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
20.0.3472129442854704114264133.1	x^20 - 10x^19 + 54x^18 - 201x^17 + 571x^16 - 1304x^15 + 2471x^14 - 3963x^13 + 5450x^12 - 6479x^11 + 6689x^10 - 6006x^9 + 4684x^8 - 3159x^7 + 1828x^6 - 896x^5 + 365x^4 - 120x^3 + 30x^2 - 5x + 1	\( 11^{18}\cdot 727\cdot 859 \)	20T409	Trivial (GRH)
20.0.4663997797513406792383141.1	x^20 - x^19 + 2x^18 - 3x^17 + 5x^16 - 8x^15 + 13x^14 - 21x^13 + 34x^12 - 55x^11 + 89x^10 - 143x^9 + 221x^8 - 309x^7 + 365x^6 - 344x^5 + 247x^4 - 129x^3 + 46x^2 - 10x + 1	\( 11^{18}\cdot 397\cdot 2113 \)	20T409	Trivial (GRH)
20.12.518869631265206280450473984.1	x^20 - 4x^19 + 20x^17 - 47x^16 + 66x^15 + 15x^14 - 236x^13 + 407x^12 - 470x^11 + 54x^10 + 664x^9 + 209x^8 - 1098x^7 - 349x^6 + 858x^5 + 29x^4 - 160x^3 - 11x^2 + 8x + 1	\( 2^{20}\cdot 11^{18}\cdot 89 \)	20T409	Trivial (GRH)
20.8.518869631265206280450473984.1	x^20 - 8x^19 + 27x^18 - 30x^17 - 55x^16 + 186x^15 - 36x^14 - 412x^13 + 327x^12 + 572x^11 - 637x^10 - 528x^9 + 656x^8 + 318x^7 - 394x^6 - 122x^5 + 132x^4 + 26x^3 - 21x^2 - 2x + 1	\( 2^{20}\cdot 11^{18}\cdot 89 \)	20T409	Trivial (GRH)
20.10.3698056327053752876991753216.1	x^20 - 5x^19 + 5x^18 + 9x^17 - 2x^16 - 49x^15 - 23x^14 + 193x^13 - 175x^12 - 433x^11 + 649x^10 + 767x^9 - 799x^8 - 1291x^7 - 236x^6 + 743x^5 + 873x^4 + 476x^3 + 136x^2 + 19x + 1	\( -\,2^{10}\cdot 3^{10}\cdot 11^{19} \)	20T409	Trivial (GRH)
20.14.3698056327053752876991753216.1	x^20 - 11x^18 + 22x^16 + 88x^14 - 264x^12 + 22x^10 + 374x^8 - 253x^6 - 22x^4 + 55x^2 - 11	\( -\,2^{10}\cdot 3^{10}\cdot 11^{19} \)	20T409	Trivial (GRH)
20.6.3698056327053752876991753216.1	x^20 + 11x^18 + 22x^16 - 88x^14 - 275x^12 + 55x^10 + 561x^8 + 176x^6 - 165x^4 - 88x^2 - 11	\( -\,2^{10}\cdot 3^{10}\cdot 11^{19} \)	20T409	Trivial (GRH)
20.10.3698056327053752876991753216.2	x^20 - 33x^16 + 22x^14 + 275x^12 - 253x^10 - 605x^8 + 550x^6 + 308x^4 - 187x^2 - 11	\( -\,2^{10}\cdot 3^{10}\cdot 11^{19} \)	20T409	Trivial (GRH)
20.14.3698056327053752876991753216.2	x^20 - 33x^16 + 33x^14 + 253x^12 - 616x^10 + 363x^8 + 231x^6 - 341x^4 + 121x^2 - 11	\( -\,2^{10}\cdot 3^{10}\cdot 11^{19} \)	20T409	Trivial (GRH)
20.6.3698056327053752876991753216.2	x^20 + 11x^18 + 22x^16 - 165x^14 - 935x^12 - 1815x^10 - 1375x^8 - 33x^6 + 418x^4 + 121x^2 - 11	\( -\,2^{10}\cdot 3^{10}\cdot 11^{19} \)	20T409	Trivial (GRH)
20.6.7193546891164309240746298359.1	x^20 - x^19 + x^18 - x^17 + 12x^16 - 12x^15 - 10x^14 + 10x^13 + 34x^12 - 34x^11 - 98x^10 + 99x^9 + 88x^8 - 77x^7 - 143x^6 + 121x^5 + 132x^4 - 143x^3 - 11x^2 + 44x - 11	\( -\,3^{10}\cdot 11^{18}\cdot 21911 \)	20T409	Trivial (GRH)
20.10.9228883441492376875877531648.1	x^20 - 4x^19 - 7x^18 + 54x^17 - 88x^16 + 56x^15 - 48x^14 + 136x^13 - 210x^12 + 154x^11 - 87x^10 + 154x^9 - 210x^8 + 136x^7 - 48x^6 + 56x^5 - 88x^4 + 54x^3 - 7x^2 - 4x + 1	\( -\,2^{20}\cdot 11^{18}\cdot 1583 \)	20T409	Trivial (GRH)
