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 17 matches)

Label	Polynomial	Discriminant	Galois group	Class group
15.5.144627327488000000000000000.1	x^15 + 5x^11 - 4x^10 - 50x^7 + 80x^6 - 32x^5 - 125x^3 + 300x^2 - 240x + 64	\( -\,2^{24}\cdot 5^{15}\cdot 7^{10} \)	15T101	Trivial (GRH)
15.7.144627327488000000000000000.1	x^15 - 20x^11 - 16x^10 + 75x^7 + 120x^6 + 48x^5 + 125x^3 + 300x^2 + 240x + 64	\( 2^{24}\cdot 5^{15}\cdot 7^{10} \)	15T101	Trivial (GRH)
15.7.144627327488000000000000000.2	x^15 - 20x^11 - 128x^10 - 800x^7 + 3200x^6 + 3072x^5 + 8000x^3 - 25600x^2 - 20480x + 32768	\( 2^{24}\cdot 5^{15}\cdot 7^{10} \)	15T101	Trivial (GRH)
15.3.168284291807861328125000000.1	x^15 + 55x^11 - 168x^10 - 1050x^7 - 1220x^6 + 5456x^5 - 15625x^3 + 25000x^2 + 30000x - 40000	\( 2^{6}\cdot 5^{19}\cdot 13^{10} \)	15T101	Trivial (GRH)
15.3.1880155257344000000000000000.1	x^15 + 25x^11 - 20x^10 + 150x^7 - 240x^6 + 96x^5 + 125x^3 - 300x^2 + 240x - 64	\( 2^{24}\cdot 5^{15}\cdot 7^{10}\cdot 13 \)	15T101	Trivial (GRH)
15.9.220573586958400000000000000000000.1	x^15 + 20x^13 - 40x^12 - 590x^11 + 1192x^10 - 7900x^9 + 33640x^8 + 19520x^7 - 201920x^6 + 244752x^5 + 132000x^4 - 778600x^3 - 120800x^2 + 310400x + 79360	\( -\,2^{24}\cdot 5^{20}\cdot 13^{10} \)	15T101	Trivial (GRH)
15.9.29492759518563811794405922500363613000000.1	x^15 - 99x^13 - 396x^12 - 1843x^11 - 11774x^10 + 108945x^9 + 1674756x^8 + 8533899x^7 + 23061222x^6 + 37151415x^5 + 37445760x^4 + 23871475x^3 + 9367350x^2 + 2068500x + 197000	\( -\,2^{6}\cdot 5^{6}\cdot 7^{10}\cdot 13\cdot 197^{4}\cdot 6791^{2}\cdot 10753^{2} \)	15T101	Trivial (GRH)
15.11.81917455001598033212058392787403072000000.1	x^15 - 153x^13 - 72x^12 + 5535x^11 + 25854x^10 - 75798x^9 - 687906x^8 - 542818x^7 + 3065428x^6 + 5465315x^5 + 600030x^4 - 3014275x^3 - 734500x^2 + 395500x + 113000	\( 2^{12}\cdot 5^{6}\cdot 7^{12}\cdot 13^{3}\cdot 113^{4}\cdot 508087^{2} \)	15T101	Trivial (GRH)
15.5.6846785245058995386515611290009600000000000.1	x^15 - 1425x^7 - 2280x^6 - 912x^5 - 2375x^3 - 5700x^2 - 4560x - 1216	\( -\,2^{24}\cdot 3^{21}\cdot 5^{11}\cdot 19^{14} \)	15T101	$[3]$ (GRH)
15.15.610201702279675842116755990922042945536000000.1	x^15 - 1386x^13 - 11088x^12 + 599872x^11 + 9930592x^10 - 30585240x^9 - 1986852672x^8 - 21167338976x^7 - 115110115456x^6 - 371202419840x^5 - 748349521920x^4 - 954137766400x^3 - 748821964800x^2 - 330710016000x - 62992384000	\( 2^{18}\cdot 5^{6}\cdot 7^{14}\cdot 13^{4}\cdot 113^{2}\cdot 139\cdot 2081603^{2} \)	15T101	Trivial (GRH)
