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 16 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.12.442082206796061081600000000.1	x^16 - 12x^14 - 8x^13 + 64x^11 + 216x^10 - 112x^9 + 516x^8 + 576x^7 - 5248x^6 - 4448x^5 + 6944x^4 + 8000x^3 + 480x^2 - 1600x - 400	\( 2^{36}\cdot 3^{6}\cdot 5^{8}\cdot 7^{4}\cdot 97^{2} \)	16T1547	Trivial (GRH)
16.4.442082206796061081600000000.1	x^16 - 4x^15 + 24x^14 - 112x^13 + 394x^12 - 1284x^11 + 3606x^10 - 9648x^9 + 21845x^8 - 44288x^7 + 78498x^6 - 127972x^5 + 177594x^4 - 154220x^3 + 78182x^2 - 41896x + 18911	\( 2^{36}\cdot 3^{6}\cdot 5^{8}\cdot 7^{4}\cdot 97^{2} \)	16T1547	$[2, 2]$ (GRH)
16.8.442082206796061081600000000.1	x^16 - 8x^13 - 26x^12 - 64x^11 - 136x^10 + 112x^9 + 191x^8 + 1888x^6 + 7056x^5 + 6162x^4 - 5280x^3 - 9400x^2 - 3256x - 31	\( 2^{36}\cdot 3^{6}\cdot 5^{8}\cdot 7^{4}\cdot 97^{2} \)	16T1547	Trivial (GRH)
16.12.442082206796061081600000000.2	x^16 - 4x^15 - 40x^14 + 136x^13 + 524x^12 - 1440x^11 - 2394x^10 + 6248x^9 + 3931x^8 - 12252x^7 - 3022x^6 + 10112x^5 + 2064x^4 - 3004x^3 - 1034x^2 + 124x + 41	\( 2^{36}\cdot 3^{6}\cdot 5^{8}\cdot 7^{4}\cdot 97^{2} \)	16T1547	Trivial (GRH)
16.4.442082206796061081600000000.2	x^16 + 4x^14 - 8x^13 - 40x^12 - 16x^11 - 348x^10 + 8x^9 - 514x^8 + 608x^7 + 12x^6 - 760x^5 + 2936x^4 - 1936x^3 + 5164x^2 - 7496x + 3649	\( 2^{36}\cdot 3^{6}\cdot 5^{8}\cdot 7^{4}\cdot 97^{2} \)	16T1547	$[2]$ (GRH)
16.8.442082206796061081600000000.2	x^16 - 22x^14 - 26x^12 - 188x^11 + 466x^10 - 600x^9 - 3817x^8 + 2176x^7 + 13586x^6 + 11892x^5 + 50x^4 - 14240x^3 - 14732x^2 - 5384x - 601	\( 2^{36}\cdot 3^{6}\cdot 5^{8}\cdot 7^{4}\cdot 97^{2} \)	16T1547	Trivial (GRH)
16.0.921980968790025830400000000.1	x^16 + 24x^14 + 250x^12 + 1668x^10 + 7307x^8 + 17940x^6 + 31022x^4 + 39468x^2 + 20449	\( 2^{44}\cdot 3^{8}\cdot 5^{8}\cdot 11^{2}\cdot 13^{2} \)	16T1547	$[2]$ (GRH)
16.8.921980968790025830400000000.1	x^16 - 24x^14 + 250x^12 - 1668x^10 + 7307x^8 - 17940x^6 + 31022x^4 - 39468x^2 + 20449	\( 2^{44}\cdot 3^{8}\cdot 5^{8}\cdot 11^{2}\cdot 13^{2} \)	16T1547	Trivial (GRH)
16.0.921980968790025830400000000.2	x^16 + 16x^14 - 16x^13 + 42x^12 - 32x^11 + 388x^10 - 416x^9 - 701x^8 + 2304x^7 - 868x^6 - 9248x^5 + 9714x^4 + 128x^3 - 18300x^2 + 20240x + 23449	\( 2^{44}\cdot 3^{8}\cdot 5^{8}\cdot 11^{2}\cdot 13^{2} \)	16T1547	$[2]$ (GRH)