20.10.9228883441492376875877531648.2	x^20 - 10x^19 + 41x^18 - 84x^17 + 38x^16 + 308x^15 - 1032x^14 + 1630x^13 - 1150x^12 - 718x^11 + 2804x^10 - 3378x^9 + 2060x^8 - 180x^7 - 819x^6 + 748x^5 - 310x^4 + 42x^3 + 17x^2 - 8x + 1	\( -\,2^{20}\cdot 11^{18}\cdot 1583 \)	20T409	Trivial (GRH)
20.12.24702188929674309323307573129.1	x^20 - x^19 - 9x^18 + 8x^17 + 38x^16 - 30x^15 - 108x^14 + 78x^13 + 232x^12 - 154x^11 - 373x^10 + 220x^9 + 441x^8 - 221x^7 - 383x^6 + 140x^5 + 225x^4 - 30x^3 - 64x^2 - 10x + 1	\( 3^{10}\cdot 11^{18}\cdot 67\cdot 1123 \)	20T409	Trivial (GRH)
20.12.81693426134005631737181457408.1	x^20 - 3x^18 - 57x^16 + 270x^14 + 477x^12 - 4995x^10 + 10530x^8 - 7533x^6 - 567x^4 + 1701x^2 + 243	\( 2^{10}\cdot 3^{15}\cdot 11^{18} \)	20T409	Trivial (GRH)
20.8.81693426134005631737181457408.1	x^20 - 5x^19 + 9x^18 - 20x^17 + 66x^16 - 65x^15 - 60x^14 - 13x^13 - 53x^12 + 1122x^11 - 1407x^10 - 528x^9 + 1832x^8 - 1537x^7 + 1935x^6 - 890x^5 - 1837x^4 + 2294x^3 - 723x^2 - x + 1	\( 2^{10}\cdot 3^{15}\cdot 11^{18} \)	20T409	Trivial (GRH)
20.12.81693426134005631737181457408.2	x^20 - 8x^19 + 19x^18 - 12x^17 + 44x^16 - 186x^15 + 36x^14 + 470x^13 - 12x^12 - 704x^11 - 912x^10 + 1804x^9 + 923x^8 - 1620x^7 - 547x^6 + 430x^5 + 198x^4 + 76x^3 + 52x^2 + 14x + 1	\( 2^{10}\cdot 3^{15}\cdot 11^{18} \)	20T409	Trivial (GRH)
20.8.81693426134005631737181457408.2	x^20 - 9x^18 - 18x^16 + 162x^14 + 225x^12 - 837x^10 - 1377x^8 + 810x^6 + 2511x^4 + 1458x^2 + 243	\( 2^{10}\cdot 3^{15}\cdot 11^{18} \)	20T409	Trivial (GRH)
20.12.81693426134005631737181457408.3	x^20 - 6x^18 - 30x^16 + 279x^14 - 387x^12 - 1242x^10 + 3294x^8 - 162x^6 - 4374x^4 + 2187x^2 + 243	\( 2^{10}\cdot 3^{15}\cdot 11^{18} \)	20T409	Trivial (GRH)
20.8.81693426134005631737181457408.3	x^20 - 4x^19 + 20x^17 - 25x^16 + 22x^15 - 18x^14 + 149x^13 - 880x^12 + 1884x^11 - 3642x^10 + 6615x^9 - 8657x^8 + 8945x^7 - 8412x^6 + 7546x^5 + 579x^4 - 5330x^3 + 547x + 67	\( 2^{10}\cdot 3^{15}\cdot 11^{18} \)	20T409	Trivial (GRH)
20.16.200540506089835653323720703125.1	x^20 - 10x^19 + 34x^18 - 21x^17 - 145x^16 + 344x^15 - 72x^14 - 722x^13 + 987x^12 + 110x^11 - 1459x^10 + 1052x^9 + 682x^8 - 1142x^7 + 98x^6 + 446x^5 - 160x^4 - 57x^3 + 34x^2 - 1	\( 5^{10}\cdot 11^{16}\cdot 446909 \)	20T409	Trivial (GRH)
20.4.312713276773351089230071194069.1	x^20 - 10x^19 + 64x^18 - 291x^17 + 1046x^16 - 3064x^15 + 7526x^14 - 15688x^13 + 28009x^12 - 42968x^11 + 56650x^10 - 63971x^9 + 61429x^8 - 49598x^7 + 33085x^6 - 17771x^5 + 7384x^4 - 2223x^3 + 430x^2 - 40x + 1	\( 3^{10}\cdot 11^{19}\cdot 131\cdot 661 \)	20T409	$[2]$ (GRH)
20.8.395929091610014438629150390625.1	x^20 - 10x^19 + 55x^18 - 210x^17 + 605x^16 - 1372x^15 + 2490x^14 - 3620x^13 + 4140x^12 - 3520x^11 + 1847x^10 + 65x^9 - 1220x^8 + 1240x^7 - 595x^6 + 14x^5 + 165x^4 - 95x^3 + 15x^2 + 5x - 1	\( 5^{34}\cdot 349\cdot 1949 \)	20T409	Trivial (GRH)
