 1192x^2 + 22x - 67	\( 2^{30}\cdot 5^{5}\cdot 11^{16} \)	20T427	Trivial (GRH)
20.8.154181708612560135336755200000.2	x^20 - 8x^19 + 20x^18 - 6x^17 - 50x^16 + 98x^15 - 20x^14 - 414x^13 + 490x^12 + 790x^11 - 620x^10 - 398x^9 - 2493x^8 + 852x^7 + 5348x^6 - 1018x^5 - 4024x^4 + 70x^3 + 1424x^2 + 88x - 131	\( 2^{30}\cdot 5^{5}\cdot 11^{16} \)	20T427	Trivial (GRH)
20.0.154181708612560135336755200000.3	x^20 - 2x^19 + 8x^18 - 20x^17 + 8x^16 - 88x^15 + 272x^14 - 64x^13 + 245x^12 - 1372x^11 + 716x^10 - 462x^9 + 3897x^8 - 3600x^7 + 362x^6 - 1132x^5 + 1653x^4 + 26x^3 - 440x^2 + 16x + 43	\( 2^{30}\cdot 5^{5}\cdot 11^{16} \)	20T427	Trivial (GRH)
20.4.154181708612560135336755200000.3	x^20 - 2x^19 - 12x^18 + 12x^17 + 92x^16 - 6x^15 - 468x^14 - 194x^13 + 1693x^12 + 1782x^11 - 3102x^10 - 5664x^9 + 2494x^8 + 11046x^7 + 3238x^6 - 15552x^5 - 25134x^4 - 19342x^3 - 8624x^2 - 2166x - 241	\( 2^{30}\cdot 5^{5}\cdot 11^{16} \)	20T427	Trivial (GRH)
20.8.154181708612560135336755200000.3	x^20 - 2x^19 - 12x^18 - 6x^17 + 10x^16 + 26x^15 - 58x^14 - 98x^13 + 211x^12 + 174x^11 + 44x^10 - 446x^9 - 173x^8 + 682x^7 - 674x^6 + 284x^5 + 125x^4 - 100x^3 + 32x^2 - 18x - 1	\( 2^{30}\cdot 5^{5}\cdot 11^{16} \)	20T427	Trivial (GRH)
20.0.154181708612560135336755200000.4	x^20 + 22x^18 + 221x^16 + 1386x^14 + 6200x^12 + 20592x^10 + 49255x^8 + 79750x^6 + 80875x^4 + 41250x^2 + 3125	\( 2^{30}\cdot 5^{5}\cdot 11^{16} \)	20T427	Trivial (GRH)
20.4.154181708612560135336755200000.4	x^20 - 4x^19 + 2x^18 + 16x^17 - 16x^16 - 130x^15 + 454x^14 - 732x^13 - 81x^12 + 2480x^11 - 2358x^10 - 3230x^9 + 5119x^8 + 328x^7 - 2098x^6 + 660x^5 - 219x^4 + 250x^3 - 110x^2 + 22x - 1	\( 2^{30}\cdot 5^{5}\cdot 11^{16} \)	20T427	Trivial (GRH)
20.8.154181708612560135336755200000.4	x^20 - 8x^19 + 18x^18 - 4x^17 - 20x^16 + 44x^15 - 56x^14 - 34x^13 - 61x^12 - 156x^11 - 186x^10 - 682x^9 - 997x^8 - 786x^7 - 740x^6 - 142x^5 + 529x^4 + 350x^3 - 66x^2 - 40x - 1	\( 2^{30}\cdot 5^{5}\cdot 11^{16} \)	20T427	Trivial (GRH)
20.4.154181708612560135336755200000.5	x^20 - 10x^19 + 58x^18 - 226x^17 + 615x^16 - 1280x^15 + 2264x^14 - 3634x^13 + 5392x^12 - 6980x^11 + 6846x^10 - 3788x^9 - 939x^8 + 4340x^7 - 5366x^6 + 4758x^5 - 3223x^4 + 1602x^3 - 588x^2 + 158x - 23	\( 2^{30}\cdot 5^{5}\cdot 11^{16} \)	20T427	Trivial (GRH)
20.8.154181708612560135336755200000.5	x^20 - 4x^19 - 10x^18 + 62x^17 - 49x^16 - 38x^15 - 132x^14 - 82x^13 + 1401x^12 - 1288x^11 + 488x^10 - 3638x^9 + 4139x^8 + 1752x^7 - 3564x^6 + 1622x^5 - 70x^4 - 1592x^3 + 390x^2 + 566x + 89	\( 2^{30}\cdot 5^{5}\cdot 11^{16} \)	20T427	Trivial (GRH)
20.4.154181708612560135336755200000.6	x^20 - 6x^19 + 18x^18 - 44x^17 + 75x^16 - 112x^15 + 220x^14 - 304x^13 - 119x^12 + 2394x^11 - 5808x^10 + 9012x^9 - 12376x^8 + 11000x^7 - 16072x^6 + 18682x^5 - 19333x^4 + 16048x^3 - 5168x^2 - 922x + 593	\( 2^{30}\cdot 5^{5}\cdot 11^{16} \)	20T427	Trivial (GRH)
