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 48 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.17767904907458357085184.1	x^20 - x^18 + 5x^16 - 8x^14 + 7x^12 - 9x^10 + 2x^8 + 13x^6 - 12x^4 + 2x^2 + 1	\( 2^{10}\cdot 1609^{6} \)	20T676	Trivial (GRH)
20.0.17767904907458357085184.2	x^20 - 3x^18 + 3x^16 - 5x^14 + 4x^12 + x^10 + x^8 + 10x^6 - x^4 + 7x^2 + 1	\( 2^{10}\cdot 1609^{6} \)	20T676	Trivial (GRH)
20.4.366845534422351504000000.1	x^20 + 9x^18 + 35x^16 + 78x^14 + 109x^12 + 93x^10 + 38x^8 - 5x^6 - 10x^4 - 2x^2 + 1	\( 2^{10}\cdot 5^{6}\cdot 13^{6}\cdot 41^{6} \)	20T676	Trivial (GRH)
20.4.889625875939928445912064.1	x^20 - 2x^18 - 5x^16 + 13x^14 + 8x^12 - 61x^10 + 98x^8 - 75x^6 + 43x^4 - 12x^2 + 1	\( 2^{10}\cdot 3089^{6} \)	20T676	Trivial (GRH)
20.4.5420872721372370875974656.1	x^20 - 10x^16 + 12x^14 + 7x^12 - 9x^10 + 43x^8 + 36x^6 - 16x^4 - 12x^2 + 1	\( 2^{10}\cdot 3^{16}\cdot 223^{6} \)	20T676	Trivial (GRH)
20.4.5420872721372370875974656.2	x^20 + 4x^18 - 15x^14 - 6x^12 + 33x^10 + 33x^8 - 21x^4 - 5x^2 + 1	\( 2^{10}\cdot 3^{16}\cdot 223^{6} \)	20T676	Trivial (GRH)
20.4.8628532102283831192126464.1	x^20 - 2x^18 - 10x^16 + 36x^14 - 69x^12 - 16x^10 + 76x^8 - 46x^6 + 18x^4 - 2x^2 + 1	\( 2^{10}\cdot 13^{6}\cdot 347^{6} \)	20T676	Trivial (GRH)
20.4.8628532102283831192126464.2	x^20 + x^18 + 3x^16 - 10x^14 - 47x^12 - 107x^10 - 166x^8 - 145x^6 - 58x^4 - 6x^2 + 1	\( 2^{10}\cdot 13^{6}\cdot 347^{6} \)	20T676	Trivial (GRH)
20.0.1455584035932861642867736576.2	x^20 - 7x^18 + 27x^16 - 54x^14 + 61x^12 + 5x^10 - 62x^8 + 66x^6 + 97x^4 + 35x^2 + 4	\( 2^{18}\cdot 19^{8}\cdot 83^{6} \)	20T676	Trivial (GRH)
20.8.1455584035932861642867736576.2	x^20 - 7x^18 + 17x^16 + 3x^14 - 75x^12 + 48x^10 + 77x^8 - 64x^6 + 8x^4 - x^2 + 1	\( 2^{18}\cdot 19^{8}\cdot 83^{6} \)	20T676	Trivial (GRH)
20.0.1455584035932861642867736576.3	x^20 + 2x^18 - 12x^16 - 32x^14 + 26x^12 + 165x^10 + 202x^8 + 79x^6 - 13x^4 - 7x^2 + 1	\( 2^{18}\cdot 19^{8}\cdot 83^{6} \)	20T676	Trivial (GRH)
20.8.1458221925285967471469372416.1	x^20 - 4x^19 - x^18 + 22x^17 - 16x^16 - 46x^15 + 44x^14 + 131x^13 - 303x^12 - 93x^11 + 979x^10 - 202x^9 - 1634x^8 - 409x^7 + 3628x^6 - 1387x^5 - 1539x^4 + 145x^3 + 1004x^2 - 224x - 97	\( 2^{10}\cdot 13^{8}\cdot 347^{6} \)	20T676	Trivial (GRH)
20.12.206548481879697235603429344256.1	x^20 - 9x^18 + 9x^16 + 82x^14 - 121x^12 - 227x^10 + 250x^8 + 107x^6 - 29x^4 - 5x^2 + 1	\( 2^{10}\cdot 61^{6}\cdot 397^{6} \)	20T676	Trivial (GRH)
