Global number field search results

Further refine search

Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying all 36 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.1837451426888215601086464.1	x^20 + 6x^18 - 4x^17 + 15x^16 - 28x^15 + 47x^14 - 104x^13 + 153x^12 - 198x^11 + 202x^10 - 106x^9 - 23x^8 + 128x^7 - 165x^6 + 98x^5 - x^4 - 38x^3 + 26x^2 - 8x + 1	\( 2^{24}\cdot 3^{14}\cdot 389^{4} \)	20T872	Trivial
20.0.16537062841993940409778176.1	x^20 - 2x^17 - x^16 + 12x^15 + 5x^14 - 112x^13 + 313x^12 - 448x^11 + 442x^10 - 380x^9 + 265x^8 - 104x^7 + 5x^6 + 18x^5 - x^4 - 4x^3 + 1	\( 2^{24}\cdot 3^{16}\cdot 389^{4} \)	20T872	$[2]$
20.0.22958077665869824000000000000.1	x^20 + 6x^18 - 5x^16 - 28x^14 + 69x^12 - 30x^10 - 75x^8 + 28x^6 + 51x^4 - 2x^2 + 1	\( 2^{50}\cdot 5^{12}\cdot 17^{4} \)	20T872	Trivial (GRH)
20.0.22958077665869824000000000000.2	x^20 + 16x^18 + 94x^16 + 268x^14 + 447x^12 + 524x^10 + 446x^8 + 172x^6 - 47x^4 - 24x^2 + 16	\( 2^{50}\cdot 5^{12}\cdot 17^{4} \)	20T872	Trivial (GRH)
20.8.48189030400000000000000000000.1	x^20 - 10x^18 - 10x^17 - 35x^16 - 90x^15 + 15x^14 + 320x^13 + 345x^12 + 200x^11 + 320x^10 + 200x^9 + 345x^8 + 320x^7 + 15x^6 - 90x^5 - 35x^4 - 10x^3 - 10x^2 + 1	\( 2^{32}\cdot 5^{20}\cdot 7^{6} \)	20T872	Trivial (GRH)
20.4.251763097600000000000000000000.1	x^20 - 10x^18 - 20x^17 + 20x^16 + 160x^15 + 200x^14 - 240x^13 - 1005x^12 - 960x^11 + 800x^10 + 2640x^9 + 1900x^8 - 720x^7 - 1770x^6 - 348x^5 + 805x^4 + 480x^3 + 20x^2 - 40x - 7	\( 2^{40}\cdot 5^{20}\cdot 7^{4} \)	20T872	Trivial (GRH)
20.8.251763097600000000000000000000.1	x^20 - 10x^18 + 35x^16 - 40x^14 - 35x^12 + 112x^10 - 85x^8 + 10x^6 + 85x^4 - 60x^2 + 4	\( 2^{40}\cdot 5^{20}\cdot 7^{4} \)	20T872	Trivial (GRH)
20.4.251763097600000000000000000000.2	x^20 + 10x^18 + 25x^16 - 30x^14 - 150x^12 + 34x^10 + 195x^8 - 30x^4 + 1	\( 2^{40}\cdot 5^{20}\cdot 7^{4} \)	20T872	Trivial (GRH)
20.8.1204725760000000000000000000000.1	x^20 - 10x^18 - 20x^17 + 35x^16 + 254x^15 - 80x^14 - 1150x^13 + 50x^12 + 3200x^11 - 1903x^10 - 4250x^9 + 9105x^8 + 3710x^7 - 21200x^6 - 5224x^5 + 24195x^4 + 4360x^3 - 8620x^2 + 960x - 4	\( 2^{32}\cdot 5^{22}\cdot 7^{6} \)	20T872	$[2]$ (GRH)
20.12.2124035093693464576000000000000.1	x^20 - 2x^19 - 17x^18 + 42x^17 + 84x^16 - 296x^15 + 71x^14 + 632x^13 - 1743x^12 + 1738x^11 + 4665x^10 - 10652x^9 - 2699x^8 + 18856x^7 - 4906x^6 - 14092x^5 + 6428x^4 + 4212x^3 - 1931x^2 - 486x + 97	\( 2^{32}\cdot 5^{12}\cdot 1193^{4} \)	20T872	Trivial (GRH)
20.8.2124035093693464576000000000000.1	x^20 - 4x^19 + 4x^18 + 8x^17 - 33x^16 + 28x^15 + 18x^14 + 52x^13 - 315x^12 + 428x^11 + 414x^10 - 1988x^9 + 2186x^8 - 488x^7 - 1160x^6 + 1440x^5 - 648x^4 - 160x^3 + 384x^2 - 192x + 32	\( 2^{32}\cdot 5^{12}\cdot 1193^{4} \)	20T872	Trivial (GRH)
20.4.4826935829249130496000000000000.1	x^20 - 6x^18 + 12x^16 - 16x^15 - 28x^14 + 20x^13 - 18x^12 - 40x^11 + 76x^10 + 12x^9 - 78x^8 + 32x^7 - 116x^6 - 36x^5 + 29x^4 - 56x^3 + 26x^2 - 12x + 2	\( 2^{48}\cdot 5^{12}\cdot 17^{4}\cdot 29^{2} \)	20T872	Trivial (GRH)
