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 53)

Label	Polynomial	Discriminant	Galois group	Class group
20.12.336186938823068443362886656.2	x^20 - 5x^18 - 8x^16 + 73x^14 - 68x^12 - 166x^10 + 324x^8 - 146x^6 - 18x^4 + 13x^2 + 1	\( 2^{10}\cdot 3^{10}\cdot 11^{18} \)	20T340	Trivial (GRH)
20.12.336186938823068443362886656.3	x^20 - 4x^18 - 17x^16 + 68x^14 + 69x^12 - 298x^10 + 26x^8 + 358x^6 - 211x^4 + 8x^2 + 1	\( 2^{10}\cdot 3^{10}\cdot 11^{18} \)	20T340	Trivial (GRH)
20.8.336186938823068443362886656.3	x^20 + 2x^18 - 29x^16 - 91x^14 + 27x^12 + 230x^10 - 13x^8 - 191x^6 + 47x^4 + 17x^2 + 1	\( 2^{10}\cdot 3^{10}\cdot 11^{18} \)	20T340	Trivial (GRH)
20.0.3084067808306675532115738624.3	x^20 + 18x^18 + 170x^16 + 1025x^14 + 4073x^12 + 10669x^10 + 18165x^8 + 19421x^6 + 12197x^4 + 3979x^2 + 529	\( 2^{20}\cdot 11^{18}\cdot 23^{2} \)	20T340	Trivial (GRH)
20.0.3084067808306675532115738624.4	x^20 + 19x^18 + 152x^16 + 710x^14 + 2248x^12 + 5004x^10 + 7989x^8 + 8956x^6 + 6781x^4 + 2944x^2 + 529	\( 2^{20}\cdot 11^{18}\cdot 23^{2} \)	20T340	Trivial (GRH)
20.12.10779662339431083287111532544.2	x^20 - 10x^19 + 59x^18 - 246x^17 + 745x^16 - 1676x^15 + 2704x^14 - 2654x^13 + 200x^12 + 4338x^11 - 7888x^10 + 6786x^9 - 1632x^8 - 2636x^7 + 2973x^6 - 1118x^5 - 97x^4 + 190x^3 - 35x^2 - 4x + 1	\( 2^{20}\cdot 11^{18}\cdot 43^{2} \)	20T340	Trivial (GRH)
20.12.10779662339431083287111532544.3	x^20 - 8x^19 + 19x^18 + 10x^17 - 132x^16 + 276x^15 - 250x^14 - 36x^13 + 428x^12 - 704x^11 + 793x^10 - 704x^9 + 428x^8 - 36x^7 - 250x^6 + 276x^5 - 132x^4 + 10x^3 + 19x^2 - 8x + 1	\( 2^{20}\cdot 11^{18}\cdot 43^{2} \)	20T340	Trivial (GRH)
20.8.10779662339431083287111532544.3	x^20 - 5x^18 - 19x^16 - 22x^15 + 51x^14 - 132x^13 + 20x^12 + 924x^11 - 89x^10 - 1804x^9 + 731x^8 + 2926x^7 - 256x^6 - 2288x^5 - 227x^4 + 946x^3 + 277x^2 - 110x - 43	\( 2^{20}\cdot 11^{18}\cdot 43^{2} \)	20T340	Trivial (GRH)
20.12.10779662339431083287111532544.4	x^20 - 6x^19 + 13x^18 - 6x^17 - 21x^16 + 22x^15 - 67x^14 + 556x^13 - 1289x^12 + 424x^11 + 2782x^10 - 4460x^9 + 1142x^8 + 3086x^7 - 2663x^6 - 308x^5 + 870x^4 - 6x^3 - 97x^2 - 6x + 1	\( 2^{20}\cdot 11^{18}\cdot 43^{2} \)	20T340	Trivial (GRH)
20.8.10779662339431083287111532544.4	x^20 - 6x^19 + 9x^18 + 20x^17 - 110x^16 + 142x^15 + 149x^14 - 636x^13 + 717x^12 + 462x^11 - 1495x^10 + 1606x^9 + 479x^8 - 1158x^7 + 2199x^6 + 32x^5 + 253x^4 + 2216x^3 + 498x^2 + 34x + 1	\( 2^{20}\cdot 11^{18}\cdot 43^{2} \)	20T340	Trivial (GRH)
20.12.10779662339431083287111532544.5	x^20 - 9x^18 + 26x^16 - 69x^14 + 313x^12 - 66x^11 - 650x^10 + 528x^9 + 471x^8 - 1100x^7 - 455x^6 + 308x^5 + 245x^4 + 66x^3 - 49x^2 + 1	\( 2^{20}\cdot 11^{18}\cdot 43^{2} \)	20T340	Trivial (GRH)
20.8.26099879633934179709805920256.3	x^20 - 6x^19 + 11x^18 - 10x^17 - 20x^16 + 64x^15 - 117x^14 + 170x^13 + 79x^12 - 254x^11 + 851x^10 - 158x^9 + 109x^8 + 1090x^7 - 879x^6 - 112x^5 + 228x^4 - 358x^3 - 209x^2 - 18x + 1	\( 2^{30}\cdot 11^{16}\cdot 23^{2} \)	20T340	Trivial (GRH)
