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 24 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.3625238658944761593856.1	x^20 - x^18 + 5x^16 - 4x^14 + 6x^12 - 10x^10 + 6x^8 - 4x^6 + 5x^4 - x^2 + 1	\( 2^{32}\cdot 11^{2}\cdot 17^{8} \)	20T277	Trivial (GRH)
20.0.30679705675697817124864.2	x^20 - 3x^16 - 8x^14 + 6x^12 + 16x^10 + 6x^8 - 8x^6 - 3x^4 + 1	\( 2^{42}\cdot 17^{8} \)	20T277	Trivial (GRH)
20.0.38912306507100625000000.1	x^20 + 4x^18 + 9x^16 + 16x^14 + 8x^12 - 7x^10 - 19x^8 + 3x^6 + 27x^4 + 18x^2 + 4	\( 2^{6}\cdot 5^{10}\cdot 53^{8} \)	20T277	Trivial
20.4.622596904113610000000000.1	x^20 - 4x^19 + 6x^18 + 3x^17 - 24x^16 + 32x^15 + 3x^14 - 61x^13 + 57x^12 + 36x^11 - 129x^10 + 91x^9 + 46x^8 - 158x^7 + 153x^6 - 66x^5 + 53x^4 - 46x^3 + 42x^2 - 12x - 4	\( 2^{10}\cdot 5^{10}\cdot 53^{8} \)	20T277	Trivial (GRH)
20.0.1963501163244660295991296.1	x^20 + 6x^18 - 8x^17 + 12x^16 - 24x^15 + 44x^14 - 32x^13 + 86x^12 - 80x^11 + 112x^10 - 148x^9 + 198x^8 - 168x^7 + 116x^6 - 152x^5 + 211x^4 - 176x^3 + 82x^2 - 20x + 2	\( 2^{48}\cdot 17^{8} \)	20T277	Trivial
20.4.5720717061332965322265625.1	x^20 - 4x^19 + 4x^18 + 7x^17 - 39x^16 + 85x^15 - 87x^14 + 33x^13 + 20x^12 - 71x^11 + 103x^10 - 58x^9 - 14x^8 + 73x^7 - 35x^6 - 31x^5 + 20x^4 + 6x^3 - 8x^2 - 5x - 1	\( 5^{10}\cdot 53^{8}\cdot 97^{2} \)	20T277	Trivial (GRH)
20.16.3051163702740134738531337890625.1	x^20 - 4x^19 - 13x^18 + 57x^17 + 39x^16 - 237x^15 + 160x^14 + 110x^13 - 1648x^12 + 1335x^11 + 5556x^10 - 2487x^9 - 8420x^8 + 833x^7 + 4784x^6 - 546x^5 - 876x^4 + 1086x^3 + 538x^2 - 58x - 31	\( 3^{18}\cdot 5^{10}\cdot 73^{8} \)	20T277	Trivial (GRH)
20.0.3440348408794801675464162130041.1	x^20 - x^19 + 3x^18 + 9x^17 + 17x^16 + 74x^15 - 47x^14 - 416x^13 + 8x^12 + 573x^11 + 1575x^10 + 522x^9 - 1254x^8 - 2010x^7 - 942x^6 + 1458x^5 + 2853x^4 + 1980x^3 + 1647x^2 + 216x + 351	\( 3^{18}\cdot 11^{8}\cdot 23^{10} \)	20T277	$[3]$ (GRH)
20.0.27460473324661212646782041015625.1	x^20 + 4x^18 - 66x^16 - 188x^14 + 1381x^12 + 3105x^10 - 4392x^8 + 4152x^6 - 1368x^4 + 531x^2 + 9	\( 3^{20}\cdot 5^{10}\cdot 73^{8} \)	20T277	$[2]$ (GRH)
20.0.27460473324661212646782041015625.2	x^20 - 6x^19 + 14x^18 - 12x^17 - 48x^16 + 60x^15 - 132x^14 + 951x^13 - 267x^12 + 744x^11 + 1077x^10 - 6060x^9 + 9858x^8 + 1950x^7 + 21891x^6 + 1167x^5 + 38958x^4 - 6303x^3 - 4030x^2 + 759x + 529	\( 3^{20}\cdot 5^{10}\cdot 73^{8} \)	20T277	$[10]$ (GRH)
20.0.54798626427212061103203500949504.1	x^20 + 13x^18 + 8x^16 - 85x^14 + 187x^12 - 232x^10 + 187x^8 - 85x^6 + 8x^4 + 13x^2 + 1	\( 2^{24}\cdot 3^{2}\cdot 881^{8} \)	20T277	$[12]$ (GRH)
20.8.278668221112378935712597132533321.1	x^20 + 2x^18 - 79x^16 - 21x^14 + 938x^12 + 439x^10 - 2874x^8 - 2507x^6 + 770x^4 + 847x^2 + 121	\( 3^{22}\cdot 11^{8}\cdot 23^{10} \)	20T277	Trivial (GRH)
20.8.295313960899290153804206624997376.1	x^20 - 12x^18 + 37x^16 - 8x^14 + 14x^12 - 56x^10 + 14x^8 - 8x^6 + 37x^4 - 12x^2 + 1	\( 2^{44}\cdot 11^{8}\cdot 23^{8} \)	20T277	Trivial (GRH)
