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 12 matches)

Label	Polynomial	Discriminant	Galois group	Class group
15.3.11147139273942777856.1	x^15 - 5x^14 + 7x^13 + 6x^12 - 21x^11 - 4x^10 + 48x^9 - 15x^8 - 73x^7 + 43x^6 + 84x^5 - 55x^4 - 72x^3 + 34x^2 + 32x - 2	\( 2^{14}\cdot 37^{2}\cdot 89^{6} \)	15T89	Trivial
15.3.17986874109670998016.1	x^15 - 4x^13 - 7x^12 + 7x^11 + 23x^10 + 19x^9 + 30x^8 + 17x^7 - 7x^6 - 4x^5 - 4x^4 - 25x^3 - 14x^2 + 5x - 1	\( 2^{14}\cdot 47^{2}\cdot 89^{6} \)	15T89	Trivial
15.7.5759064874224632479744.1	x^15 - 6x^14 + 8x^13 + 30x^12 - 122x^11 + 90x^10 + 325x^9 - 728x^8 + 58x^7 + 1440x^6 - 1327x^5 - 904x^4 + 1775x^3 - 218x^2 - 716x + 296	\( 2^{14}\cdot 29^{4}\cdot 89^{6} \)	15T89	Trivial
15.7.27837728923955327156224.1	x^15 - 2x^14 - 3x^13 + 11x^12 - 30x^11 + 122x^9 - 174x^8 + 126x^7 + 282x^6 - 476x^5 - 4x^4 + 72x^3 - 216x^2 + 112x + 16	\( 2^{14}\cdot 43^{4}\cdot 89^{6} \)	15T89	Trivial
15.3.236236656513512990640321.1	x^15 - 18x^13 - 8x^12 + 198x^11 + 84x^10 - 1243x^9 - 819x^8 + 4659x^7 + 4065x^6 - 8514x^5 - 12567x^4 - 7323x^3 - 5130x^2 - 2331x - 1013	\( 3^{20}\cdot 19^{4}\cdot 151^{4} \)	15T89	Trivial (GRH)
15.3.236236656513512990640321.2	x^15 + 3x^13 - 12x^12 + 18x^11 + 225x^10 + 110x^9 - 18x^8 - 3204x^7 - 2828x^6 + 3636x^5 + 2940x^4 - 1765x^3 - 53802x^2 - 67569x + 12377	\( 3^{20}\cdot 19^{4}\cdot 151^{4} \)	15T89	Trivial (GRH)
15.7.476081340356745953854630586535361.1	x^15 - 5x^14 - 75x^13 + 271x^12 + 2056x^11 - 3072x^10 - 28992x^9 - 28869x^8 + 188292x^7 + 579191x^6 + 359939x^5 - 1857141x^4 - 5503034x^3 - 7914792x^2 - 6186220x - 2598643	\( 61^{4}\cdot 139^{2}\cdot 397^{4}\cdot 267661^{2} \)	15T89	$[3]$ (GRH)
15.7.290987344534580290346324872872346209.1	x^15 - 144x^13 - 530x^12 + 6975x^11 + 42771x^10 - 98527x^9 - 1111410x^8 - 534909x^7 + 10317297x^6 + 8157366x^5 - 69930507x^4 - 62787342x^3 + 238047714x^2 + 105565329x - 436825811	\( 3^{20}\cdot 37^{2}\cdot 61^{4}\cdot 397^{4}\cdot 421^{2} \)	15T89	$[3]$ (GRH)
15.11.582873779843746055527120888504182961.1	x^15 - x^14 - 186x^13 - 169x^12 + 13042x^11 + 34845x^10 - 388062x^9 - 1748786x^8 + 3122317x^7 + 29742540x^6 + 42132858x^5 - 69864557x^4 - 294637932x^3 - 458139413x^2 - 439035709x - 204947137	\( 61^{4}\cdot 397^{4}\cdot 1301806921^{2} \)	15T89	$[3]$ (GRH)
15.11.1543040910519569546921019055910525041.1	x^15 - 3x^14 - 126x^13 + 531x^12 + 5769x^11 - 34514x^10 - 95880x^9 + 1029924x^8 - 622189x^7 - 13231140x^6 + 37048867x^5 + 26547802x^4 - 288701374x^3 + 540249339x^2 - 423492779x + 120987661	\( 61^{4}\cdot 397^{4}\cdot 28309^{2}\cdot 74821^{2} \)	15T89	$[3]$ (GRH)
15.15.5902598614225707628542494671273721856.1	x^15 - 204x^13 - 84x^12 + 16047x^11 + 10104x^10 - 624766x^9 - 441828x^8 + 12590520x^7 + 8195912x^6 - 121663908x^5 - 51121392x^4 + 419212416x^3 - 56685888x^2 - 57125376x + 3863552	\( 2^{26}\cdot 3^{20}\cdot 7^{2}\cdot 11^{4}\cdot 181^{6} \)	15T89	Trivial (GRH)
15.15.61170892447385797247321113311726286561.1	x^15 - 4x^14 - 186x^13 + 438x^12 + 12766x^11 - 13709x^10 - 391193x^9 + 100840x^8 + 5468724x^7 + 731596x^6 - 35856634x^5 - 10209282x^4 + 105247589x^3 + 30695428x^2 - 107138692x - 21039807	\( 193^{2}\cdot 89417^{4}\cdot 5068447^{2} \)	15T89	$[3]$ (GRH)