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 69)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.38798116011178581010939904.2	x^20 + 7x^18 + 16x^16 + 2x^14 - 52x^12 - 84x^10 + 9x^8 + 180x^6 + 217x^4 + 116x^2 + 29	\( 2^{20}\cdot 29^{3}\cdot 79^{8} \)	20T845	Trivial (GRH)
20.4.38798116011178581010939904.2	x^20 - 4x^18 + 8x^16 - 8x^14 - 4x^12 - 8x^10 + 47x^8 - 53x^6 + 12x^4 + 29x^2 + 29	\( 2^{20}\cdot 29^{3}\cdot 79^{8} \)	20T845	Trivial (GRH)
20.0.38798116011178581010939904.3	x^20 + 11x^18 + 55x^16 + 173x^14 + 378x^12 + 600x^10 + 704x^8 + 606x^6 + 369x^4 + 145x^2 + 29	\( 2^{20}\cdot 29^{3}\cdot 79^{8} \)	20T845	Trivial (GRH)
20.4.38798116011178581010939904.3	x^20 - 7x^18 + 16x^16 - 2x^14 - 52x^12 + 84x^10 + 9x^8 - 180x^6 + 217x^4 - 116x^2 + 29	\( 2^{20}\cdot 29^{3}\cdot 79^{8} \)	20T845	Trivial (GRH)
20.4.3363579537281480927197709312.1	x^20 - 7x^19 + 12x^18 + 14x^17 - 35x^16 - 65x^15 + 129x^14 + 67x^13 - 100x^12 - 106x^11 - 23x^10 - 344x^9 + 1722x^8 - 2076x^7 + 971x^6 - 746x^5 + 1481x^4 - 1317x^3 + 472x^2 - 52x + 1	\( 2^{10}\cdot 17^{3}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.6.8329874258111902796909124608.1	x^20 - x^18 - 16x^16 + 48x^14 - 11x^12 - 61x^10 - 105x^8 + 90x^6 + 111x^4 + 138x^2 - 23	\( -\,2^{10}\cdot 23^{3}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.6.8329874258111902796909124608.2	x^20 - 8x^19 + 31x^18 - 68x^17 + 74x^16 - 9x^15 - 52x^14 - 9x^13 + 95x^12 + 124x^11 - 551x^10 + 295x^9 + 750x^8 - 1039x^7 - 76x^6 + 877x^5 - 443x^4 - 58x^3 + 226x^2 - 42x - 1	\( -\,2^{10}\cdot 23^{3}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.10.13757744271328447008064363083.1	x^20 - 2x^19 - 9x^18 + 15x^17 - 74x^15 + 32x^14 + 96x^13 + 46x^12 - 14x^11 + 16x^10 + 96x^9 - 505x^8 + 589x^7 + 504x^6 - 1005x^5 + 452x^4 + 140x^3 - 154x^2 + 28x - 1	\( -\,3^{7}\cdot 97^{2}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.14.13757744271328447008064363083.1	x^20 - 8x^19 + 20x^18 - 5x^17 - 64x^16 + 169x^15 - 274x^14 + 192x^13 + 204x^12 - 680x^11 + 1106x^10 - 1042x^9 + 322x^8 + 210x^7 - 582x^6 + 543x^5 + 90x^4 - 201x^3 - 9x^2 + 10x + 1	\( -\,3^{7}\cdot 97^{2}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.2.18928607174182451592746237952.1	x^20 + 8x^18 + 25x^16 + 14x^14 - 145x^12 - 366x^10 - 550x^8 + 16x^6 + 46x^4 - 9x^2 - 3	\( -\,2^{20}\cdot 3^{3}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.2.18928607174182451592746237952.2	x^20 + 9x^18 + 36x^16 + 84x^14 + 124x^12 + 115x^10 + 57x^8 - 2x^6 - 23x^4 - 15x^2 - 3	\( -\,2^{20}\cdot 3^{3}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.0.41833721538894852503784084373.1	x^20 - 3x^19 + 10x^18 - 32x^17 + 49x^16 - 135x^15 + 207x^14 - 254x^13 + 561x^12 - 58x^11 + 635x^10 + 514x^9 + 350x^8 + 364x^7 - 114x^6 - 17x^5 - 265x^4 + 137x^3 + 129x^2 - 117x + 27	\( 397^{3}\cdot 401^{8} \)	20T845	$[3]$ (GRH)