20.8.46179397182603358960092184576.1	x^20 - 8x^19 + 29x^18 - 84x^17 + 251x^16 - 652x^15 + 1403x^14 - 2726x^13 + 4823x^12 - 7568x^11 + 10330x^10 - 11352x^9 + 8897x^8 - 3350x^7 - 2555x^6 + 4392x^5 - 2713x^4 + 952x^3 + 604x^2 - 158x - 43	\( 2^{20}\cdot 11^{18}\cdot 89^{2} \)	20T340	Trivial (GRH)
20.12.46179397182603358960092184576.2	x^20 - 13x^18 + 15x^16 - 66x^15 + 212x^14 + 374x^13 - 853x^12 - 506x^11 + 1497x^10 - 396x^9 - 1652x^8 + 1276x^7 + 1247x^6 - 836x^5 - 536x^4 + 176x^3 + 82x^2 - 22x + 1	\( 2^{20}\cdot 11^{18}\cdot 89^{2} \)	20T340	Trivial (GRH)
20.8.344255425354822086003595935744.1	x^20 + 6x^18 - 8x^16 - 70x^14 - 13x^12 + 197x^10 + 159x^8 - 36x^6 - 40x^4 + 2x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T340	Trivial (GRH)
20.8.344255425354822086003595935744.2	x^20 + 5x^18 - 8x^16 - 73x^14 - 68x^12 + 166x^10 + 324x^8 + 146x^6 - 18x^4 - 13x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T340	Trivial (GRH)
20.16.344255425354822086003595935744.3	x^20 - 9x^18 + 15x^16 + 74x^14 - 259x^12 + 43x^10 + 724x^8 - 961x^6 + 410x^4 - 38x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T340	Trivial (GRH)
20.4.344255425354822086003595935744.3	x^20 + 17x^18 + 113x^16 + 370x^14 + 581x^12 + 197x^10 - 666x^8 - 949x^6 - 458x^4 - 64x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T340	$[2]$ (GRH)
20.8.344255425354822086003595935744.3	x^20 - 9x^18 + 4x^16 + 85x^14 + 16x^12 - 210x^10 - 134x^8 + 128x^6 + 146x^4 + 39x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T340	Trivial (GRH)
20.16.344255425354822086003595935744.4	x^20 - 7x^18 - 6x^16 + 119x^14 - 195x^12 - 131x^10 + 499x^8 - 391x^6 + 130x^4 - 19x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T340	Trivial (GRH)
20.4.344255425354822086003595935744.4	x^20 + 9x^18 + 15x^16 - 74x^14 - 259x^12 - 43x^10 + 724x^8 + 961x^6 + 410x^4 + 38x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T340	Trivial (GRH)
20.8.344255425354822086003595935744.4	x^20 + 7x^18 - 17x^16 - 53x^14 + 58x^12 + 131x^10 - 51x^8 - 104x^6 + 9x^4 + 19x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T340	Trivial (GRH)
20.16.344255425354822086003595935744.5	x^20 - 9x^18 + 15x^16 + 63x^14 - 215x^12 + 142x^10 + 141x^8 - 213x^6 + 91x^4 - 16x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T340	Trivial (GRH)
20.4.344255425354822086003595935744.5	x^20 + 7x^18 - 6x^16 - 119x^14 - 195x^12 + 131x^10 + 499x^8 + 391x^6 + 130x^4 + 19x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T340	$[2]$ (GRH)
20.8.344255425354822086003595935744.5	x^20 + 10x^18 + 12x^16 - 122x^14 - 417x^12 - 331x^10 + 331x^8 + 538x^6 + 100x^4 - 56x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T340	Trivial (GRH)
