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 all 23 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.4.26180786556913794244673536.7	x^20 - 4x^18 + 7x^16 - 20x^14 + 77x^12 - 138x^10 + 105x^8 - 60x^6 + 22x^4 - 4x^2 + 1	\( 2^{40}\cdot 47^{8} \)	20T324	Trivial (GRH)
20.4.26180786556913794244673536.8	x^20 - 6x^18 + 14x^16 - 16x^14 + 6x^12 - 22x^10 + 63x^8 - 68x^6 + 36x^4 - 10x^2 + 1	\( 2^{40}\cdot 47^{8} \)	20T324	Trivial (GRH)
20.0.26180786556913794244673536.9	x^20 + 4x^18 + 7x^16 + 20x^14 + 77x^12 + 138x^10 + 105x^8 + 60x^6 + 22x^4 + 4x^2 + 1	\( 2^{40}\cdot 47^{8} \)	20T324	Trivial (GRH)
20.0.26180786556913794244673536.10	x^20 + 6x^18 + 14x^16 + 16x^14 + 6x^12 + 22x^10 + 63x^8 + 68x^6 + 36x^4 + 10x^2 + 1	\( 2^{40}\cdot 47^{8} \)	20T324	Trivial (GRH)
20.4.545383254783122586260848117921.2	x^20 - 8x^18 - 9x^17 + 13x^16 + 166x^15 + 5x^14 - 971x^13 + 131x^12 + 2424x^11 + 448x^10 - 3591x^9 - 5712x^8 + 8026x^7 + 12602x^6 - 17257x^5 - 9296x^4 + 21397x^3 - 7953x^2 - 1230x + 823	\( 13^{8}\cdot 401^{8} \)	20T324	Trivial (GRH)
20.4.18232983695318565156084788494336.1	x^20 - 16x^16 - x^14 + 80x^12 + 34x^10 - 99x^8 - 84x^6 - 38x^4 - 9x^2 + 4	\( 2^{20}\cdot 1429^{8} \)	20T324	Trivial (GRH)
20.4.92169770058347717078083331928649.2	x^20 - 2x^19 + 11x^18 - 18x^17 + 50x^16 - 44x^15 - 164x^14 + 735x^13 - 2730x^12 + 6291x^11 - 13789x^10 + 24027x^9 - 31916x^8 + 31405x^7 - 24585x^6 + 16773x^5 - 4091x^4 + 2808x^3 + 4094x^2 + 4114x + 881	\( 13^{10}\cdot 401^{8} \)	20T324	Trivial (GRH)
20.4.291727739125097042497356615909376.1	x^20 + 15x^18 + 33x^16 - 175x^14 + 126x^12 + 10x^10 + 175x^8 - 269x^6 - 811x^4 + 95x^2 + 64	\( 2^{24}\cdot 1429^{8} \)	20T324	Trivial (GRH)
20.8.291727739125097042497356615909376.1	x^20 - 16x^16 + x^14 + 80x^12 - 34x^10 - 99x^8 + 84x^6 - 38x^4 + 9x^2 + 4	\( 2^{24}\cdot 1429^{8} \)	20T324	Trivial (GRH)
20.8.735114192454649568937610340990976.3	x^20 - 20x^18 + 176x^16 - 896x^14 + 2832x^12 - 5312x^10 + 4416x^8 + 2560x^6 - 7936x^4 + 3072x^2 + 1024	\( 2^{40}\cdot 401^{8} \)	20T324	Trivial (GRH)
20.8.271489728101173730019304802954487841.2	x^20 - x^19 - 13x^18 - 9x^17 + 115x^16 + 781x^15 - 482x^14 - 6205x^13 - 13667x^12 + 7949x^11 + 121525x^10 + 81464x^9 - 232598x^8 - 650515x^7 + 72642x^6 + 2836966x^5 - 365610x^4 - 6377373x^3 + 661053x^2 + 5356703x + 243531	\( 67^{8}\cdot 401^{8} \)	20T324	Trivial (GRH)
20.8.271489728101173730019304802954487841.3	x^20 - 2x^19 - 10x^18 + 61x^17 - 256x^16 + 329x^15 + 889x^14 - 1258x^13 - 1827x^12 + 4117x^11 - 27692x^10 - 39071x^9 + 531811x^8 - 643326x^7 - 1085253x^6 + 1882929x^5 + 547496x^4 - 108351x^3 - 3163643x^2 + 1716738x + 507429	\( 67^{8}\cdot 401^{8} \)	20T324	Trivial (GRH)
20.12.569045856917786506070759387613895321.2	x^20 - 3x^19 - 34x^18 + 78x^17 + 374x^16 - 656x^15 - 1014x^14 + 3385x^13 - 4905x^12 - 28802x^11 + 24342x^10 + 191138x^9 + 6059x^8 - 554727x^7 - 306540x^6 + 910323x^5 + 462455x^4 - 744664x^3 + 5818x^2 + 166564x - 167289	\( 67^{6}\cdot 97^{2}\cdot 401^{8} \)	20T324	Trivial (GRH)