20.8.6294077440000000000000000000000.1	x^20 - 10x^18 + 25x^16 + 130x^14 - 1010x^12 + 2210x^10 + 1375x^8 - 17000x^6 + 36650x^4 - 35400x^2 + 13225	\( 2^{40}\cdot 5^{22}\cdot 7^{4} \)	20T872	$[2]$ (GRH)
20.4.15241120055446994944000000000000.1	x^20 - 6x^19 + 7x^18 - 24x^17 + 172x^16 - 236x^15 + 142x^14 - 952x^13 + 2419x^12 - 962x^11 - 4619x^10 + 4248x^9 + 3596x^8 - 5268x^7 - 4330x^6 + 4472x^5 + 7760x^4 + 5120x^3 + 1924x^2 + 544x + 64	\( 2^{38}\cdot 5^{12}\cdot 17^{6}\cdot 97^{2} \)	20T872	Trivial (GRH)
20.0.16112838246400000000000000000000.1	x^20 + 10x^18 + 25x^16 - 40x^14 - 235x^12 - 176x^10 + 385x^8 + 710x^6 + 425x^4 + 120x^2 + 16	\( 2^{46}\cdot 5^{20}\cdot 7^{4} \)	20T872	Trivial (GRH)
20.12.53100877342336614400000000000000.1	x^20 + 14x^18 - 53x^16 - 588x^14 + 985x^12 + 1948x^10 - 3413x^8 - 434x^6 + 2381x^4 - 940x^2 + 100	\( 2^{32}\cdot 5^{14}\cdot 1193^{4} \)	20T872	$[2]$ (GRH)
20.8.53100877342336614400000000000000.1	x^20 - 2x^19 - 19x^18 - 18x^17 + 69x^16 + 238x^15 + 308x^14 + 22x^13 - 679x^12 - 1464x^11 - 1812x^10 - 1464x^9 - 679x^8 + 22x^7 + 308x^6 + 238x^5 + 69x^4 - 18x^3 - 19x^2 - 2x + 1	\( 2^{32}\cdot 5^{14}\cdot 1193^{4} \)	20T872	$[2]$ (GRH)
20.12.151120799334400000000000000000000.1	x^20 - 20x^18 - 20x^17 + 95x^16 + 296x^15 + 330x^14 - 1280x^13 - 2460x^12 + 1040x^11 + 5036x^10 + 6000x^9 - 18265x^8 + 16560x^7 - 10240x^6 + 784x^5 + 2330x^4 - 520x^3 - 100x^2 + 20x + 1	\( 2^{38}\cdot 5^{20}\cdot 7^{8} \)	20T872	Trivial (GRH)
20.4.151120799334400000000000000000000.1	x^20 - 20x^16 - 180x^14 - 860x^12 - 1526x^10 - 700x^8 - 980x^6 - 2940x^4 + 2401	\( 2^{38}\cdot 5^{20}\cdot 7^{8} \)	20T872	Trivial (GRH)
20.0.257805411942400000000000000000000.1	x^20 + 40x^14 + 5x^12 + 2x^10 + 900x^8 + 1750x^6 + 965x^4 + 130x^2 + 1	\( 2^{50}\cdot 5^{20}\cdot 7^{4} \)	20T872	Trivial (GRH)
20.16.543752983985526931456000000000000.1	x^20 - 32x^18 - 16x^17 + 361x^16 + 344x^15 - 1776x^14 - 2612x^13 + 3440x^12 + 8312x^11 - 122x^10 - 10700x^9 - 5244x^8 + 6088x^7 + 4092x^6 - 3992x^5 - 4287x^4 - 784x^3 + 290x^2 + 84x + 2	\( 2^{40}\cdot 5^{12}\cdot 1193^{4} \)	20T872	Trivial (GRH)
20.12.789529074073600000000000000000000.1	x^20 - 20x^18 + 150x^16 - 560x^14 + 1150x^12 - 1354x^10 + 1000x^8 - 1220x^6 + 3200x^4 - 4620x^2 + 2401	\( 2^{46}\cdot 5^{20}\cdot 7^{6} \)	20T872	Trivial (GRH)
20.4.789529074073600000000000000000000.1	x^20 + 10x^18 - 5x^16 - 140x^14 - 20x^12 - 306x^10 + 920x^8 + 1740x^6 + 3945x^4 + 4760x^2 + 784	\( 2^{46}\cdot 5^{20}\cdot 7^{6} \)	20T872	Trivial (GRH)
20.4.2241999772057600000000000000000000.1	x^20 - 140x^16 - 300x^14 + 740x^12 + 3004x^10 + 3700x^8 + 2120x^6 + 600x^4 + 80x^2 + 4	\( 2^{48}\cdot 5^{20}\cdot 17^{4} \)	20T872	Trivial (GRH)