20.16.206548481879697235603429344256.1	x^20 - 9x^18 + 9x^16 + 122x^14 - 437x^12 + 515x^10 - 80x^8 - 271x^6 + 182x^4 - 34x^2 + 1	\( 2^{10}\cdot 61^{6}\cdot 397^{6} \)	20T676	Trivial (GRH)
20.4.206548481879697235603429344256.1	x^20 - 5x^19 + 10x^18 - 23x^17 + 111x^16 - 312x^15 + 476x^14 - 660x^13 + 1296x^12 - 1948x^11 + 1832x^10 - 1941x^9 + 2587x^8 - 2149x^7 + 1162x^6 - 921x^5 + 649x^4 - 187x^3 + 38x^2 - 16x + 1	\( 2^{10}\cdot 61^{6}\cdot 397^{6} \)	20T676	$[2]$ (GRH)
20.8.206548481879697235603429344256.1	x^20 + 5x^18 - 31x^16 - 154x^14 + 167x^12 + 1275x^10 + 586x^8 - 2787x^6 - 3547x^4 - 1187x^2 + 1	\( 2^{10}\cdot 61^{6}\cdot 397^{6} \)	20T676	Trivial (GRH)
20.12.206548481879697235603429344256.2	x^20 + x^18 - 52x^16 - 80x^14 + 591x^12 + 985x^10 - 849x^8 - 1022x^6 + 641x^4 - 68x^2 + 1	\( 2^{10}\cdot 61^{6}\cdot 397^{6} \)	20T676	Trivial (GRH)
20.16.206548481879697235603429344256.2	x^20 - 14x^18 + 68x^16 - 115x^14 - 75x^12 + 464x^10 - 466x^8 + 80x^6 + 66x^4 - 21x^2 + 1	\( 2^{10}\cdot 61^{6}\cdot 397^{6} \)	20T676	Trivial (GRH)
20.4.206548481879697235603429344256.2	x^20 + 4x^18 - 39x^16 - 335x^14 - 1048x^12 - 1675x^10 - 1422x^8 - 585x^6 - 79x^4 + 6x^2 + 1	\( 2^{10}\cdot 61^{6}\cdot 397^{6} \)	20T676	$[2]$ (GRH)
20.8.206548481879697235603429344256.2	x^20 - 6x^18 - 22x^16 + 134x^14 + 71x^12 - 551x^10 - 177x^8 + 192x^6 + 106x^4 + 18x^2 + 1	\( 2^{10}\cdot 61^{6}\cdot 397^{6} \)	20T676	Trivial (GRH)
20.12.206548481879697235603429344256.3	x^20 - 8x^18 - 24x^16 + 109x^14 + 249x^12 - 226x^10 - 432x^8 + 230x^6 + 140x^4 - 39x^2 + 1	\( 2^{10}\cdot 61^{6}\cdot 397^{6} \)	20T676	Trivial (GRH)
20.16.206548481879697235603429344256.3	x^20 - x^18 - 52x^16 + 204x^14 - 219x^12 - 125x^10 + 439x^8 - 362x^6 + 135x^4 - 22x^2 + 1	\( 2^{10}\cdot 61^{6}\cdot 397^{6} \)	20T676	Trivial (GRH)
20.8.206548481879697235603429344256.3	x^20 + 12x^18 + 19x^16 - 180x^14 - 419x^12 + 594x^10 + 1134x^8 + 230x^6 - 71x^4 - 8x^2 + 1	\( 2^{10}\cdot 61^{6}\cdot 397^{6} \)	20T676	$[2]$ (GRH)
20.8.206548481879697235603429344256.4	x^20 + 13x^18 + 14x^16 - 193x^14 - 239x^12 + 485x^10 + 463x^8 - 245x^6 - 90x^4 + 23x^2 + 1	\( 2^{10}\cdot 61^{6}\cdot 397^{6} \)	20T676	$[2]$ (GRH)
20.8.206548481879697235603429344256.5	x^20 + 3x^18 - 22x^16 - 83x^14 + 48x^12 + 444x^10 + 432x^8 - 18x^6 - 116x^4 - 19x^2 + 1	\( 2^{10}\cdot 61^{6}\cdot 397^{6} \)	20T676	Trivial (GRH)
