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 14 matches)

Label	Polynomial	Discriminant	Galois group	Class group
25.25.6118625560089276488733958103694021701812744140625.1	x^25 - 5x^24 - 60x^23 + 290x^22 + 1490x^21 - 6836x^20 - 20165x^19 + 85905x^18 + 165640x^17 - 634300x^16 - 876915x^15 + 2860245x^14 + 3104180x^13 - 7920370x^12 - 7429455x^11 + 13143679x^10 + 11662900x^9 - 12187240x^8 - 11034960x^7 + 5336420x^6 + 5352834x^5 - 670950x^4 - 973795x^3 - 7365x^2 + 53905x + 4751	\( 5^{40}\cdot 11^{20} \)	$C_5^2$ (as 25T2)	Trivial (GRH)
25.25.451947074858779414061989271610218361957576637330801.1	x^25 - 84x^23 - 66x^22 + 2826x^21 + 4072x^20 - 48221x^19 - 96798x^18 + 441736x^17 + 1150294x^16 - 2099287x^15 - 7477592x^14 + 3886133x^13 + 27115460x^12 + 5785190x^11 - 52524876x^10 - 37286821x^9 + 46080424x^8 + 57112611x^7 - 6485584x^6 - 31826729x^5 - 10040832x^4 + 4451908x^3 + 3356864x^2 + 718016x + 51424	\( 11^{20}\cdot 31^{20} \)	$C_5^2$ (as 25T2)	Trivial (GRH)
25.25.121207875070942751916201424921290281964762434202234001.1	x^25 - 104x^23 - 76x^22 + 4358x^21 + 5884x^20 - 94439x^19 - 178142x^18 + 1136264x^17 + 2743554x^16 - 7517715x^15 - 23379160x^14 + 23943273x^13 + 111486276x^12 - 11753214x^11 - 284820250x^10 - 119774447x^9 + 352085268x^8 + 260565807x^7 - 179794682x^6 - 185477445x^5 + 22993680x^4 + 45549604x^3 + 1956424x^2 - 3466480x - 359776	\( 11^{20}\cdot 41^{20} \)	$C_5^2$ (as 25T2)	Trivial (GRH)
25.25.342334290668031200335701860762422121140804207127700374401.1	x^25 - 144x^23 - 10x^22 + 8430x^21 + 1042x^20 - 262485x^19 - 40058x^18 + 4796520x^17 + 739142x^16 - 53660765x^15 - 7391668x^14 + 371551113x^13 + 45584040x^12 - 1568386838x^11 - 207652438x^10 + 3871967469x^9 + 721456442x^8 - 5197520035x^7 - 1434566212x^6 + 3265983995x^5 + 1212591512x^4 - 677788540x^3 - 346963496x^2 - 30059216x + 944416	\( 11^{20}\cdot 61^{20} \)	$C_5^2$ (as 25T2)	Trivial (GRH)
25.25.6109899266621889928830047225355883711017668247222900390625.1	x^25 - 5x^24 - 100x^23 + 540x^22 + 3680x^21 - 22336x^20 - 61675x^19 + 461155x^18 + 442680x^17 - 5240530x^16 - 46803x^15 + 33718945x^14 - 18329830x^13 - 120156280x^12 + 106088075x^11 + 219291821x^10 - 242987100x^9 - 172562760x^8 + 224926530x^7 + 51074860x^6 - 81703398x^5 - 7421440x^4 + 12227675x^3 + 650425x^2 - 581975x - 11035	\( 5^{40}\cdot 31^{20} \)	$C_5^2$ (as 25T2)	Trivial (GRH)
25.25.7128869711569640297994415184144957376207195381442155291601.1	x^25 - 164x^23 - 272x^22 + 10686x^21 + 33950x^20 - 328747x^19 - 1607358x^18 + 4077128x^17 + 35351982x^16 + 11554131x^15 - 347862808x^14 - 688461999x^13 + 1048835196x^12 + 4696914774x^11 + 2103035116x^10 - 10682929821x^9 - 15119768150x^8 + 3751400425x^7 + 21035443090x^6 + 11310231959x^5 - 5969323408x^4 - 7701909436x^3 - 1993261592x^2 + 164644368x + 73350496	\( 11^{20}\cdot 71^{20} \)	$C_5^2$ (as 25T2)	Trivial (GRH)
25.25.1638616440290397163180658445206072428845800459384918212890625.1	x^25 - 5x^24 - 120x^23 + 490x^22 + 6060x^21 - 19326x^20 - 169085x^19 + 399035x^18 + 2867330x^17 - 4699810x^16 - 30641007x^15 + 32118865x^14 + 207946490x^13 - 120400780x^12 - 883452625x^11 + 183446647x^10 + 2251577330x^9 + 209338160x^8 - 3125972470x^7 - 1080207840x^6 + 1848883042x^5 + 1050477480x^4 - 112036295x^3 - 124937795x^2 - 1592555x + 3976207	\( 5^{40}\cdot 41^{20} \)	$C_5^2$ (as 25T2)	Trivial (GRH)