20.8.2241999772057600000000000000000000.1	x^20 - 120x^16 + 80x^14 + 1400x^12 + 136x^10 - 4480x^8 - 2560x^6 + 2640x^4 + 1760x^2 + 16	\( 2^{48}\cdot 5^{20}\cdot 17^{4} \)	20T872	Trivial (GRH)
20.16.3398456149909543321600000000000000.2	x^20 - 42x^18 + 699x^16 - 5940x^14 + 27365x^12 - 65710x^10 + 67485x^8 - 4500x^6 - 21325x^4 - 3450x^2 + 25	\( 2^{38}\cdot 5^{14}\cdot 1193^{4} \)	20T872	Trivial (GRH)
20.4.3398456149909543321600000000000000.2	x^20 + 14x^18 - 20x^17 + 50x^16 - 120x^15 + 134x^14 - 420x^13 + 144x^12 - 720x^11 + 452x^10 - 800x^9 + 543x^8 - 40x^7 + 1190x^6 - 360x^5 - 577x^4 - 320x^3 + 618x^2 + 280x - 200	\( 2^{38}\cdot 5^{14}\cdot 1193^{4} \)	20T872	Trivial (GRH)
20.8.34800190975073723613184000000000000.1	x^20 + 12x^18 + 8x^16 - 356x^14 - 1109x^12 + 1538x^10 + 9852x^8 + 10746x^6 + 1129x^4 - 1358x^2 + 1	\( 2^{46}\cdot 5^{12}\cdot 1193^{4} \)	20T872	Trivial (GRH)
20.0.139200763900294894452736000000000000.1	x^20 + 28x^18 + 314x^16 + 1880x^14 + 6691x^12 + 14790x^10 + 20412x^8 + 17026x^6 + 7835x^4 + 1574x^2 + 49	\( 2^{48}\cdot 5^{12}\cdot 1193^{4} \)	20T872	$[2, 394]$ (GRH)
20.0.573951941646745600000000000000000000.1	x^20 + 30x^18 + 375x^16 + 2560x^14 + 10520x^12 + 26988x^10 + 43240x^8 + 41920x^6 + 22875x^4 + 6070x^2 + 529	\( 2^{56}\cdot 5^{20}\cdot 17^{4} \)	20T872	$[1104]$ (GRH)
20.20.1368902819004704358400000000000000000000.1	x^20 - 90x^18 - 40x^17 + 2760x^16 + 1840x^15 - 37030x^14 - 33060x^13 + 232690x^12 + 237960x^11 - 680984x^10 - 627620x^9 + 1085935x^8 + 672640x^7 - 970350x^6 - 197964x^5 + 399385x^4 - 70720x^3 - 20390x^2 + 4900x + 34	\( 2^{40}\cdot 5^{20}\cdot 97^{2}\cdot 193^{4} \)	20T872	Trivial (GRH)
20.20.6096448022178797977600000000000000000000.1	x^20 - 90x^18 - 40x^17 + 3080x^16 + 2280x^15 - 52700x^14 - 52020x^13 + 490950x^12 + 581720x^11 - 2506780x^10 - 3253820x^9 + 6840010x^8 + 8539280x^7 - 10571900x^6 - 10171560x^5 + 9821380x^4 + 4761040x^3 - 4563040x^2 - 327680x + 514706	\( 2^{48}\cdot 5^{20}\cdot 17^{6}\cdot 97^{2} \)	20T872	Trivial (GRH)
20.12.270099487931191892377600000000000000000000.1	x^20 - 30x^18 + 175x^16 + 1800x^14 - 17330x^12 + 13048x^10 + 159250x^8 - 205800x^6 - 228095x^4 + 168070x^2 + 117649	\( 2^{58}\cdot 5^{20}\cdot 7^{6}\cdot 17^{4} \)	20T872	Trivial (GRH)
20.4.2895165532916258147798358163456000000000000.1	x^20 + 44x^18 + 456x^16 + 140x^14 - 19878x^12 - 94388x^10 - 23716x^8 + 864360x^6 + 2324168x^4 + 2151296x^2 + 470596	\( 2^{58}\cdot 5^{12}\cdot 7^{6}\cdot 769^{4} \)	20T872	$[2]$ (GRH)
20.12.6752487198279797309440000000000000000000000.1	x^20 + 20x^18 - 3590x^16 + 68240x^14 + 66910x^12 - 7141820x^10 + 11872700x^8 + 199488800x^6 - 201203800x^4 - 652111600x^2 + 576480100	\( 2^{58}\cdot 5^{22}\cdot 7^{6}\cdot 17^{4} \)	20T872	$[2]$ (GRH)
20.4.72379138322906453694958954086400000000000000.1	x^20 + 78x^18 + 1381x^16 - 24096x^14 - 1118946x^12 - 14722988x^10 - 85646316x^8 - 211359344x^6 - 201345459x^4 - 58320290x^2 + 2941225	\( 2^{58}\cdot 5^{14}\cdot 7^{6}\cdot 769^{4} \)	20T872	$[2, 2]$ (GRH)