20.4.41833721538894852503784084373.1	x^20 - 7x^19 + 19x^18 - 32x^17 + 73x^16 - 218x^15 + 358x^14 - 124x^13 - 500x^12 + 1306x^11 - 1245x^10 + 2081x^9 - 1486x^8 - 101x^7 + 681x^6 - 619x^5 + 431x^4 - 232x^3 + 102x^2 - 26x + 1	\( 397^{3}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.8.41833721538894852503784084373.1	x^20 - 3x^19 - 9x^18 + 43x^17 - 4x^16 - 228x^15 + 245x^14 + 453x^13 - 935x^12 - 283x^11 + 1267x^10 + 40x^9 - 708x^8 - 45x^7 + 184x^6 + 52x^5 + 7x^4 - 11x^3 - 13x^2 - x + 1	\( 397^{3}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.0.41833721538894852503784084373.2	x^20 + 8x^18 + 66x^16 - 87x^15 + 419x^14 - 494x^13 + 1075x^12 - 614x^11 + 722x^10 + 200x^9 + 15x^8 + 391x^7 - 35x^6 + 142x^5 + 49x^4 - 22x^3 + 39x^2 - 9x + 1	\( 397^{3}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.8.126788395124724058080709420032.1	x^20 - 19x^18 + 143x^16 - 593x^14 + 1612x^12 - 2975x^10 + 2897x^8 + 126x^6 - 1733x^4 - 285x^2 + 57	\( 2^{10}\cdot 3^{3}\cdot 19^{3}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.8.126788395124724058080709420032.2	x^20 - 9x^19 + 35x^18 - 76x^17 + 67x^16 + 184x^15 - 860x^14 + 1741x^13 - 2128x^12 + 458x^11 + 4801x^10 - 8525x^9 + 1446x^8 + 8656x^7 - 3982x^6 - 6658x^5 + 4264x^4 + 2724x^3 - 2169x^2 - 360x + 381	\( 2^{10}\cdot 3^{3}\cdot 19^{3}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.4.972074486274347987960137991168.1	x^20 - 2x^19 - 17x^18 + 11x^17 + 104x^16 + 158x^15 - 364x^14 - 1251x^13 + 444x^12 + 2655x^11 - 598x^10 - 2657x^9 + 755x^8 + 1133x^7 - 457x^6 + 92x^5 + 2x^4 - 242x^3 + 122x^2 + 55x - 37	\( 2^{10}\cdot 17^{5}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.2.1114377285977604207653213409723.1	x^20 + 2x^18 - 9x^17 + 23x^16 - 141x^15 + 250x^14 + 144x^13 - 1591x^12 + 4519x^11 - 7998x^10 + 10024x^9 - 9203x^8 + 5630x^7 - 2414x^6 + 1809x^5 - 4613x^4 + 7595x^3 - 7681x^2 + 4573x - 1433	\( -\,3^{11}\cdot 97^{2}\cdot 401^{8} \)	20T845	$[2]$ (GRH)
20.6.1114377285977604207653213409723.1	x^20 - x^19 - 8x^18 - 20x^17 + 50x^16 + 55x^15 + 57x^14 - 207x^13 + 592x^12 - 608x^11 + 174x^10 - 847x^9 + 2218x^8 - 5078x^7 + 2613x^6 + 13752x^5 - 33379x^4 + 38448x^3 - 24415x^2 + 6053x - 359	\( -\,3^{11}\cdot 97^{2}\cdot 401^{8} \)	20T845	$[2]$ (GRH)
20.4.1141095556122516522726384780288.1	x^20 - 9x^19 + 41x^18 - 127x^17 + 252x^16 - 283x^15 - 74x^14 + 1246x^13 - 3238x^12 + 6640x^11 - 10833x^10 + 16742x^9 - 21316x^8 + 25449x^7 - 25410x^6 + 25326x^5 - 20825x^4 + 16167x^3 - 8013x^2 + 1608x + 813	\( 2^{10}\cdot 3^{5}\cdot 19^{3}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.4.1141095556122516522726384780288.2	x^20 - x^19 - 21x^17 - 14x^16 - 85x^15 + 6x^14 - 177x^13 + 91x^12 - 332x^11 + 524x^10 - 159x^9 - 322x^8 + 1033x^7 - 824x^6 + 44x^5 + 150x^4 - 20x^3 - 12x^2 + 1	\( 2^{10}\cdot 3^{5}\cdot 19^{3}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.10.1533217181108778579012445274112.1	x^20 - x^18 - 10x^16 + 16x^14 + 12x^12 - 35x^10 + 21x^8 + 10x^6 - 25x^4 + 15x^2 - 3	\( -\,2^{20}\cdot 3^{7}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.6.1533217181108778579012445274112.1	x^20 + 9x^18 + 16x^16 - 42x^14 - 107x^12 + 26x^10 + 46x^8 - 67x^6 + 35x^4 + 3x^2 - 3	\( -\,2^{20}\cdot 3^{7}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.10.1533217181108778579012445274112.2	x^20 + 2x^16 - 37x^14 + 142x^10 - 86x^8 - 76x^6 + 44x^4 + 12x^2 - 3	\( -\,2^{20}\cdot 3^{7}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.6.1533217181108778579012445274112.2	