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
20.0.5423033725190914100428800.1	x^20 - 10x^19 + 53x^18 - 192x^17 + 522x^16 - 1116x^15 + 1918x^14 - 2668x^13 + 2982x^12 - 2604x^11 + 1656x^10 - 608x^9 - 59x^8 + 206x^7 - 73x^6 - 42x^5 + 45x^4 - 8x^3 - 5x^2 + 2x + 1	\( 2^{20}\cdot 3^{12}\cdot 5^{2}\cdot 17\cdot 389^{4} \)	20T925	Trivial (GRH)
20.0.48807303526718226903859200.1	x^20 + x^18 - 2x^17 - 6x^16 + 4x^15 + 30x^14 - 36x^13 - 15x^12 + 12x^11 + 48x^10 + 12x^9 - 123x^8 + 36x^7 + 153x^6 - 124x^5 - 66x^4 + 110x^3 - 11x^2 - 30x + 10	\( 2^{20}\cdot 3^{14}\cdot 5^{2}\cdot 17\cdot 389^{4} \)	20T925	$[2]$
20.2.22958077665869824000000000000.1	x^20 - 6x^18 + 21x^16 - 52x^14 + 77x^12 - 34x^10 + 179x^8 - 228x^6 + 83x^4 - 6x^2 - 1	\( -\,2^{50}\cdot 5^{12}\cdot 17^{4} \)	20T925	Trivial (GRH)
20.2.22958077665869824000000000000.2	x^20 + 6x^18 + 21x^16 + 52x^14 + 77x^12 + 34x^10 + 179x^8 + 228x^6 + 83x^4 + 6x^2 - 1	\( -\,2^{50}\cdot 5^{12}\cdot 17^{4} \)	20T925	Trivial (GRH)
20.6.192756121600000000000000000000.1	x^20 - 10x^18 + 15x^16 + 170x^14 - 910x^12 + 1726x^10 + 655x^8 - 9940x^6 + 14560x^4 - 1960x^2 - 49	\( -\,2^{34}\cdot 5^{20}\cdot 7^{6} \)	20T925	Trivial (GRH)
20.0.369961078353821696000000000000.1	x^20 - 10x^18 + 30x^16 - 40x^14 + 115x^12 - 230x^10 - 40x^9 + 450x^8 - 160x^7 - 100x^6 + 88x^5 - 135x^4 + 80x^3 + 10x^2 - 40x + 28	\( 2^{46}\cdot 5^{12}\cdot 7^{4}\cdot 8969 \)	20T925	Trivial (GRH)
20.0.413849871682895872000000000000.1	x^20 + 10x^18 + 50x^16 + 120x^14 + 115x^12 - 226x^10 - 40x^9 - 290x^8 - 480x^7 + 1100x^6 - 1512x^5 + 3425x^4 - 1360x^3 + 750x^2 - 200x + 56	\( 2^{46}\cdot 5^{12}\cdot 7^{4}\cdot 79\cdot 127 \)	20T925	Trivial (GRH)
20.10.1007052390400000000000000000000.1	x^20 - 10x^18 + 35x^16 - 40x^14 - 35x^12 + 96x^10 - 5x^8 - 70x^6 + 5x^4 + 20x^2 - 4	\( -\,2^{42}\cdot 5^{20}\cdot 7^{4} \)	20T925	Trivial (GRH)
20.2.1007052390400000000000000000000.1	x^20 + 10x^18 + 35x^16 + 40x^14 - 35x^12 - 96x^10 - 5x^8 + 70x^6 + 5x^4 - 20x^2 - 4	\( -\,2^{42}\cdot 5^{20}\cdot 7^{4} \)	20T925	Trivial (GRH)
20.6.1007052390400000000000000000000.1	x^20 - 10x^18 + 5x^16 + 100x^14 - 95x^12 + 214x^10 + 1255x^8 + 1360x^6 + 475x^4 + 10x^2 - 1	\( -\,2^{42}\cdot 5^{20}\cdot 7^{4} \)	20T925	Trivial (GRH)