20.16.344255425354822086003595935744.6	x^20 - 17x^18 + 113x^16 - 370x^14 + 581x^12 - 197x^10 - 666x^8 + 949x^6 - 458x^4 + 64x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T340	Trivial (GRH)
20.4.344255425354822086003595935744.6	x^20 + 9x^18 + 15x^16 - 63x^14 - 215x^12 - 142x^10 + 141x^8 + 213x^6 + 91x^4 + 16x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T340	Trivial (GRH)
20.8.344255425354822086003595935744.6	x^20 + 8x^18 + 9x^16 - 49x^14 - 84x^12 + 43x^10 + 124x^8 + 35x^6 - 17x^4 - 4x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T340	Trivial (GRH)
20.12.344255425354822086003595935744.7	x^20 - 2x^18 - 29x^16 + 91x^14 + 27x^12 - 230x^10 - 13x^8 + 191x^6 + 47x^4 - 17x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T340	Trivial (GRH)
20.8.344255425354822086003595935744.7	x^20 + 4x^18 - 17x^16 - 68x^14 + 69x^12 + 298x^10 + 26x^8 - 358x^6 - 211x^4 - 8x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T340	Trivial (GRH)
20.12.344255425354822086003595935744.8	x^20 - 7x^18 - 17x^16 + 53x^14 + 58x^12 - 131x^10 - 51x^8 + 104x^6 + 9x^4 - 19x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T340	Trivial (GRH)
20.8.344255425354822086003595935744.8	x^20 + 3x^18 - 13x^16 - 50x^14 - 7x^12 + 111x^10 + 80x^8 - 35x^6 - 28x^4 + 4x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T340	Trivial (GRH)
20.12.344255425354822086003595935744.9	x^20 + 9x^18 + 4x^16 - 85x^14 + 16x^12 + 210x^10 - 134x^8 - 128x^6 + 146x^4 - 39x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T340	Trivial (GRH)
20.8.344255425354822086003595935744.9	x^20 - 6x^18 - 8x^16 + 59x^14 + 64x^12 - 153x^10 - 281x^8 - 140x^6 - 7x^4 + 9x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T340	Trivial (GRH)
20.12.344255425354822086003595935744.10	x^20 - 6x^18 - 8x^16 + 70x^14 - 13x^12 - 197x^10 + 159x^8 + 36x^6 - 40x^4 - 2x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T340	Trivial (GRH)
20.8.344255425354822086003595935744.10	x^20 + 7x^18 + 5x^16 - 42x^14 - 63x^12 + 43x^10 + 92x^8 - 5x^6 - 35x^4 - 3x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T340	Trivial (GRH)
20.12.344255425354822086003595935744.11	x^20 - 3x^18 - 13x^16 + 50x^14 - 7x^12 - 111x^10 + 80x^8 + 35x^6 - 28x^4 - 4x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T340	Trivial (GRH)
20.8.344255425354822086003595935744.11	x^20 + 6x^18 - 8x^16 - 103x^14 - 156x^12 + 98x^10 + 269x^8 - 47x^6 - 139x^4 + 46x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T340	Trivial (GRH)
20.12.344255425354822086003595935744.12	x^20 - 6x^18 - 8x^16 + 103x^14 - 156x^12 - 98x^10 + 269x^8 + 47x^6 - 139x^4 - 46x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T340	Trivial (GRH)
20.12.344255425354822086003595935744.13	x^20 - 10x^18 + 12x^16 + 122x^14 - 417x^12 + 331x^10 + 331x^8 - 538x^6 + 100x^4 + 56x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T340	Trivial (GRH)