15.9.4831264310017778731576326598323772072448000000.1	x^15 - 126x^13 - 1008x^12 - 72268x^11 - 1126048x^10 - 2073960x^9 + 91965888x^8 + 1073983904x^7 + 5909943424x^6 + 19089311360x^5 + 38490439680x^4 + 49074905600x^3 + 38514739200x^2 + 17009664000x + 3239936000	\( -\,2^{15}\cdot 5^{6}\cdot 7^{14}\cdot 113^{4}\cdot 292113919^{2} \)	15T101	Trivial (GRH)
15.11.162871129811887303525838290060177920845248000000.1	x^15 - 369x^13 - 1476x^12 + 39227x^11 + 324886x^10 - 289215x^9 - 13717404x^8 - 73968941x^7 - 201456698x^6 - 324898985x^5 - 327507840x^4 - 208784525x^3 - 81928650x^2 - 18091500x - 1723000	\( 2^{12}\cdot 5^{6}\cdot 7^{10}\cdot 127\cdot 167^{2}\cdot 1723^{4}\cdot 537221^{2} \)	15T101	Trivial (GRH)
15.7.285616238046894465829329548900066635436032000000.1	x^15 - 666x^13 - 5328x^12 + 118592x^11 + 2057312x^10 + 5330520x^9 - 132034752x^8 - 1605430816x^7 - 8877159296x^6 - 28692461440x^5 - 57857310720x^4 - 73767462400x^3 - 57893836800x^2 - 25568256000x - 4870144000	\( 2^{18}\cdot 5^{6}\cdot 7^{10}\cdot 13\cdot 29^{4}\cdot 41^{4}\cdot 211^{2}\cdot 659^{2}\cdot 701^{2} \)	15T101	Trivial (GRH)
15.13.77174683442309589098663731731426228356468718082330624000.1	x^15 - 1628x^13 - 5920x^12 + 1105179x^11 + 7903120x^10 - 388843381x^9 - 4223348520x^8 + 69563456700x^7 + 1121721226000x^6 - 4146108150000x^5 - 145380612000000x^4 - 422827275000000x^3 + 6657280500000000x^2 + 53977950000000000x + 119951000000000000	\( -\,2^{15}\cdot 5^{3}\cdot 7^{10}\cdot 13^{4}\cdot 1973^{2}\cdot 9227^{4}\cdot 9097717^{2} \)	15T101	Trivial (GRH)
15.7.626870103658230384189023990781533773422403883667456000000.1	x^15 - 2484x^13 - 39744x^12 + 1586292x^11 + 55530624x^10 + 421080120x^9 - 7864615296x^8 - 219580868736x^7 - 2464952159232x^6 - 15966575400960x^5 - 64404675624960x^4 - 164230567526400x^3 - 257781340569600x^2 - 227693297664000x - 86740303872000	\( 2^{18}\cdot 3^{24}\cdot 5^{6}\cdot 17^{4}\cdot 37^{2}\cdot 521\cdot 811^{4}\cdot 4585573^{2} \)	15T101	Trivial (GRH)
15.11.3805507799533955316962266792656268375035273432076288000000.1	x^15 - 54x^13 - 864x^12 - 909588x^11 - 29003136x^10 - 655037640x^9 - 16826161536x^8 - 301773467776x^7 - 3198404365312x^6 - 20553073039360x^5 - 82841158287360x^4 - 211243210342400x^3 - 331573827993600x^2 - 292872781824000x - 111570583552000	\( 2^{18}\cdot 5^{6}\cdot 7^{10}\cdot 337\cdot 53201^{4}\cdot 1103777641^{2} \)	15T101	Trivial (GRH)
15.11.25030409738237508654535690145991819085872813409237356544000000.1	x^15 - 234x^13 - 3744x^12 - 1149208x^11 - 36325376x^10 - 818687880x^9 - 20997415296x^8 - 376447428736x^7 - 3989611359232x^6 - 25637180200960x^5 - 103333059624960x^4 - 263497127526400x^3 - 413593180569600x^2 - 365318897664000x - 139169103872000	\( 2^{18}\cdot 5^{6}\cdot 7^{10}\cdot 13^{2}\cdot 421\cdot 66361^{4}\cdot 3959620477^{2} \)	15T101	Trivial (GRH)