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 6 matches)

Label	Polynomial	Discriminant	Galois group	Class group
29.29.38358032782038398419973086399760468678777161743121.1	x^29 - x^28 - 28x^27 + 27x^26 + 351x^25 - 325x^24 - 2600x^23 + 2300x^22 + 12650x^21 - 10626x^20 - 42504x^19 + 33649x^18 + 100947x^17 - 74613x^16 - 170544x^15 + 116280x^14 + 203490x^13 - 125970x^12 - 167960x^11 + 92378x^10 + 92378x^9 - 43758x^8 - 31824x^7 + 12376x^6 + 6188x^5 - 1820x^4 - 560x^3 + 105x^2 + 15x - 1	\( 59^{28} \)	$C_{29}$ (as 29T1)	Trivial (GRH)
29.29.1931816133436230496253440348173909042983780087233421135736506627041.1	x^29 - x^28 - 112x^27 + 91x^26 + 5198x^25 - 3644x^24 - 132219x^23 + 83238x^22 + 2053518x^21 - 1187959x^20 - 20553532x^19 + 11071128x^18 + 136460842x^17 - 69042962x^16 - 609473492x^15 + 292259011x^14 + 1836592125x^13 - 845018358x^12 - 3706016039x^11 + 1661552324x^10 + 4906886664x^9 - 2177019390x^8 - 4095369839x^7 + 1819962089x^6 + 1998032360x^5 - 895362174x^4 - 490947342x^3 + 221892059x^2 + 42927079x - 19524467	\( 233^{28} \)	$C_{29}$ (as 29T1)	Trivial (GRH)
29.29.158165571476523684791187605131317359442300677347381843010071500056545201.1	x^29 - x^28 - 168x^27 + 353x^26 + 11480x^25 - 34328x^24 - 410190x^23 + 1556443x^22 + 8267052x^21 - 38827232x^20 - 94788585x^19 + 575669857x^18 + 574148959x^17 - 5286405734x^16 - 1118675686x^15 + 30698615326x^14 - 6935797323x^13 - 112817035992x^12 + 51055206761x^11 + 256367413593x^10 - 136472035194x^9 - 340428884896x^8 + 170672875682x^7 + 236550118296x^6 - 94550319984x^5 - 69592403677x^4 + 18732474566x^3 + 3480965541x^2 - 875365500x + 10242329	\( 349^{28} \)	$C_{29}$ (as 29T1)	Trivial (GRH)
29.29.13123427860740340635045684158089751314114754706664887333885491004189525894481.1	x^29 - x^28 - 252x^27 + 493x^26 + 26301x^25 - 70613x^24 - 1477005x^23 + 4757585x^22 + 49139083x^21 - 176708296x^20 - 1019533247x^19 + 3897692875x^18 + 13650905238x^17 - 52791707208x^16 - 121558760223x^15 + 441031541121x^14 + 744433170879x^13 - 2221117761731x^12 - 3198643328695x^11 + 6333895042002x^10 + 9161654939551x^9 - 8623697894872x^8 - 14867816867065x^7 + 2648025494151x^6 + 9891108006231x^5 + 1898151784214x^4 - 1956687026062x^3 - 891062263511x^2 - 130453149826x - 6306528127	\( 523^{28} \)	$C_{29}$ (as 29T1)	Trivial (GRH)
29.29.7839491297426657080705875253942679356383134413463412253884527413516798034573044321.1	x^29 - 406x^27 - 261x^26 + 60784x^25 - 10237x^24 - 4881280x^23 + 6951010x^22 + 231791925x^21 - 664329796x^20 - 6378435885x^19 + 29829836682x^18 + 83025301615x^17 - 713976297106x^16 + 200377868604x^15 + 8552568793352x^14 - 19940770675013x^13 - 30466827556936x^12 + 199293371073354x^11 - 244879309451696x^10 - 341168817490702x^9 + 1410119390706929x^8 - 1755729397271788x^7 + 798559330062447x^6 + 263826444292294x^5 - 372309027818008x^4 + 45256457625802x^3 + 48917493171904x^2 - 7142036935967x - 2480435158303	\( 29^{56} \)	$C_{29}$ (as 29T1)	n/a
29.29.127186199976511404062972685561977327455002805301971051425559672113022697399314124161.1	x^29 - x^28 - 448x^27 + 107x^26 + 76138x^25 - 43560x^24 - 6896718x^23 + 8492788x^22 + 374467531x^21 - 737137472x^20 - 12707566814x^19 + 34389111341x^18 + 270515586354x^17 - 939536322456x^16 - 3528471156331x^15 + 15628114907220x^14 + 26518327124887x^13 - 161458375653531x^12 - 93674380846644x^11 + 1045971567643780x^10 - 54383106047402x^9 - 4238937042324143x^8 + 1725076964802557x^7 + 10520005444822970x^6 - 6101874655993302x^5 - 15103434975606529x^4 + 9152562248392343x^3 + 10944332007104174x^2 - 5127494290967802x - 2711408412652309	\( 929^{28} \)	$C_{29}$ (as 29T1)	n/a