20.8.154181708612560135336755200000.6	x^20 - 8x^19 + 16x^18 + 58x^17 - 370x^16 + 640x^15 + 528x^14 - 3956x^13 + 5301x^12 + 2988x^11 - 16592x^10 + 16168x^9 + 1893x^8 - 11998x^7 + 2722x^6 + 4620x^5 - 293x^4 - 2588x^3 + 426x^2 + 642x - 199	\( 2^{30}\cdot 5^{5}\cdot 11^{16} \)	20T427	Trivial (GRH)
20.4.154181708612560135336755200000.7	x^20 - 4x^19 + 10x^18 - 26x^17 + 77x^16 - 158x^15 + 210x^14 - 354x^13 + 877x^12 - 1066x^11 - 1148x^10 + 6284x^9 - 12611x^8 + 24762x^7 - 53038x^6 + 81924x^5 - 74932x^4 + 38244x^3 - 10818x^2 + 2008x - 241	\( 2^{30}\cdot 5^{5}\cdot 11^{16} \)	20T427	Trivial (GRH)
20.4.154181708612560135336755200000.8	x^20 - 6x^19 + 58x^17 - 66x^16 - 156x^15 + 154x^14 - 46x^13 + 743x^12 + 862x^11 - 2974x^10 - 2834x^9 + 566x^8 - 602x^7 - 2256x^6 + 834x^5 - 770x^4 - 1388x^3 + 994x^2 + 1936x - 571	\( 2^{30}\cdot 5^{5}\cdot 11^{16} \)	20T427	Trivial (GRH)
20.4.154181708612560135336755200000.9	x^20 - 4x^19 + 14x^18 - 46x^17 + 180x^16 - 618x^15 + 1328x^14 - 1394x^13 - 1026x^12 + 5804x^11 - 7998x^10 + 2298x^9 + 7589x^8 - 8836x^7 + 542x^6 + 1968x^5 + 2174x^4 - 1134x^3 - 990x^2 + 302x + 199	\( 2^{30}\cdot 5^{5}\cdot 11^{16} \)	20T427	Trivial (GRH)
20.4.154181708612560135336755200000.10	x^20 - 2x^19 + 4x^18 - 44x^17 + 64x^16 + 90x^15 - 46x^14 - 518x^13 + 527x^12 + 162x^11 + 44x^10 - 412x^9 + 116x^8 - 690x^7 + 814x^6 + 484x^5 - 560x^4 - 122x^3 + 104x^2 + 50x - 23	\( 2^{30}\cdot 5^{5}\cdot 11^{16} \)	20T427	Trivial (GRH)
20.4.154181708612560135336755200000.11	x^20 - 4x^19 + 4x^18 - 2x^17 - 21x^16 + 40x^15 - 142x^14 + 40x^13 + 68x^12 - 1016x^11 + 1998x^10 - 4996x^9 + 7261x^8 - 11594x^7 + 12906x^6 - 15220x^5 + 12925x^4 - 9614x^3 + 4786x^2 - 456x - 131	\( 2^{30}\cdot 5^{5}\cdot 11^{16} \)	20T427	Trivial (GRH)
20.4.154181708612560135336755200000.12	x^20 - 4x^19 + 4x^18 - 20x^17 + 89x^16 - 120x^15 + 184x^14 - 618x^13 + 1203x^12 - 1716x^11 + 2036x^10 - 6204x^9 + 9861x^8 - 2720x^7 + 20646x^6 - 24794x^5 - 1254x^4 - 33150x^3 + 11828x^2 - 5954x + 1541	\( 2^{30}\cdot 5^{5}\cdot 11^{16} \)	20T427	Trivial (GRH)
20.10.197120048377878430584468291779.1	x^20 - 3x^19 - 8x^18 + 13x^17 + 19x^16 - 15x^15 - 30x^14 + 13x^13 + 42x^12 - 11x^11 - 43x^10 - 11x^9 + 42x^8 + 13x^7 - 30x^6 - 15x^5 + 19x^4 + 13x^3 - 8x^2 - 3x + 1	\( -\,11^{17}\cdot 727^{2}\cdot 859^{2} \)	20T427	Trivial (GRH)
20.0.411365037663364424760694931456.1	x^20 + 12x^18 + 62x^16 + 184x^14 + 355x^12 + 485x^10 + 517x^8 + 462x^6 + 308x^4 + 110x^2 + 11	\( 2^{20}\cdot 11^{17}\cdot 881^{2} \)	20T427	$[2]$ (GRH)
20.12.411365037663364424760694931456.1	x^20 - 12x^18 + 62x^16 - 184x^14 + 355x^12 - 485x^10 + 517x^8 - 462x^6 + 308x^4 - 110x^2 + 11	\( 2^{20}\cdot 11^{17}\cdot 881^{2} \)	20T427	Trivial (GRH)
20.0.542178436518981590310346293248.1	x^20 + 8x^18 + 29x^16 + 68x^14 + 122x^12 + 185x^10 + 244x^8 + 272x^6 + 232x^4 + 128x^2 + 32	\( 2^{25}\cdot 11^{16}\cdot 593^{2} \)	20T427	Trivial (GRH)
20.4.542178436518981590310346293248.1	x^20 - 8x^18 + 29x^16 - 68x^14 + 122x^12 - 185x^10 + 244x^8 - 272x^6 + 232x^4 - 128x^2 + 32	\( 2^{25}\cdot 11^{16}\cdot 593^{2} \)	20T427	Trivial (GRH)