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
16.0.37682348496175843883614208.1	x^16 - 4x^14 - 8x^12 - 112x^10 + 920x^8 + 816x^6 + 3808x^4 + 272	\( 2^{40}\cdot 17^{11} \)	16T1230	$[8]$
16.0.37682348496175843883614208.2	x^16 - 16x^14 + 118x^12 - 432x^10 + 865x^8 - 680x^6 - 68x^4 - 2448x^2 + 5508	\( 2^{40}\cdot 17^{11} \)	16T1230	$[8]$
16.0.613463401591299200000000000.3	x^16 + 12x^14 + 65x^12 + 194x^10 + 364x^8 + 950x^6 + 2305x^4 + 1100x^2 + 1805	\( 2^{16}\cdot 5^{11}\cdot 61^{8} \)	16T1230	$[2, 2]$ (GRH)
16.8.613463401591299200000000000.3	x^16 - 20x^14 + 121x^12 - 130x^10 - 696x^8 + 750x^6 + 1725x^4 + 360x^2 + 5	\( 2^{16}\cdot 5^{11}\cdot 61^{8} \)	16T1230	Trivial (GRH)
16.0.613463401591299200000000000.4	x^16 + 9x^14 + 45x^12 + 32x^10 + 244x^8 - 2800x^6 + 6160x^4 - 4800x^2 + 1280	\( 2^{16}\cdot 5^{11}\cdot 61^{8} \)	16T1230	$[2, 2]$ (GRH)
16.8.613463401591299200000000000.4	x^16 - x^15 - 23x^14 + 66x^13 + 39x^12 - 262x^11 - 180x^10 + 824x^9 + 636x^8 - 1849x^7 - 1441x^6 + 2676x^5 + 2549x^4 - 1396x^3 - 2368x^2 - 918x - 109	\( 2^{16}\cdot 5^{11}\cdot 61^{8} \)	16T1230	Trivial (GRH)
16.4.808028645078657974143025152.1	x^16 + 24x^14 + 110x^12 - 928x^10 + 55x^8 + 728x^6 + 3094x^4 + 1560x^2 + 117	\( 2^{36}\cdot 3^{8}\cdot 13^{11} \)	16T1230	Trivial (GRH)
16.4.808028645078657974143025152.2	x^16 - 12x^14 + 4x^12 + 608x^10 - 3748x^8 + 8944x^6 + 1248x^4 - 1664x^2 + 208	\( 2^{36}\cdot 3^{8}\cdot 13^{11} \)	16T1230	Trivial (GRH)
16.0.138870981735380017471819830544433646927872.3	x^16 + 448x^14 + 73388x^12 + 5577768x^10 + 217602126x^8 + 4457348896x^6 + 45900154748x^4 + 197267724080x^2 + 135973824098	\( 2^{67}\cdot 7^{14}\cdot 193^{4} \)	16T1230	$[2, 2, 2, 2, 2, 4, 1486716]$ (GRH)
16.16.138870981735380017471819830544433646927872.3	x^16 - 504x^14 + 97636x^12 - 9256128x^10 + 451462452x^8 - 11042447136x^6 + 128727776128x^4 - 608711834304x^2 + 543895296392	\( 2^{67}\cdot 7^{14}\cdot 193^{4} \)	16T1230	Trivial (GRH)
16.0.138870981735380017471819830544433646927872.4	x^16 + 560x^14 + 123928x^12 + 13756064x^10 + 800459128x^8 + 23105342400x^6 + 282979163040x^4 + 1397782730624x^2 + 2175581185568	\( 2^{67}\cdot 7^{14}\cdot 193^{4} \)	16T1230	$[2, 2, 2, 2, 2, 4, 933928]$ (GRH)
16.16.138870981735380017471819830544433646927872.4	x^16 - 392x^14 + 59052x^12 - 4308304x^10 + 162056636x^8 - 3333705984x^6 + 37993384016x^4 - 225448827520x^2 + 543895296392	\( 2^{67}\cdot 7^{14}\cdot 193^{4} \)	16T1230	Trivial (GRH)