20.10.1007052390400000000000000000000.2	x^20 - 10x^18 + 15x^16 + 120x^14 - 435x^12 + 456x^10 - 105x^8 + 70x^6 - 215x^4 + 120x^2 - 16	\( -\,2^{42}\cdot 5^{20}\cdot 7^{4} \)	20T925	Trivial (GRH)
20.2.1007052390400000000000000000000.2	x^20 + 10x^18 + 15x^16 - 120x^14 - 435x^12 - 456x^10 - 105x^8 - 70x^6 - 215x^4 - 120x^2 - 16	\( -\,2^{42}\cdot 5^{20}\cdot 7^{4} \)	20T925	Trivial (GRH)
20.6.1007052390400000000000000000000.2	x^20 + 10x^18 + 25x^16 - 60x^14 - 470x^12 - 1014x^10 - 720x^8 + 300x^6 + 305x^4 + 20x^2 - 4	\( -\,2^{42}\cdot 5^{20}\cdot 7^{4} \)	20T925	Trivial (GRH)
20.6.1007052390400000000000000000000.3	x^20 - 10x^18 + 25x^16 + 60x^14 - 470x^12 + 1014x^10 - 720x^8 - 300x^6 + 305x^4 - 20x^2 - 4	\( -\,2^{42}\cdot 5^{20}\cdot 7^{4} \)	20T925	Trivial (GRH)
20.12.1349292851200000000000000000000.1	x^20 - 20x^18 - 20x^17 + 115x^16 + 188x^15 - 60x^14 + 20x^13 - 150x^12 - 3060x^11 - 5252x^10 + 960x^9 + 10915x^8 + 11800x^7 + 4220x^6 - 1196x^5 - 1390x^4 - 280x^3 + 50x^2 + 20x + 1	\( 2^{34}\cdot 5^{20}\cdot 7^{7} \)	20T925	Trivial (GRH)
20.8.1349292851200000000000000000000.1	x^20 - 10x^17 + 10x^16 + 14x^15 + 55x^14 + 160x^13 - 150x^12 + 30x^11 - 1821x^10 + 2060x^9 - 1635x^8 + 820x^7 + 2350x^6 - 2726x^5 + 245x^4 + 540x^3 - 80x^2 - 40x - 1	\( 2^{34}\cdot 5^{20}\cdot 7^{7} \)	20T925	Trivial (GRH)
20.4.2219560225793376256000000000000.1	x^20 + 10x^18 + 50x^16 + 120x^14 + 115x^12 - 250x^10 - 40x^9 - 1010x^8 - 480x^7 - 3100x^6 - 1512x^5 - 3775x^4 - 1360x^3 - 2250x^2 - 200x + 8	\( 2^{46}\cdot 5^{12}\cdot 7^{5}\cdot 7687 \)	20T925	Trivial (GRH)
20.4.2302387948542230528000000000000.1	x^20 - 10x^18 + 30x^16 - 40x^14 + 115x^12 - 254x^10 - 40x^9 - 30x^8 - 160x^7 - 460x^6 + 88x^5 + 585x^4 + 80x^3 - 110x^2 - 40x + 28	\( 2^{46}\cdot 5^{12}\cdot 7^{4}\cdot 55817 \)	20T925	Trivial (GRH)
20.0.7049366732800000000000000000000.1	x^20 + 20x^18 + 140x^16 + 540x^14 + 1445x^12 + 2610x^10 + 2890x^8 + 1850x^6 + 645x^4 + 110x^2 + 7	\( 2^{42}\cdot 5^{20}\cdot 7^{5} \)	20T925	$[2]$ (GRH)
20.12.7049366732800000000000000000000.1	x^20 - 20x^18 + 140x^16 - 540x^14 + 1445x^12 - 2610x^10 + 2890x^8 - 1850x^6 + 645x^4 - 110x^2 + 7	\( 2^{42}\cdot 5^{20}\cdot 7^{5} \)	20T925	Trivial (GRH)
