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 14 matches)

Label	Polynomial	Discriminant	Galois group	Class group
19.19.141346398682951205607977379416171732.1	x^19 - 3x^18 - 16x^17 + 49x^16 + 103x^15 - 319x^14 - 343x^13 + 1059x^12 + 631x^11 - 1911x^10 - 631x^9 + 1866x^8 + 312x^7 - 948x^6 - 67x^5 + 236x^4 + 4x^3 - 26x^2 + 1	\( 2^{2}\cdot 31\cdot 30833917\cdot 92683485343\cdot 398870581726553 \)	$S_{19}$ (as 19T8)	Trivial (GRH)
19.19.4379339948779445965938732832699226041.1	x^19 - 66x^17 + 1650x^15 - 77x^14 - 20317x^13 + 4257x^12 + 134959x^11 - 60665x^10 - 479512x^9 + 349019x^8 + 801636x^7 - 833723x^6 - 391512x^5 + 661705x^4 - 118602x^3 - 56947x^2 + 6820x + 1023	\( 11^{18}\cdot 31^{12} \)	$C_{19}:C_{3}$ (as 19T3)	Trivial (GRH)
19.19.222262197774010870252934365204894747669.1	x^19 - 2x^18 - 78x^17 + 264x^16 + 1763x^15 - 8614x^14 - 9209x^13 + 96924x^12 - 60856x^11 - 443620x^10 + 727151x^9 + 587984x^8 - 2232580x^7 + 1188184x^6 + 1637520x^5 - 2688288x^4 + 1618560x^3 - 475264x^2 + 61952x - 2048	\( 18229^{9} \)	$D_{19}$ (as 19T2)	Trivial (GRH)
19.19.1603710409222789970596991622167567965561.1	x^19 - 3x^18 - 82x^17 + 265x^16 + 2391x^15 - 8370x^14 - 31377x^13 + 122460x^12 + 188431x^11 - 899712x^10 - 382602x^9 + 3261556x^8 - 573488x^7 - 5156662x^6 + 2280774x^5 + 2646791x^4 - 646414x^3 - 707173x^2 - 118143x - 1726	\( 11^{18}\cdot 19^{16} \)	$C_{19}:C_{9}$ (as 19T5)	Trivial (GRH)
19.19.102875245824411623227124507531682584199168.1	x^19 - 57x^17 + 1368x^15 - 17955x^13 + 140049x^11 - 660231x^9 + 1828332x^7 - 2742498x^5 + 1869885x^3 - 373977x - 67446	\( 2^{27}\cdot 3^{18}\cdot 19^{19} \)	$F_{19}$ (as 19T6)	Trivial (GRH)
19.19.114445997944945591651333831028437092270721.1	x^19 - x^18 - 90x^17 + 57x^16 + 3044x^15 - 1124x^14 - 51184x^13 + 4822x^12 + 474003x^11 + 90110x^10 - 2465084x^9 - 1153239x^8 + 6854098x^7 + 5023125x^6 - 8711114x^5 - 8950277x^4 + 2600136x^3 + 5125792x^2 + 1553447x + 117649	\( 191^{18} \)	$C_{19}$ (as 19T1)	Trivial (GRH)
19.19.1978419655660313589123979000000000000000000.1	x^19 - 95x^17 + 3800x^15 - 83125x^13 + 1080625x^11 - 8490625x^9 + 39187500x^7 - 97968750x^5 + 111328125x^3 - 37109375x - 8731210	\( 2^{18}\cdot 5^{18}\cdot 19^{19} \)	$F_{19}$ (as 19T6)	Trivial (GRH)
19.19.2999429662895796650415561622892044448017561.1	x^19 - x^18 - 108x^17 + 213x^16 + 4270x^15 - 11618x^14 - 74320x^13 + 248057x^12 + 559431x^11 - 2225275x^10 - 1928935x^9 + 9223494x^8 + 3299920x^7 - 17492482x^6 - 3737798x^5 + 13322064x^4 + 4255245x^3 - 3318455x^2 - 1865379x - 251347	\( 229^{18} \)	$C_{19}$ (as 19T1)	Trivial (GRH)
19.19.10842505080063916320800450434338728415281531281.1	x^19 - 171x^17 - 133x^16 + 11476x^15 + 15580x^14 - 385833x^13 - 673436x^12 + 6916190x^11 + 13391960x^10 - 66283229x^9 - 126730380x^8 + 339213156x^7 + 582575340x^6 - 861915924x^5 - 1264657480x^4 + 868638105x^3 + 1138104275x^2 - 137550709x - 221874931	\( 19^{36} \)	$C_{19}$ (as 19T1)	Trivial (GRH)
19.19.158435468857090504879482314342339950574787173641.1	x^19 - x^18 - 198x^17 + 37x^16 + 12055x^15 - 1727x^14 - 335304x^13 + 70692x^12 + 4834266x^11 - 1201976x^10 - 37345852x^9 + 7325624x^8 + 153105664x^7 - 3418584x^6 - 328284116x^5 - 65770266x^4 + 325674937x^3 + 129492371x^2 - 92941225x - 41768519	\( 419^{18} \)	$C_{19}$ (as 19T1)	Trivial (GRH)
19.19.755947441066272696677489606263668936388276269649.1	x^19 - x^18 - 216x^17 + 329x^16 + 17417x^15 - 31517x^14 - 670894x^13 + 1275207x^12 + 13251603x^11 - 24036830x^10 - 137385192x^9 + 209490406x^8 + 773799359x^7 - 862308300x^6 - 2305645775x^5 + 1693728828x^4 + 3278226422x^3 - 1551959900x^2 - 1701753321x + 554402371	\( 457^{18} \)	$C_{19}$ (as 19T1)	Trivial (GRH)
19.19.41634173570364661205169708858211372543325791407961.1	x^19 - x^18 - 270x^17 + 351x^16 + 28987x^15 - 41181x^14 - 1648168x^13 + 2453428x^12 + 55186847x^11 - 85340779x^10 - 1133336624x^9 + 1826548777x^8 + 14258200659x^7 - 24108274876x^6 - 104945874488x^5 + 187074906809x^4 + 398834944226x^3 - 749021546949x^2 - 549551190705x + 1072348621073	\( 571^{18} \)	$C_{19}$ (as 19T1)	Trivial (GRH)
19.19.394709020826813768130190448054073575320458976755889.1	x^19 - x^18 - 306x^17 - 79x^16 + 29370x^15 + 130x^14 - 1361758x^13 + 704483x^12 + 34401066x^11 - 34840236x^10 - 488507308x^9 + 678792838x^8 + 3902105097x^7 - 6509889712x^6 - 16762277726x^5 + 31790175776x^4 + 33454527221x^3 - 71781895812x^2 - 18736713884x + 50781641759	\( 647^{18} \)	$C_{19}$ (as 19T1)	Trivial (GRH)
19.19.7326960021331421245780688833073465007173042939202481.1	x^19 - x^18 - 360x^17 - 173x^16 + 45376x^15 + 58762x^14 - 2558302x^13 - 4227138x^12 + 70534890x^11 + 120121397x^10 - 973700212x^9 - 1501612590x^8 + 6678374954x^7 + 8595059019x^6 - 21259099080x^5 - 21796436285x^4 + 27241052007x^3 + 18814754704x^2 - 12659238391x - 3483379661	\( 761^{18} \)	$C_{19}$ (as 19T1)	Trivial (GRH)