x^20 + x^18 - 4x^16 - 122x^14 - 334x^12 - 233x^10 + 112x^8 + 186x^6 + 53x^4 - 6x^2 - 3	\( -\,2^{20}\cdot 3^{7}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.0.3444305446176236469450454335488.1	x^20 - 6x^16 + 31x^14 + 12x^12 + 89x^10 - 65x^8 + 22x^6 + 31x^4 - 51x^2 + 17	\( 2^{20}\cdot 17^{3}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.12.3444305446176236469450454335488.1	x^20 - 6x^19 + 3x^18 + 64x^17 - 282x^16 + 704x^15 - 1118x^14 + 984x^13 + 92x^12 - 1700x^11 + 2728x^10 - 4420x^9 + 7505x^8 - 5654x^7 - 3233x^6 + 8202x^5 - 2680x^4 - 2020x^3 + 568x^2 + 114x - 9	\( 2^{20}\cdot 17^{3}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.10.14382957316547706433208621360883.1	x^20 - 10x^19 + 22x^18 + 87x^17 - 427x^16 + 152x^15 + 2019x^14 - 3431x^13 - 1586x^12 + 10205x^11 - 9459x^10 - 5654x^9 + 17810x^8 - 7995x^7 - 6470x^6 + 1546x^5 + 8400x^4 - 7168x^3 + 1728x^2 + 230x - 127	\( -\,3^{5}\cdot 97^{4}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.14.14382957316547706433208621360883.1	x^20 - 10x^18 + 31x^16 + 158x^14 - 2265x^12 + 10815x^10 - 25856x^8 + 31584x^6 - 17283x^4 + 2493x^2 - 27	\( -\,3^{5}\cdot 97^{4}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.4.124758449885036538447790454341632.1	x^20 + 13x^18 + 67x^16 + 161x^14 + 103x^12 - 378x^10 - 992x^8 - 950x^6 - 323x^4 + 26x^2 + 13	\( 2^{20}\cdot 3^{4}\cdot 13^{3}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.8.124758449885036538447790454341632.1	x^20 - 13x^18 + 67x^16 - 161x^14 + 103x^12 + 378x^10 - 992x^8 + 950x^6 - 323x^4 - 26x^2 + 13	\( 2^{20}\cdot 3^{4}\cdot 13^{3}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.10.129446615848929357898877592247947.1	x^20 - 2x^19 - 28x^18 + 78x^17 + 209x^16 - 975x^15 + 345x^14 + 4000x^13 - 7353x^12 + 26x^11 + 10727x^10 - 6050x^9 - 3720x^8 - 6944x^7 + 11829x^6 + 13294x^5 - 6337x^4 - 6160x^3 - 11575x^2 + 3897x + 1129	\( -\,3^{7}\cdot 97^{4}\cdot 401^{8} \)	20T845	$[2]$ (GRH)
20.6.129446615848929357898877592247947.1	x^20 + 2x^18 - 4x^17 - 59x^16 + 329x^15 - 546x^14 - 99x^13 + 816x^12 - 7011x^11 + 9027x^10 - 14854x^9 + 16916x^8 - 10119x^7 + 17874x^6 - 11823x^5 + 16942x^4 - 15102x^3 + 5145x^2 - 1131x - 2661	\( -\,3^{7}\cdot 97^{4}\cdot 401^{8} \)	20T845	$[2]$ (GRH)
20.12.393613485959461667208104449865557.1	x^20 - x^19 - 27x^18 + 16x^17 + 287x^16 - 90x^15 - 1843x^14 + 644x^13 + 8804x^12 - 3820x^11 - 31952x^10 + 15179x^9 + 100191x^8 - 5711x^7 - 175095x^6 - 60509x^5 + 92100x^4 + 56930x^3 + 6417x^2 - 173x + 1	\( 97^{2}\cdot 397^{3}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.8.393613485959461667208104449865557.1	x^20 - 8x^19 + 18x^18 + 49x^17 - 433x^16 + 1090x^15 - 491x^14 - 2271x^13 + 1735x^12 + 7265x^11 - 13225x^10 - 3826x^9 + 19965x^8 + 3271x^7 - 3165x^6 - 7523x^5 + 33345x^4 - 25275x^3 - 47003x^2 - 13767x - 549	\( 97^{2}\cdot 397^{3}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.12.393613485959461667208104449865557.2	x^20 - 7x^19 - 5x^18 + 114x^17 - 125x^16 - 819x^15 + 2259x^14 + 1282x^13 - 14515x^12 + 17719x^11 + 29314x^10 - 89436x^9 + 30771x^8 + 114942x^7 - 111444x^6 - 37021x^5 + 77709x^4 - 7377x^3 - 16655x^2 + 2853x + 647	\( 97^{2}\cdot 397^{3}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.6.735114192454649568937610340990976.1	x^20 - 10x^18 + x^16 + 40x^14 - 603x^12 - 1136x^10 - 138x^8 + 310x^6 + 59x^4 - 16x^2 - 1	\( -\,2^{40}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.6.735114192454649568937610340990976.2	x^20 - 8x^18 - 20x^16 + 302x^14 - 675x^12 - 26x^10 + 1197x^8 - 474x^6 - 401x^4 - 52x^2 - 1	\( -\,2^{40}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.6.735114192454649568937610340990976.3	x^20 - 14x^18 + 35x^16 + 212x^14 - 671x^12 - 1144x^10 + 2231x^8 + 1264x^6 - 684x^4 - 66x^2 - 1	\( -\,2^{40}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.6.735114192454649568937610340990976.4	x^20 - 4x^18 - 13x^16 + 116x^14 - 326x^12 - 172x^10 + 1294x^8 - 244x^6 - 315x^4 - 48x^2 - 1	\( -\,2^{40}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.10.735114192454649568937610340990976.5	x^20 + 14x^18 + 35x^16 - 212x^14 - 671x^12 + 1144x^10 + 2231x^8 - 1264x^6 - 684x^4 + 66x^2 - 1	\( -\,2^{40}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.2.735114192454649568937610340990976.5	x^20 + 16x^18 + 74x^16 + 46x^14 - 185x^12 + 522x^10 + 1330x^8 - 352x^6 - 968x^4 - 62x^2 - 1	\( -\,2^{40}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.10.735114192454649568937610340990976.6	x^20 + 4x^18 - 13x^16 - 116x^14 - 326x^12 + 172x^10 + 1294x^8 + 244x^6 - 315x^4 + 48x^2 - 1	\( -\,2^{40}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.10.735114192454649568937610340990976.7	x^20 + 10x^18 + x^16 - 40x^14 - 603x^12 + 1136x^10 - 138x^8 - 310x^6 + 59x^4 + 16x^2 - 1	\( -\,2^{40}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.8.3526968776884466144717265239539712.1	x^20 - 12x^18 - 64x^16 + 618x^14 + 1452x^12 - 6438x^10 - 7427x^8 + 10560x^6 + 13306x^4 + 2720x^2 + 153	\( 2^{30}\cdot 17^{3}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.12.6593371018023678808268905753944157.1	x^20 - 8x^19 + 11x^18 + 29x^17 - 72x^16 + 237x^15 - 310x^14 - 901x^13 + 1075x^12 - 2452x^11 + 3035x^10 + 10258x^9 - 12838x^8 - 8195x^7 + 14408x^6 + 6508x^5 - 7671x^4 - 2630x^3 + 1993x^2 + 332x - 193	\( 397^{5}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.4.6593371018023678808268905753944157.1	x^20 - 7x^19 + 45x^18 - 141x^17 + 582x^16 - 1090x^15 + 3580x^14 - 4118x^13 + 12022x^12 - 7451x^11 + 20480x^10 - 4272x^9 + 2690x^8 - 1925x^7 - 57973x^6 - 25696x^5 - 96742x^4 - 50445x^3 - 36839x^2 - 22491x + 21929	\( 397^{5}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.12.6593371018023678808268905753944157.2	x^20 - 10x^19 + 21x^18 + 81x^17 - 371x^16 + 98x^15 + 2306x^14 - 3882x^13 - 9644x^12 + 18414x^11 + 37347x^10 - 23785x^9 - 87556x^8 - 43734x^7 + 41876x^6 + 74464x^5 + 74186x^4 + 44571x^3 + 2095x^2 - 5386x + 487	\( 397^{5}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.0.6593371018023678808268905753944157.3	x^20 - 6x^19 + 31x^18 - 152x^17 + 706x^16 - 2906x^15 + 9830x^14 - 25769x^13 + 53282x^12 - 89868x^11 + 128026x^10 - 134825x^9 + 131311x^8 - 127579x^7 + 108632x^6 - 43565x^5 + 21600x^4 - 11684x^3 + 8365x^2 + 588x + 153	\( 397^{5}\cdot 401^{8} \)	20T845	$[2]$ (GRH)