20.0.1404428859331790362883274100506624.1	x^20 - 21x^18 + 284x^16 - 2265x^14 + 13093x^12 - 51096x^10 + 146412x^8 - 269784x^6 + 351216x^4 - 233280x^2 + 104976	\( 2^{16}\cdot 3^{10}\cdot 881^{8} \)	20T277	$[6, 6]$ (GRH)
20.0.1404428859331790362883274100506624.2	x^20 - 15x^18 + 146x^16 - 833x^14 + 3445x^12 - 9260x^10 + 18112x^8 - 21768x^6 + 18000x^4 - 5616x^2 + 1296	\( 2^{16}\cdot 3^{10}\cdot 881^{8} \)	20T277	$[2, 6]$ (GRH)
20.12.1806627930211353113514833291015625.1	x^20 - x^19 - 22x^18 + 56x^17 + 220x^16 - 857x^15 - 962x^14 + 6806x^13 - 172x^12 - 32469x^11 + 18864x^10 + 90045x^9 - 84323x^8 - 131413x^7 + 176120x^6 + 76952x^5 - 171224x^4 - 485x^3 + 57265x^2 + 71x - 751	\( 3^{16}\cdot 5^{10}\cdot 73^{10} \)	20T277	Trivial (GRH)
20.4.1806627930211353113514833291015625.1	x^20 - 10x^19 + 27x^18 + 42x^17 - 284x^16 + 28x^15 + 1386x^14 - 400x^13 - 5377x^12 + 1166x^11 + 16307x^10 - 1076x^9 - 35399x^8 - 6192x^7 + 50275x^6 + 31415x^5 - 48995x^4 - 43179x^3 + 10583x^2 + 29682x + 4061	\( 3^{16}\cdot 5^{10}\cdot 73^{10} \)	20T277	$[3]$ (GRH)
20.12.1806627930211353113514833291015625.2	x^20 - 4x^19 - 21x^18 + 128x^17 + 8x^16 - 1238x^15 + 2095x^14 + 2205x^13 - 10259x^12 + 18915x^11 - 13815x^10 - 65409x^9 + 112870x^8 + 82145x^7 - 150225x^6 - 77692x^5 + 37862x^4 + 41674x^3 + 23377x^2 + 7623x + 829	\( 3^{16}\cdot 5^{10}\cdot 73^{10} \)	20T277	Trivial (GRH)
20.16.1906977314212584211582086181640625.1	x^20 - 10x^19 + 11x^18 + 186x^17 - 651x^16 - 300x^15 + 4740x^14 - 6714x^13 - 3027x^12 + 11792x^11 + 961x^10 - 16460x^9 + 7140x^8 + 8298x^7 - 6774x^6 - 360x^5 + 1458x^4 - 222x^3 - 85x^2 + 16x + 1	\( 3^{18}\cdot 5^{14}\cdot 73^{8} \)	20T277	Trivial (GRH)
20.0.16259651371902178021633499619140625.1	x^20 - 6x^19 + 9x^18 + 4x^17 + 72x^16 - 312x^15 + 115x^14 + 762x^13 - 540x^12 + 2796x^11 - 9528x^10 + 1575x^9 + 3953x^8 + 51663x^7 - 40776x^6 - 340038x^5 + 1515159x^4 - 3483729x^3 + 4716981x^2 - 3496365x + 1120149	\( 3^{18}\cdot 5^{10}\cdot 73^{10} \)	20T277	$[180]$ (GRH)
20.4.20001321003068090975284576416015625.1	x^20 + 15x^18 + 80x^16 - 325x^14 - 665x^12 + 1637x^10 + 1225x^8 - 4305x^6 + 435x^4 - 50x^2 + 1	\( 5^{26}\cdot 41^{10} \)	20T277	$[4]$ (GRH)
20.20.146336862347119602194701496572265625.1	x^20 - x^19 - 58x^18 - 2x^17 + 1256x^16 + 806x^15 - 13678x^14 - 14543x^13 + 82315x^12 + 116040x^11 - 275583x^10 - 490494x^9 + 468538x^8 + 1127252x^7 - 247384x^6 - 1318055x^5 - 257359x^4 + 631244x^3 + 263720x^2 - 62207x - 31319	\( 3^{20}\cdot 5^{10}\cdot 73^{10} \)	20T277	Trivial (GRH)
20.0.1209605983843492469982030335989252096.1	x^20 + 46x^18 + 815x^16 + 7496x^14 + 39716x^12 + 125480x^10 + 234718x^8 + 246784x^6 + 128208x^4 + 23616x^2 + 64	\( 2^{56}\cdot 11^{8}\cdot 23^{8} \)	20T277	$[1176]$ (GRH)
20.20.3199377030764439523590236160000000000.2	x^20 - 51x^18 + 906x^16 - 7312x^14 + 30531x^12 - 71718x^10 + 97339x^8 - 73827x^6 + 27474x^4 - 3321x^2 + 9	\( 2^{20}\cdot 3^{18}\cdot 5^{10}\cdot 73^{8} \)	20T277	Trivial (GRH)