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
16.6.134001919047114586890352.1	x^16 - 7x^15 + 18x^14 - 19x^13 - 10x^12 + 86x^11 - 255x^10 + 326x^9 + 305x^8 - 839x^7 + 299x^6 + 603x^5 - 66x^4 - 110x^3 - 3x^2 + 7x + 1	\( -\,2^{4}\cdot 7^{5}\cdot 163^{8} \)	16T1518	Trivial
16.6.134001919047114586890352.2	x^16 - 5x^15 + 17x^14 - 48x^13 + 118x^12 - 234x^11 + 371x^10 - 510x^9 + 551x^8 - 336x^7 - 147x^6 + 509x^5 - 378x^4 + 58x^3 + 104x^2 - 21x - 7	\( -\,2^{4}\cdot 7^{5}\cdot 163^{8} \)	16T1518	Trivial
16.2.6566094033308614757627248.1	x^16 - 5x^14 + 28x^12 - 137x^10 + 835x^8 - 1445x^6 + 2869x^4 - 7263x^2 - 567	\( -\,2^{4}\cdot 7^{7}\cdot 163^{8} \)	16T1518	Trivial
16.2.6566094033308614757627248.2	x^16 - 2x^15 + 15x^14 - 22x^13 + 87x^12 - 68x^11 + 151x^10 + 83x^9 - 301x^8 + 700x^7 - 1385x^6 + 628x^5 - 891x^4 - 457x^3 + 549x^2 + 180x - 2025	\( -\,2^{4}\cdot 7^{7}\cdot 163^{8} \)	16T1518	Trivial
16.0.440986031955498378847059968.1	x^16 - 2x^14 + 174x^12 - 1400x^10 + 14581x^8 - 60200x^6 + 211582x^4 - 368186x^2 + 240737	\( 2^{40}\cdot 7^{10}\cdot 17^{5} \)	16T1518	$[2]$ (GRH)
16.0.440986031955498378847059968.2	x^16 + 2x^14 + 174x^12 + 1400x^10 + 14581x^8 + 60200x^6 + 211582x^4 + 368186x^2 + 240737	\( 2^{40}\cdot 7^{10}\cdot 17^{5} \)	16T1518	$[2]$ (GRH)
16.12.1235524419793656585106371140048.1	x^16 - 8x^15 - 30x^14 + 271x^13 + 420x^12 - 3108x^11 - 3701x^10 + 12676x^9 + 16021x^8 - 5107x^7 - 9238x^6 - 15667x^5 - 24469x^4 - 13644x^3 - 6954x^2 - 4888x - 1084	\( 2^{4}\cdot 163^{8}\cdot 173^{5} \)	16T1518	Trivial (GRH)
16.4.1235524419793656585106371140048.1	x^16 - 8x^15 + 42x^14 - 94x^13 - 98x^12 + 1429x^11 - 4084x^10 + 3120x^9 + 10902x^8 - 34593x^7 - 124234x^6 + 410792x^5 - 1441217x^4 + 1180437x^3 + 9897052x^2 - 12275732x + 6719144	\( 2^{4}\cdot 163^{8}\cdot 173^{5} \)	16T1518	Trivial (GRH)
16.8.26181488684730995417116128593561.1	x^16 - x^15 - 24x^14 + 61x^13 - 377x^12 - 109x^11 - 5474x^10 - 1389x^9 + 283817x^8 - 423891x^7 - 587974x^6 + 2942271x^5 - 9646748x^4 + 9669233x^3 + 14865913x^2 - 64829181x + 67279599	\( 89^{5}\cdot 97^{2}\cdot 163^{8} \)	16T1518	Trivial (GRH)
16.8.26181488684730995417116128593561.2	x^16 - 2x^15 - 45x^14 + 335x^13 - 280x^12 - 7258x^11 + 39600x^10 - 63598x^9 - 222958x^8 + 1465935x^7 - 3407382x^6 + 2268504x^5 + 7928120x^4 - 24536211x^3 + 29571391x^2 - 13651434x - 535357	\( 89^{5}\cdot 97^{2}\cdot 163^{8} \)	16T1518	Trivial (GRH)
16.12.73930914322948009059130451759201.1	x^16 - 4x^15 - 89x^14 + 94x^13 + 3029x^12 + 7131x^11 - 45741x^10 - 294515x^9 + 183074x^8 + 4007947x^7 + 2346236x^6 - 23054771x^5 - 23619289x^4 + 52233129x^3 + 53780434x^2 - 44413090x - 19843377	\( 89^{5}\cdot 163^{10} \)	16T1518	Trivial (GRH)
16.4.73930914322948009059130451759201.1	x^16 - 2x^15 + 98x^14 - 219x^13 + 3404x^12 - 4965x^11 + 47601x^10 - 19767x^9 + 244397x^8 + 244297x^7 - 77665x^6 + 2192657x^5 - 4093277x^4 + 5911629x^3 + 13239578x^2 - 17101737x + 4505283	\( 89^{5}\cdot 163^{10} \)	16T1518	$[4]$ (GRH)
16.0.8403621967231401423280940753903439872.1	x^16 - 6x^15 + 277x^14 - 1338x^13 + 27774x^12 - 101750x^11 + 1294224x^10 - 3759386x^9 + 31550961x^8 - 70606372x^7 + 378425631x^6 - 549401298x^5 + 2530352237x^4 - 2407813268x^3 + 14049903847x^2 - 16854186966x + 57550982508	\( 2^{12}\cdot 163^{10}\cdot 173^{5} \)	16T1518	$[2, 2, 2848108]$ (GRH)
16.16.8403621967231401423280940753903439872.1	x^16 - 390x^14 + 46922x^12 - 2584854x^10 + 76299811x^8 - 1288109619x^6 + 12470133581x^4 - 64409871681x^2 + 137566762973	\( 2^{12}\cdot 163^{10}\cdot 173^{5} \)	16T1518	Trivial (GRH)
16.0.8403621967231401423280940753903439872.2	x^16 - 7x^15 + 351x^14 - 1774x^13 + 47083x^12 - 168953x^11 + 3176992x^10 - 8025465x^9 + 119353024x^8 - 236695503x^7 + 2590238519x^6 - 5204344770x^5 + 28709400122x^4 - 57922541292x^3 + 48526186028x^2 - 62534007816x + 111288111496	\( 2^{12}\cdot 163^{10}\cdot 173^{5} \)	16T1518	$[2, 2, 2764680]$ (GRH)
16.16.8403621967231401423280940753903439872.2	x^16 - 7x^15 - 375x^14 + 2556x^13 + 44134x^12 - 293372x^11 - 2209198x^10 + 14315850x^9 + 48143023x^8 - 304732459x^7 - 394643403x^6 + 2523625128x^5 + 638786405x^4 - 7025084645x^3 + 1602954741x^2 + 4517590230x - 1591133436	\( 2^{12}\cdot 163^{10}\cdot 173^{5} \)	16T1518	Trivial (GRH)