20.8.750553614330423255547227138649.1	x^20 - 2x^19 - x^18 + 4x^17 - 27x^16 + 10x^15 + 98x^14 - 70x^13 - 164x^12 + 412x^11 + 465x^10 - 1087x^9 - 1065x^8 + 1358x^7 + 1104x^6 - 1703x^5 - 1215x^4 + 2238x^3 + 1453x^2 - 1075x - 661	\( 61^{8}\cdot 397^{6} \)	20T676	Trivial (GRH)
20.12.750553614330423255547227138649.3	x^20 - 4x^19 - 11x^18 + 51x^17 + 7x^16 - 53x^15 - 248x^14 - 63x^13 + 1303x^12 - 898x^11 + 126x^10 - 2220x^9 + 1483x^8 + 4033x^7 - 4627x^6 + 283x^5 + 974x^4 - 69x^3 - 68x^2 + 1	\( 61^{8}\cdot 397^{6} \)	20T676	Trivial (GRH)
20.4.750553614330423255547227138649.3	x^20 - 9x^19 + 37x^18 - 119x^17 + 252x^16 - 449x^15 + 593x^14 - 577x^13 + 340x^12 - 43x^11 - 207x^10 - 125x^9 + 977x^8 - 1404x^7 + 1668x^6 - 1314x^5 + 287x^4 + 205x^3 - 67x^2 + 1	\( 61^{8}\cdot 397^{6} \)	20T676	$[2]$ (GRH)
20.12.750553614330423255547227138649.4	x^20 - 5x^19 + 15x^18 - 18x^17 - 59x^16 + 263x^15 - 433x^14 - 263x^13 + 2342x^12 - 1807x^11 - 3860x^10 + 4702x^9 + 2515x^8 - 3695x^7 - 737x^6 + 432x^5 + 292x^4 + 378x^3 - x^2 - 14x - 1	\( 61^{8}\cdot 397^{6} \)	20T676	Trivial (GRH)
20.4.750553614330423255547227138649.4	x^20 - 2x^19 - 2x^18 + 11x^17 + 2x^16 - 76x^15 + 30x^14 + 220x^13 - 233x^12 - 923x^11 + 1233x^10 + 2307x^9 - 1730x^8 - 2707x^7 + 3776x^6 + 3030x^5 - 7257x^4 + 2070x^3 + 4265x^2 + 3398x - 12757	\( 61^{8}\cdot 397^{6} \)	20T676	Trivial (GRH)
20.12.2420153776720347042437666538496.1	x^20 + 12x^18 + 7x^16 - 220x^14 - 227x^12 + 1423x^10 + 573x^8 - 3536x^6 + 2030x^4 - 401x^2 + 25	\( 2^{10}\cdot 36497^{6} \)	20T676	Trivial (GRH)
20.16.2420153776720347042437666538496.1	x^20 - 12x^18 + 28x^16 + 86x^14 - 361x^12 + 101x^10 + 893x^8 - 1130x^6 + 416x^4 - 48x^2 + 1	\( 2^{10}\cdot 36497^{6} \)	20T676	Trivial (GRH)
20.8.2420153776720347042437666538496.1	x^20 + 17x^18 + 95x^16 + 144x^14 - 343x^12 - 911x^10 + 342x^8 + 1106x^6 - 312x^4 - 196x^2 + 25	\( 2^{10}\cdot 36497^{6} \)	20T676	Trivial (GRH)
20.12.2420153776720347042437666538496.2	x^20 - 7x^18 - 8x^16 + 152x^14 - 206x^12 - 692x^10 + 1362x^8 + 993x^6 - 1930x^4 - 895x^2 + 49	\( 2^{10}\cdot 36497^{6} \)	20T676	Trivial (GRH)
20.8.2420153776720347042437666538496.2	x^20 - 7x^18 - 7x^16 + 99x^14 + 32x^12 - 461x^10 - 279x^8 + 596x^6 + 679x^4 + 231x^2 + 25	\( 2^{10}\cdot 36497^{6} \)	20T676	$[2]$ (GRH)
20.8.2420153776720347042437666538496.3	x^20 - 7x^18 - 20x^16 + 102x^14 + 165x^12 - 269x^10 - 407x^8 + 104x^6 + 219x^4 + 30x^2 + 1	\( 2^{10}\cdot 36497^{6} \)	20T676	Trivial (GRH)