16.8.921980968790025830400000000.2	x^16 - 20x^14 - 16x^13 + 42x^12 + 160x^11 + 88x^10 - 1280x^9 + 2779x^8 + 2688x^7 - 13744x^6 + 7072x^5 + 15222x^4 - 12448x^3 - 5940x^2 + 5264x + 121	\( 2^{44}\cdot 3^{8}\cdot 5^{8}\cdot 11^{2}\cdot 13^{2} \)	16T1547	Trivial (GRH)
16.4.5305550361918544281600000000.1	x^16 + 14x^14 - 41x^12 - 92x^10 - 2731x^8 - 24264x^6 - 13149x^4 - 30618x^2 + 35721	\( 2^{32}\cdot 3^{6}\cdot 5^{8}\cdot 7^{2}\cdot 97^{4} \)	16T1547	Trivial (GRH)
16.4.5305550361918544281600000000.2	x^16 - 14x^14 - 41x^12 + 92x^10 - 2731x^8 + 24264x^6 - 13149x^4 + 30618x^2 + 35721	\( 2^{32}\cdot 3^{6}\cdot 5^{8}\cdot 7^{2}\cdot 97^{4} \)	16T1547	Trivial (GRH)
16.16.36387146957833308423870594234187776000000.1	x^16 - 4x^15 - 824x^14 + 1004x^13 + 258716x^12 + 362012x^11 - 37641976x^10 - 137669268x^9 + 2442903326x^8 + 13272467508x^7 - 54499332552x^6 - 367215551292x^5 + 544143437772x^4 + 3910405446324x^3 - 3349786075272x^2 - 13332861193500x + 9414762766137	\( 2^{40}\cdot 3^{6}\cdot 5^{6}\cdot 13^{8}\cdot 1249^{2}\cdot 1511^{2} \)	16T1547	$[2]$ (GRH)
16.0.101075408216203634510751650650521600000000.1	x^16 + 1168x^14 - 1716x^13 + 511010x^12 - 1113408x^11 + 112405248x^10 - 267407364x^9 + 13586028503x^8 - 29544777456x^7 + 903868150860x^6 - 1458109683324x^5 + 30925819337576x^4 - 25388246588088x^3 + 490041878843476x^2 - 119034342218376x + 3136651030534129	\( 2^{40}\cdot 3^{4}\cdot 5^{8}\cdot 13^{8}\cdot 1249^{2}\cdot 1511^{2} \)	16T1547	$[2, 2, 2, 2, 2, 31008660]$ (GRH)
16.16.101075408216203634510751650650521600000000.1	x^16 - 4x^15 - 548x^14 + 2088x^13 + 110802x^12 - 451356x^11 - 10768336x^10 + 46124992x^9 + 542450360x^8 - 2261845988x^7 - 14780454956x^6 + 52722098664x^5 + 221710558722x^4 - 528960304284x^3 - 1673580561096x^2 + 1473945897104x + 3640607603231	\( 2^{40}\cdot 3^{4}\cdot 5^{8}\cdot 13^{8}\cdot 1249^{2}\cdot 1511^{2} \)	16T1547	$[2, 2]$ (GRH)
16.0.101075408216203634510751650650521600000000.2	x^16 - 4x^15 + 516x^14 - 2936x^13 + 107194x^12 - 641420x^11 + 11627920x^10 - 66371504x^9 + 728118680x^8 - 3717247748x^7 + 27035672060x^6 - 114044064440x^5 + 572310574986x^4 - 1784176112812x^3 + 6210498313016x^2 - 11384486485632x + 25628389555519	\( 2^{40}\cdot 3^{4}\cdot 5^{8}\cdot 13^{8}\cdot 1249^{2}\cdot 1511^{2} \)	16T1547	$[2, 2, 2, 2, 2, 29994700]$ (GRH)