20.12.569045856917786506070759387613895321.3	x^20 - 7x^19 + 22x^18 - 72x^17 - 44x^16 + 1617x^15 - 4797x^14 + 2319x^13 + 17202x^12 - 46190x^11 + 62099x^10 - 60057x^9 + 30496x^8 + 24789x^7 - 61993x^6 + 7098x^5 + 29446x^4 + 1392x^3 - 5017x^2 - 1440x - 117	\( 67^{6}\cdot 97^{2}\cdot 401^{8} \)	20T324	Trivial (GRH)
20.8.571875791767467549011055076097130496.1	x^20 - 28x^18 + 261x^16 + 125x^14 - 18520x^12 + 28301x^10 + 59228x^8 - 78585x^6 + 18759x^4 - 92274x^2 + 28561	\( 2^{20}\cdot 13^{8}\cdot 401^{8} \)	20T324	Trivial (GRH)
20.8.571875791767467549011055076097130496.2	x^20 - 32x^18 + 87x^16 + 3052x^14 - 19169x^12 + 5369x^10 + 73671x^8 - 197054x^6 + 158522x^4 - 94471x^2 + 28561	\( 2^{20}\cdot 13^{8}\cdot 401^{8} \)	20T324	Trivial (GRH)
20.0.63416710432928568752221553366630662144.3	x^20 + 72x^18 + 2148x^16 + 34469x^14 + 323346x^12 + 1806187x^10 + 5857425x^8 + 10134540x^6 + 7361131x^4 + 395769x^2 + 4489	\( 2^{20}\cdot 67^{6}\cdot 401^{8} \)	20T324	$[4, 4072]$ (GRH)
20.0.63416710432928568752221553366630662144.4	x^20 + 73x^18 + 2072x^16 + 29319x^14 + 223804x^12 + 942126x^10 + 2139944x^8 + 2415464x^6 + 1122426x^4 + 184585x^2 + 4489	\( 2^{20}\cdot 67^{6}\cdot 401^{8} \)	20T324	$[2, 8144]$ (GRH)
20.12.2554446851703943625751638890998776095969.1	x^20 - 4x^19 - 93x^18 + 293x^17 + 2739x^16 - 2934x^15 - 44666x^14 - 47045x^13 + 393985x^12 + 879764x^11 - 1278851x^10 - 3594836x^9 - 2375133x^8 - 3886749x^7 + 16327638x^6 + 37153684x^5 - 209653x^4 - 12836259x^3 - 8231425x^2 - 37393192x - 27760407	\( 67^{8}\cdot 97^{2}\cdot 401^{8} \)	20T324	Trivial (GRH)
20.20.64938711483318854402274870647429798035456.1	x^20 - 146x^18 + 8288x^16 - 234552x^14 + 3580864x^12 - 30148032x^10 + 136956416x^8 - 309179392x^6 + 287341056x^4 - 94507520x^2 + 4596736	\( 2^{30}\cdot 67^{6}\cdot 401^{8} \)	20T324	Trivial (GRH)
20.20.64938711483318854402274870647429798035456.2	x^20 - 144x^18 + 8592x^16 - 275752x^14 + 5173536x^12 - 57797984x^10 + 374875200x^8 - 1297221120x^6 + 1884449536x^4 - 202633728x^2 + 4596736	\( 2^{30}\cdot 67^{6}\cdot 401^{8} \)	20T324	Trivial (GRH)
20.4.91503142838236987962684180287701981512121.1	x^20 - 6x^19 + 69x^18 - 392x^17 + 1721x^16 - 6400x^15 - 8529x^14 - 15865x^13 - 292744x^12 - 31417x^11 + 1827235x^10 + 17210930x^9 + 52223204x^8 + 135136937x^7 + 10192854x^6 + 308863742x^5 + 5041155426x^4 + 14711875985x^3 + 9284598425x^2 + 1411756642x + 93206090471	\( 67^{6}\cdot 97^{2}\cdot 401^{10} \)	20T324	$[2, 2]$ (GRH)
20.4.91503142838236987962684180287701981512121.2	x^20 - 8x^19 + 60x^18 - 494x^17 + 1261x^16 - 5153x^15 + 24512x^14 + 51422x^13 - 78134x^12 + 264162x^11 - 7087777x^10 - 8047339x^9 + 54599027x^8 + 248179146x^7 - 84208667x^6 - 1275639545x^5 - 814155270x^4 + 2185244296x^3 + 4978153918x^2 - 9067788804x + 8276198479	\( 67^{6}\cdot 97^{2}\cdot 401^{10} \)	20T324	$[2, 2]$ (GRH)