20.4.7049366732800000000000000000000.1	x^20 - 20x^16 - 10x^14 + 130x^12 + 88x^10 - 475x^8 - 830x^6 - 435x^4 - 20x^2 + 28	\( 2^{42}\cdot 5^{20}\cdot 7^{5} \)	20T925	Trivial (GRH)
20.8.7049366732800000000000000000000.1	x^20 - 20x^16 + 10x^14 + 130x^12 - 88x^10 - 475x^8 + 830x^6 - 435x^4 + 20x^2 + 28	\( 2^{42}\cdot 5^{20}\cdot 7^{5} \)	20T925	Trivial (GRH)
20.4.7049366732800000000000000000000.2	x^20 + 10x^18 + 15x^16 - 120x^14 - 435x^12 - 292x^10 + 715x^8 + 1430x^6 + 1005x^4 + 300x^2 + 28	\( 2^{42}\cdot 5^{20}\cdot 7^{5} \)	20T925	Trivial (GRH)
20.8.7049366732800000000000000000000.2	x^20 - 10x^18 + 15x^16 - 10x^14 + 30x^12 + 190x^10 - 265x^8 - 420x^6 + 220x^4 + 160x^2 + 7	\( 2^{42}\cdot 5^{20}\cdot 7^{5} \)	20T925	Trivial (GRH)
20.4.7049366732800000000000000000000.3	x^20 + 20x^18 + 160x^16 + 670x^14 + 1630x^12 + 2420x^10 + 2125x^8 + 850x^6 - 115x^4 - 180x^2 + 28	\( 2^{42}\cdot 5^{20}\cdot 7^{5} \)	20T925	Trivial (GRH)
20.10.8496140374773858304000000000000.1	x^20 - 24x^18 + 214x^16 - 800x^14 + 611x^12 + 2820x^10 - 2314x^8 - 6460x^6 - 3551x^4 - 604x^2 - 4	\( -\,2^{34}\cdot 5^{12}\cdot 1193^{4} \)	20T925	Trivial (GRH)
20.6.8496140374773858304000000000000.1	x^20 - 4x^19 - 2x^18 - 8x^17 + 75x^16 + 108x^15 - 216x^14 - 490x^13 - 783x^12 + 1436x^11 + 3404x^10 - 2164x^9 - 2526x^8 + 1226x^7 - 1567x^6 + 212x^5 + 894x^4 + 198x^3 + 13x^2 + 142x + 17	\( -\,2^{34}\cdot 5^{12}\cdot 1193^{4} \)	20T925	Trivial (GRH)
20.10.8496140374773858304000000000000.2	x^20 + 4x^18 - 76x^16 - 274x^14 + 990x^12 + 3120x^10 - 3919x^8 - 9866x^6 + 5805x^4 + 9068x^2 - 2116	\( -\,2^{34}\cdot 5^{12}\cdot 1193^{4} \)	20T925	Trivial (GRH)
20.6.8496140374773858304000000000000.2	x^20 - 6x^19 + 21x^18 - 38x^17 + 40x^16 + 4x^15 - 235x^14 + 878x^13 - 1254x^12 + 576x^11 + 32x^10 - 1748x^9 + 4933x^8 - 3182x^7 - 3876x^6 + 5760x^5 - 1009x^4 - 1748x^3 + 818x^2 + 32x - 49	\( -\,2^{34}\cdot 5^{12}\cdot 1193^{4} \)	20T925	Trivial (GRH)
20.2.9445049958400000000000000000000.1	x^20 + 10x^18 - 5x^16 - 120x^14 + 645x^12 + 672x^10 - 6965x^8 + 11270x^6 + 2205x^4 - 20580x^2 - 9604	\( -\,2^{34}\cdot 5^{20}\cdot 7^{8} \)	20T925	$[2]$ (GRH)