20.12.3370778611471959737030176850944.1	x^20 - 5x^19 - 2x^18 + 39x^17 + 14x^16 - 194x^15 - 172x^14 + 977x^13 - 189x^12 - 1536x^11 + 1083x^10 + 327x^9 - 615x^8 + 579x^7 - 316x^6 - 135x^5 + 220x^4 - 22x^3 - 36x^2 + 1	\( 2^{10}\cdot 38569^{6} \)	20T676	Trivial (GRH)
20.8.3370778611471959737030176850944.1	x^20 - 5x^18 - 22x^16 + 106x^14 + 203x^12 - 687x^10 - 1173x^8 + 1200x^6 + 3053x^4 + 1738x^2 + 289	\( 2^{10}\cdot 38569^{6} \)	20T676	$[2]$ (GRH)
20.12.211505645444809969257911648518144.5	x^20 - x^18 - 57x^16 - 32x^14 + 529x^12 + 199x^10 - 1134x^8 + 207x^6 + 230x^4 - 64x^2 + 1	\( 2^{20}\cdot 61^{6}\cdot 397^{6} \)	20T676	Trivial (GRH)
20.8.211505645444809969257911648518144.5	x^20 + 11x^18 + 18x^16 - 175x^14 - 628x^12 + 130x^10 + 2154x^8 + 368x^6 - 2100x^4 + 89x^2 + 1	\( 2^{20}\cdot 61^{6}\cdot 397^{6} \)	20T676	Trivial (GRH)
20.12.211505645444809969257911648518144.6	x^20 - 4x^18 - 45x^16 + 214x^14 + 221x^12 - 1436x^10 - 525x^8 + 2328x^6 + 832x^4 - 616x^2 + 1	\( 2^{20}\cdot 61^{6}\cdot 397^{6} \)	20T676	Trivial (GRH)
20.8.211505645444809969257911648518144.6	x^20 + 4x^18 - 45x^16 - 214x^14 + 221x^12 + 1436x^10 - 525x^8 - 2328x^6 + 832x^4 + 616x^2 + 1	\( 2^{20}\cdot 61^{6}\cdot 397^{6} \)	20T676	Trivial (GRH)
20.12.211505645444809969257911648518144.7	x^20 + 6x^18 - 22x^16 - 134x^14 + 71x^12 + 551x^10 - 177x^8 - 192x^6 + 106x^4 - 18x^2 + 1	\( 2^{20}\cdot 61^{6}\cdot 397^{6} \)	20T676	Trivial (GRH)
20.12.211505645444809969257911648518144.8	x^20 - 11x^18 + 18x^16 + 175x^14 - 628x^12 - 130x^10 + 2154x^8 - 368x^6 - 2100x^4 - 89x^2 + 1	\( 2^{20}\cdot 61^{6}\cdot 397^{6} \)	20T676	Trivial (GRH)
20.0.787012506700137895608689244136013824.1	x^20 + 32x^18 + 425x^16 + 3096x^14 + 13737x^12 + 38877x^10 + 71141x^8 + 83054x^6 + 59048x^4 + 22997x^2 + 3721	\( 2^{20}\cdot 61^{8}\cdot 397^{6} \)	20T676	$[2, 2, 2, 522]$ (GRH)
20.0.787012506700137895608689244136013824.2	x^20 + 48x^18 + 969x^16 + 10694x^14 + 70153x^12 + 278236x^10 + 648293x^8 + 820206x^6 + 482754x^4 + 89304x^2 + 3721	\( 2^{20}\cdot 61^{8}\cdot 397^{6} \)	20T676	$[2, 2340]$ (GRH)
20.20.787012506700137895608689244136013824.2	x^20 - 32x^18 + 425x^16 - 3096x^14 + 13737x^12 - 38877x^10 + 71141x^8 - 83054x^6 + 59048x^4 - 22997x^2 + 3721	\( 2^{20}\cdot 61^{8}\cdot 397^{6} \)	20T676	Trivial (GRH)
20.20.787012506700137895608689244136013824.3	x^20 - 48x^18 + 969x^16 - 10694x^14 + 70153x^12 - 278236x^10 + 648293x^8 - 820206x^6 + 482754x^4 - 89304x^2 + 3721	\( 2^{20}\cdot 61^{8}\cdot 397^{6} \)	20T676	Trivial (GRH)