25.25.4628037546532860960147412376577678523972281254827976226806640625.1	x^25 - 5x^24 - 160x^23 + 760x^22 + 10200x^21 - 46346x^20 - 341415x^19 + 1481655x^18 + 6679000x^17 - 27473160x^16 - 80350625x^15 + 308241235x^14 + 609685640x^13 - 2105459870x^12 - 2953591475x^11 + 8503890713x^10 + 9144688380x^9 - 18676720520x^8 - 17431228350x^7 + 17746925340x^6 + 17044842134x^5 - 1993468850x^4 - 3196341625x^3 + 104189315x^2 + 171719495x - 9926699	\( 5^{40}\cdot 61^{20} \)	$C_5^2$ (as 25T2)	Trivial (GRH)
25.25.96375611759789726717489130716177918666289770044386386871337890625.1	x^25 - 5x^24 - 180x^23 + 570x^22 + 13920x^21 - 20596x^20 - 584805x^19 + 57555x^18 + 14152650x^17 + 13892640x^16 - 196009889x^15 - 368334245x^14 + 1439989960x^13 + 4092190190x^12 - 4248220395x^11 - 21126485889x^10 - 2960488270x^9 + 45375238060x^8 + 23961479550x^7 - 47424572900x^6 - 28270808806x^5 + 26925541130x^4 + 10679386965x^3 - 7540471425x^2 - 84655405x + 134965843	\( 5^{40}\cdot 71^{20} \)	$C_5^2$ (as 25T2)	$[2, 2, 2, 2]$ (GRH)
25.25.110975637648877348008932048428738579805221888818778097629547119140625.1	x^25 - 5x^24 - 240x^23 + 530x^22 + 24890x^21 + 7594x^20 - 1338125x^19 - 3194595x^18 + 36250180x^17 + 160854770x^16 - 368499261x^15 - 3289109505x^14 - 2303086930x^13 + 26271143660x^12 + 64633222815x^11 - 30799326749x^10 - 299666707460x^9 - 327731536960x^8 + 145297331040x^7 + 451866407240x^6 + 151466421774x^5 - 107311399140x^4 - 38719949575x^3 + 9313043145x^2 + 546159595x - 30329857	\( 5^{40}\cdot 101^{20} \)	$C_5^2$ (as 25T2)	Trivial (GRH)
25.25.20147728344624516737564339110181128448344688877114094793796539306640625.1	x^25 - 5x^24 - 300x^23 + 1680x^22 + 34860x^21 - 221956x^20 - 1972695x^19 + 14802975x^18 + 54719040x^17 - 536477370x^16 - 560170703x^15 + 10672153285x^14 - 4512083030x^13 - 113804899720x^12 + 148895760435x^11 + 602962608969x^10 - 1156119349540x^9 - 1392866509160x^8 + 3432829509630x^7 + 1636194190540x^6 - 4591675173046x^5 - 1431049624960x^4 + 2568415257135x^3 + 889938263265x^2 - 184088651755x + 3793733257	\( 5^{40}\cdot 131^{20} \)	$C_5^2$ (as 25T2)	Trivial (GRH)
25.25.345413350438014986350888987668177302412259459742926992475986480712890625.1	x^25 - 5x^24 - 340x^23 + 1455x^22 + 50015x^21 - 181231x^20 - 4180150x^19 + 12672730x^18 + 219332280x^17 - 548593630x^16 - 7542224736x^15 + 15285369820x^14 + 172402155845x^13 - 275695602415x^12 - 2603477810110x^11 + 3146307382901x^10 + 25320004393065x^9 - 21459822962985x^8 - 151078351731360x^7 + 78900095706790x^6 + 509438422551999x^5 - 138336432441715x^4 - 834575863497100x^3 + 138192470603395x^2 + 486510203387995x - 125065035541807	\( 5^{40}\cdot 151^{20} \)	$C_5^2$ (as 25T2)	n/a
25.25.12953038931091714779183434289245559553901690387647249735891819000244140625.1	x^25 - 5x^24 - 400x^23 + 2250x^22 + 62750x^21 - 398086x^20 - 4886245x^19 + 35508745x^18 + 195237720x^17 - 1712570110x^16 - 3601148553x^15 + 45027904315x^14 + 15017327870x^13 - 640862104660x^12 + 371426734895x^11 + 4911284705363x^10 - 5158532346840x^9 - 19407576480120x^8 + 24640171762500x^7 + 34441335142480x^6 - 45133153562130x^5 - 18090480890620x^4 + 21125601745505x^3 + 999608868745x^2 - 1596471019745x - 187339360201	\( 5^{40}\cdot 181^{20} \)	$C_5^2$ (as 25T2)	Trivial (GRH)
25.25.37972353775599550581612761468462973090283165229266160167753696441650390625.1	x^25 - 5x^24 - 420x^23 + 3510x^22 + 61290x^21 - 796816x^20 - 2353665x^19 + 76430385x^18 - 234426780x^17 - 2670442740x^16 + 22400877853x^15 - 24561224315x^14 - 427122481340x^13 + 2381625278510x^12 - 4492862723775x^11 - 3489773984829x^10 + 30848179881080x^9 - 45208123167080x^8 - 17703547775880x^7 + 120222850235380x^6 - 101516189962054x^5 - 45711997402870x^4 + 108147977960025x^3 - 30832950658125x^2 - 24154429512175x + 11923703816995	\( 5^{40}\cdot 191^{20} \)	$C_5^2$ (as 25T2)	$[11]$ (GRH)