20.10.16112838246400000000000000000000.1	x^20 - 10x^18 + 65x^16 - 260x^14 + 570x^12 - 778x^10 + 640x^8 - 260x^6 + 15x^4 + 20x^2 - 4	\( -\,2^{46}\cdot 5^{20}\cdot 7^{4} \)	20T925	Trivial (GRH)
20.2.16112838246400000000000000000000.1	x^20 + 10x^18 + 15x^16 - 30x^14 + 30x^12 - 102x^10 - 415x^8 + 900x^6 - 440x^4 - 60x^2 - 1	\( -\,2^{46}\cdot 5^{20}\cdot 7^{4} \)	20T925	Trivial (GRH)
20.10.16112838246400000000000000000000.2	x^20 - 20x^18 + 150x^16 - 520x^14 + 730x^12 + 266x^10 - 1670x^8 + 720x^6 + 220x^4 + 60x^2 - 49	\( -\,2^{46}\cdot 5^{20}\cdot 7^{4} \)	20T925	Trivial (GRH)
20.0.112789867724800000000000000000000.1	x^20 + 20x^18 + 140x^16 + 640x^14 + 2095x^12 + 4210x^10 + 4690x^8 + 2710x^6 + 765x^4 + 110x^2 + 7	\( 2^{46}\cdot 5^{20}\cdot 7^{5} \)	20T925	$[2]$ (GRH)
20.4.112789867724800000000000000000000.1	x^20 - 50x^16 - 40x^14 + 415x^12 + 774x^10 + 600x^8 + 1210x^6 + 725x^4 + 130x^2 + 7	\( 2^{46}\cdot 5^{20}\cdot 7^{5} \)	20T925	Trivial (GRH)
20.8.112789867724800000000000000000000.1	x^20 - 50x^16 - 80x^14 + 380x^12 + 506x^10 - 630x^8 - 860x^6 - 230x^4 - 180x^2 + 7	\( 2^{46}\cdot 5^{20}\cdot 7^{5} \)	20T925	Trivial (GRH)
20.10.212403509369346457600000000000000.1	x^20 - 2x^19 - 21x^18 + 18x^17 + 213x^16 + 50x^15 - 1204x^14 - 1312x^13 + 3017x^12 + 7012x^11 + 1460x^10 - 12366x^9 - 20583x^8 - 7546x^7 + 16659x^6 + 22110x^5 + 6743x^4 - 5936x^3 - 5114x^2 - 404x + 446	\( -\,2^{34}\cdot 5^{14}\cdot 1193^{4} \)	20T925	Trivial (GRH)
20.14.212403509369346457600000000000000.1	x^20 - 4x^18 - 74x^16 + 520x^14 - 730x^12 - 1470x^10 + 3190x^8 + 300x^6 - 1050x^4 + 300x^2 - 25	\( -\,2^{34}\cdot 5^{14}\cdot 1193^{4} \)	20T925	Trivial (GRH)
20.10.2175011935942107725824000000000000.1	x^20 - 86x^16 - 104x^14 + 1666x^12 + 1958x^10 - 7414x^8 - 7716x^6 + 8754x^4 + 6768x^2 - 529	\( -\,2^{42}\cdot 5^{12}\cdot 1193^{4} \)	20T925	Trivial (GRH)
20.14.2175011935942107725824000000000000.1	x^20 - 14x^18 + 23x^16 + 232x^14 - 839x^12 + 504x^10 + 887x^8 - 742x^6 - 131x^4 + 76x^2 - 4	\( -\,2^{42}\cdot 5^{12}\cdot 1193^{4} \)	20T925	Trivial (GRH)