20.12.6113193735657808322804901216256.1	x^20 + 8x^18 - 2x^16 - 82x^14 + 70x^12 + 186x^10 - 327x^8 + 178x^6 - 28x^4 - 4x^2 + 1	\( 2^{40}\cdot 11^{18} \)	20T340	Trivial (GRH)
20.12.6113193735657808322804901216256.2	x^20 - 4x^18 - 17x^16 + 46x^14 + 91x^12 - 100x^10 - 139x^8 + 50x^6 + 42x^4 - 14x^2 + 1	\( 2^{40}\cdot 11^{18} \)	20T340	Trivial (GRH)
20.16.14609322487882432594514132598784.1	x^20 - 8x^19 + 19x^18 - 12x^17 + 22x^16 + 78x^15 - 1559x^14 + 6564x^13 - 14059x^12 + 13244x^11 + 12365x^10 - 51150x^9 + 52117x^8 - 1620x^7 - 40389x^6 + 36048x^5 - 13860x^4 + 2232x^3 - 3x^2 - 30x + 1	\( 2^{20}\cdot 11^{18}\cdot 1583^{2} \)	20T340	Trivial (GRH)
20.8.14609322487882432594514132598784.1	x^20 - 8x^19 + 29x^18 - 128x^17 + 493x^16 - 1180x^15 + 2151x^14 - 3166x^13 + 2535x^12 + 484x^11 - 3002x^10 + 9438x^9 - 10408x^8 + 5692x^7 - 4601x^6 - 3330x^5 + 10982x^4 - 6748x^3 + 703x^2 + 546x - 131	\( 2^{20}\cdot 11^{18}\cdot 1583^{2} \)	20T340	Trivial (GRH)
20.0.12569066605710630176407970532818944.1	x^20 - 4x^19 + 32x^18 + 6x^17 + 202x^16 + 938x^15 + 1790x^14 + 5494x^13 + 12527x^12 + 17820x^11 + 50458x^10 + 56452x^9 + 119267x^8 + 113984x^7 + 353348x^6 + 19962x^5 + 844391x^4 - 209964x^3 + 1076236x^2 - 150400x + 539177	\( 2^{30}\cdot 11^{18}\cdot 1451^{2} \)	20T340	$[2, 850]$ (GRH)
20.16.12569066605710630176407970532818944.1	x^20 - 2x^19 - 54x^18 + 70x^17 + 946x^16 - 584x^15 - 7764x^14 - 1332x^13 + 33381x^12 + 32098x^11 - 61522x^10 - 124784x^9 - 33982x^8 + 155766x^7 + 265504x^6 + 26850x^5 - 228250x^4 - 101494x^3 + 6220x^2 + 7296x + 617	\( 2^{30}\cdot 11^{18}\cdot 1451^{2} \)	20T340	Trivial (GRH)
20.8.12569066605710630176407970532818944.1	x^20 - 4x^19 + 6x^18 + 104x^17 - 586x^16 + 2008x^15 - 4416x^14 + 9552x^13 - 21108x^12 + 44176x^11 - 68936x^10 + 21824x^9 + 132672x^8 - 295200x^7 + 157856x^6 + 195552x^5 - 226768x^4 + 36768x^3 + 57888x^2 - 21248x + 1376	\( 2^{30}\cdot 11^{18}\cdot 1451^{2} \)	20T340	$[2]$ (GRH)
20.0.12569066605710630176407970532818944.2	x^20 - 6x^19 + 28x^18 - 54x^17 + 56x^16 + 184x^15 + 1638x^14 - 16140x^13 + 84550x^12 - 301356x^11 + 842392x^10 - 1926386x^9 + 3717519x^8 - 6131704x^7 + 8726846x^6 - 10659646x^5 + 11152518x^4 - 9762542x^3 + 6937796x^2 - 3721474x + 1233541	\( 2^{30}\cdot 11^{18}\cdot 1451^{2} \)	20T340	$[2, 878]$ (GRH)
20.20.29506901376440972086193367040000000000.1	x^20 - 100x^18 + 4203x^16 - 96966x^14 + 1345774x^12 - 11586862x^10 + 61552481x^8 - 193568871x^6 + 327924125x^4 - 247730077x^2 + 62710561	\( 2^{20}\cdot 5^{10}\cdot 11^{16}\cdot 7919^{2} \)	20T340	Trivial (GRH)
20.20.29506901376440972086193367040000000000.2	x^20 - 100x^18 + 4236x^16 - 99122x^14 + 1400389x^12 - 12254584x^10 + 65535196x^8 - 203748744x^6 + 334595163x^4 - 244419935x^2 + 62710561	\( 2^{20}\cdot 5^{10}\cdot 11^{16}\cdot 7919^{2} \)	20T340	Trivial (GRH)