20.14.470525233802978928640000000000.1	x^20 - 13x^18 + 56x^16 - 56x^14 - 213x^12 + 524x^10 - 150x^8 - 309x^6 + 43x^4 + 9x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 11^{16} \)	20T409	Trivial (GRH)
20.18.470525233802978928640000000000.1	x^20 - 19x^18 + 136x^16 - 447x^14 + 624x^12 - 88x^10 - 640x^8 + 641x^6 - 240x^4 + 34x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 11^{16} \)	20T409	Trivial (GRH)
20.2.470525233802978928640000000000.1	x^20 + 19x^18 + 136x^16 + 447x^14 + 624x^12 + 88x^10 - 640x^8 - 641x^6 - 240x^4 - 34x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 11^{16} \)	20T409	$[3]$ (GRH)
20.6.470525233802978928640000000000.1	x^20 + 8x^18 - 6x^16 - 123x^14 - 78x^12 + 488x^10 + 500x^8 - 314x^6 - 306x^4 - 38x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 11^{16} \)	20T409	Trivial (GRH)
20.10.470525233802978928640000000000.2	x^20 - x^18 - 24x^16 + 19x^14 + 145x^12 - 66x^10 - 239x^8 + 51x^6 + 29x^4 - 3x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 11^{16} \)	20T409	Trivial (GRH)
20.14.470525233802978928640000000000.2	x^20 - 11x^18 + 35x^16 - 170x^12 + 198x^10 + 119x^8 - 253x^6 + 81x^4 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 11^{16} \)	20T409	Trivial (GRH)
20.6.470525233802978928640000000000.2	x^20 + 4x^18 - 21x^16 - 127x^14 - 148x^12 + 176x^10 + 419x^8 + 174x^6 - 25x^4 - 13x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 11^{16} \)	20T409	Trivial (GRH)
20.10.470525233802978928640000000000.3	x^20 + x^18 - 24x^16 - 19x^14 + 145x^12 + 66x^10 - 239x^8 - 51x^6 + 29x^4 + 3x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 11^{16} \)	20T409	Trivial (GRH)
20.14.470525233802978928640000000000.3	x^20 - 4x^18 - 18x^16 + 91x^14 + 13x^12 - 480x^10 + 652x^8 - 238x^6 - 47x^4 + 32x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 11^{16} \)	20T409	Trivial (GRH)
20.6.470525233802978928640000000000.3	x^20 + 5x^18 - 24x^16 - 126x^14 + 50x^12 + 678x^10 + 947x^8 + 530x^6 + 116x^4 + 3x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 11^{16} \)	20T409	Trivial (GRH)
20.10.470525233802978928640000000000.4	x^20 - x^18 - 19x^16 + 4x^14 + 96x^12 + 4x^10 - 167x^8 - 41x^6 + 95x^4 + 40x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 11^{16} \)	20T409	Trivial (GRH)
20.14.470525233802978928640000000000.4	x^20 - 8x^18 - 6x^16 + 123x^14 - 78x^12 - 488x^10 + 500x^8 + 314x^6 - 306x^4 + 38x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 11^{16} \)	20T409	Trivial (GRH)
20.6.470525233802978928640000000000.4	x^20 + 8x^18 + 5x^16 - 101x^14 - 276x^12 - 106x^10 + 401x^8 + 544x^6 + 255x^4 + 39x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 11^{16} \)	20T409	Trivial (GRH)
20.10.470525233802978928640000000000.5	x^20 + 2x^18 - 30x^16 - 64x^14 + 164x^12 + 253x^10 - 182x^8 - 280x^6 - 23x^4 + 29x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 11^{16} \)	20T409	Trivial (GRH)