20.6.2175011935942107725824000000000000.1	x^20 + 12x^18 + 44x^16 + 20x^14 - 183x^12 - 274x^10 + 46x^8 + 190x^6 + 53x^4 - 2x^2 - 1	\( -\,2^{42}\cdot 5^{12}\cdot 1193^{4} \)	20T925	Trivial (GRH)
20.14.2175011935942107725824000000000000.2	x^20 - 20x^18 + 82x^16 + 216x^14 - 1730x^12 + 1878x^10 + 2758x^8 - 3976x^6 - 230x^4 + 1344x^2 - 289	\( -\,2^{42}\cdot 5^{12}\cdot 1193^{4} \)	20T925	Trivial (GRH)
20.6.2175011935942107725824000000000000.2	x^20 + 12x^18 + 12x^16 - 220x^14 - 367x^12 + 1262x^10 + 2198x^8 - 1970x^6 - 3963x^4 - 1298x^2 - 49	\( -\,2^{42}\cdot 5^{12}\cdot 1193^{4} \)	20T925	Trivial (GRH)
20.14.2175011935942107725824000000000000.3	x^20 - 12x^18 + 12x^16 + 220x^14 - 367x^12 - 1262x^10 + 2198x^8 + 1970x^6 - 3963x^4 + 1298x^2 - 49	\( -\,2^{42}\cdot 5^{12}\cdot 1193^{4} \)	20T925	Trivial (GRH)
20.8.13186009861649028087808000000000000.1	x^20 + 2x^18 - 8x^17 - 40x^16 + 224x^15 - 396x^14 + 12x^13 + 635x^12 + 4928x^11 + 2368x^10 - 50860x^9 + 96318x^8 - 27684x^7 - 248298x^6 + 481528x^5 - 336023x^4 - 92876x^3 + 134326x^2 - 11392x - 2209	\( 2^{38}\cdot 5^{12}\cdot 97\cdot 1193^{4} \)	20T925	Trivial (GRH)
20.2.34800190975073723613184000000000000.1	x^20 + 24x^18 + 232x^16 + 1138x^14 + 2826x^12 + 2292x^10 - 4897x^8 - 14338x^6 - 14661x^4 - 6748x^2 - 1156	\( -\,2^{46}\cdot 5^{12}\cdot 1193^{4} \)	20T925	$[2]$ (GRH)
20.2.34800190975073723613184000000000000.2	x^20 + 22x^18 + 187x^16 + 784x^14 + 1712x^12 + 1866x^10 + 748x^8 - 224x^6 - 257x^4 - 60x^2 - 4	\( -\,2^{46}\cdot 5^{12}\cdot 1193^{4} \)	20T925	$[2]$ (GRH)
20.12.52744039446596112351232000000000000.1	x^20 - 40x^18 - 16x^17 + 587x^16 + 400x^15 - 3874x^14 - 3156x^13 + 11528x^12 + 7340x^11 - 16672x^10 + 11480x^9 + 52793x^8 - 8592x^7 - 94656x^6 - 35332x^5 + 52202x^4 + 19460x^3 + 140x^2 + 5376x + 1423	\( 2^{40}\cdot 5^{12}\cdot 97\cdot 1193^{4} \)	20T925	Trivial (GRH)
20.18.139200763900294894452736000000000000.1	x^20 - 24x^18 + 232x^16 - 1138x^14 + 2826x^12 - 2292x^10 - 4897x^8 + 14338x^6 - 14661x^4 + 6748x^2 - 1156	\( -\,2^{48}\cdot 5^{12}\cdot 1193^{4} \)	20T925	Trivial (GRH)
20.18.139200763900294894452736000000000000.2	x^20 - 22x^18 + 187x^16 - 784x^14 + 1712x^12 - 1866x^10 + 748x^8 + 224x^6 - 257x^4 + 60x^2 - 4	\( -\,2^{48}\cdot 5^{12}\cdot 1193^{4} \)	20T925	Trivial (GRH)