20.14.470525233802978928640000000000.5	x^20 - 4x^18 - 21x^16 + 127x^14 - 148x^12 - 176x^10 + 419x^8 - 174x^6 - 25x^4 + 13x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 11^{16} \)	20T409	Trivial (GRH)
20.6.470525233802978928640000000000.5	x^20 + 11x^18 + 35x^16 - 170x^12 - 198x^10 + 119x^8 + 253x^6 + 81x^4 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 11^{16} \)	20T409	Trivial (GRH)
20.10.470525233802978928640000000000.6	x^20 - 26x^16 + 11x^14 + 101x^12 - 44x^10 - 127x^8 + 44x^6 + 53x^4 - 11x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 11^{16} \)	20T409	Trivial (GRH)
20.14.470525233802978928640000000000.6	x^20 - 8x^18 + 5x^16 + 101x^14 - 276x^12 + 106x^10 + 401x^8 - 544x^6 + 255x^4 - 39x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 11^{16} \)	20T409	Trivial (GRH)
20.10.470525233802978928640000000000.7	x^20 - 8x^18 - 6x^16 + 112x^14 + 21x^12 - 257x^10 - 6x^8 + 171x^6 - 9x^4 - 17x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 11^{16} \)	20T409	Trivial (GRH)
20.10.470525233802978928640000000000.8	x^20 + 8x^18 - 6x^16 - 112x^14 + 21x^12 + 257x^10 - 6x^8 - 171x^6 - 9x^4 + 17x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 11^{16} \)	20T409	Trivial (GRH)
20.10.470525233802978928640000000000.9	x^20 - x^18 - 19x^16 + 26x^14 + 85x^12 - 117x^10 - 112x^8 + 146x^6 - 4x^4 - 15x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 11^{16} \)	20T409	Trivial (GRH)
20.10.470525233802978928640000000000.10	x^20 - 2x^18 - 30x^16 + 64x^14 + 164x^12 - 253x^10 - 182x^8 + 280x^6 - 23x^4 - 29x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 11^{16} \)	20T409	Trivial (GRH)
20.10.470525233802978928640000000000.11	x^20 - 26x^16 - 11x^14 + 101x^12 + 44x^10 - 127x^8 - 44x^6 + 53x^4 + 11x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 11^{16} \)	20T409	Trivial (GRH)
20.8.531322502415571231181285359616.1	x^20 - 2x^19 - 10x^18 + 26x^17 - 11x^16 - 122x^15 + 68x^14 + 164x^13 - 235x^12 - 264x^11 + 408x^10 + 902x^9 + 679x^8 - 104x^7 - 1092x^6 - 1178x^5 - 528x^4 - 74x^3 + 38x^2 + 14x + 1	\( 2^{30}\cdot 11^{18}\cdot 89 \)	20T409	Trivial (GRH)
20.18.610351562500000000000000000000.1	x^20 - 5x^18 - 25x^16 + 255x^14 - 825x^12 + 1374x^10 - 1285x^8 + 675x^6 - 190x^4 + 25x^2 - 1	\( -\,2^{20}\cdot 5^{34} \)	20T409	Trivial (GRH)
20.2.610351562500000000000000000000.1	x^20 + 5x^18 - 25x^16 - 255x^14 - 825x^12 - 1374x^10 - 1285x^8 - 675x^6 - 190x^4 - 25x^2 - 1	\( -\,2^{20}\cdot 5^{34} \)	20T409	Trivial (GRH)
20.4.2016025246120989322662353515625.1	x^20 - 10x^19 + 65x^18 - 300x^17 + 1100x^16 - 3292x^15 + 8290x^14 - 17760x^13 + 32700x^12 - 51900x^11 + 71069x^10 - 83695x^9 + 84205x^8 - 71600x^7 + 50575x^6 - 28938x^5 + 12870x^4 - 4155x^3 + 850x^2 - 75x + 1	\( 5^{35}\cdot 149\cdot 4649 \)	20T409	Trivial (GRH)