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 32 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.776739269203984384.2	x^16 - 6x^14 + 15x^12 - 22x^10 + 18x^8 - 2x^6 - 5x^4 + 2x^2 + 1	\( 2^{38}\cdot 41^{4} \)	16T1744	Trivial
16.0.3106957076815937536.2	x^16 - 4x^14 + 7x^12 - 14x^10 + 24x^8 - 24x^6 + 19x^4 - 6x^2 + 1	\( 2^{40}\cdot 41^{4} \)	16T1744	Trivial
16.4.15727971179812890625.1	x^16 - x^15 - 13x^13 + x^12 - x^11 + 57x^10 + 40x^9 + 33x^8 - 40x^7 - 80x^6 - 27x^5 - 23x^4 - 6x^3 - 25x^2 - 48x - 19	\( 5^{8}\cdot 11^{4}\cdot 229^{4} \)	16T1744	Trivial (GRH)
16.4.1003875856000000000000.1	x^16 - 2x^15 - x^14 - 10x^13 + 8x^12 - 10x^11 - 19x^10 + 22x^9 - 42x^8 + 22x^7 - 19x^6 - 10x^5 + 8x^4 - 10x^3 - x^2 - 2x + 1	\( 2^{16}\cdot 5^{12}\cdot 89^{4} \)	16T1744	Trivial (GRH)
16.8.1003875856000000000000.1	x^16 - 5x^15 + 3x^14 + 23x^13 - 57x^12 + 58x^11 - 40x^10 + 5x^9 + 76x^8 - 108x^7 + 70x^6 - 61x^5 + 25x^4 + 25x^3 - 13x^2 - 2x + 1	\( 2^{16}\cdot 5^{12}\cdot 89^{4} \)	16T1744	Trivial (GRH)
16.4.1003875856000000000000.2	x^16 + 7x^14 + 25x^12 + 82x^10 + 174x^8 + 118x^6 - 75x^4 - 77x^2 + 1	\( 2^{16}\cdot 5^{12}\cdot 89^{4} \)	16T1744	Trivial (GRH)
16.8.1003875856000000000000.2	x^16 - 7x^14 + 25x^12 - 82x^10 + 174x^8 - 118x^6 - 75x^4 + 77x^2 + 1	\( 2^{16}\cdot 5^{12}\cdot 89^{4} \)	16T1744	Trivial (GRH)
16.4.9829981987383056640625.1	x^16 - 4x^15 + 10x^14 - 17x^13 + 10x^12 + 114x^11 - 644x^10 + 2256x^9 - 6174x^8 + 13856x^7 - 25282x^6 + 35414x^5 - 35562x^4 + 21589x^3 - 2884x^2 - 6153x + 3541	\( 5^{12}\cdot 11^{4}\cdot 229^{4} \)	16T1744	Trivial (GRH)
16.0.230273226043640531640625.1	x^16 - 2x^15 + 24x^14 - 59x^13 + 277x^12 - 700x^11 + 2209x^10 - 3985x^9 + 12970x^8 - 12719x^7 + 46476x^6 - 31444x^5 + 86265x^4 - 63926x^3 + 75124x^2 - 59689x + 32069	\( 5^{8}\cdot 11^{8}\cdot 229^{4} \)	16T1744	$[2, 2]$ (GRH)
16.8.230273226043640531640625.1	x^16 - x^15 - 17x^14 + 6x^13 + 107x^12 - 5x^11 - 347x^10 + 356x^9 + 1093x^8 - 1980x^7 - 4495x^6 + 135x^5 + 12143x^4 + 4038x^3 - 14481x^2 - 7443x + 41	\( 5^{8}\cdot 11^{8}\cdot 229^{4} \)	16T1744	$[2]$ (GRH)
16.0.1030748319240217600000000.1	x^16 + 19x^14 + 230x^12 + 2420x^10 + 16898x^8 + 66935x^6 + 140835x^4 + 141522x^2 + 52441	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 229^{4} \)	16T1744	$[4]$ (GRH)
16.4.1030748319240217600000000.1	x^16 - 19x^14 + 133x^12 - 103x^10 - 3894x^8 + 20286x^6 - 43281x^4 + 17175x^2 + 52441	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 229^{4} \)	16T1744	Trivial (GRH)
16.8.1030748319240217600000000.1	x^16 - 19x^14 + 230x^12 - 2420x^10 + 16898x^8 - 66935x^6 + 140835x^4 - 141522x^2 + 52441	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 229^{4} \)	16T1744	Trivial (GRH)
16.4.1030748319240217600000000.2	x^16 - 101x^12 - 611x^10 + 1226x^8 + 688x^6 - 27022x^4 + 13969x^2 + 52441	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 229^{4} \)	16T1744	Trivial (GRH)
16.0.3025960667798491717697536.1	x^16 + 8x^14 + 68x^12 + 288x^10 + 1372x^8 + 3968x^6 + 8624x^4 + 10304x^2 + 8464	\( 2^{52}\cdot 7^{4}\cdot 23^{4} \)	16T1744	$[2]$ (GRH)
16.0.3025960667798491717697536.2	x^16 + 8x^14 + 72x^12 + 288x^10 + 542x^8 + 248x^6 - 584x^4 - 736x^2 + 529	\( 2^{52}\cdot 7^{4}\cdot 23^{4} \)	16T1744	$[2]$ (GRH)
16.0.4860398022531481600000000.1	x^16 + 4x^14 - 2x^12 - 72x^10 + 251x^8 + 1064x^6 + 614x^4 - 1740x^2 + 841	\( 2^{44}\cdot 5^{8}\cdot 29^{4} \)	16T1744	Trivial (GRH)
16.0.4860398022531481600000000.2	x^16 + 8x^14 + 60x^12 + 200x^10 + 908x^8 + 2000x^6 + 6560x^4 + 6496x^2 + 13456	\( 2^{44}\cdot 5^{8}\cdot 29^{4} \)	16T1744	Trivial (GRH)
16.0.8924358963806233600000000.1	x^16 + 16x^14 + 138x^12 + 1108x^10 + 6985x^8 + 26381x^6 + 54060x^4 + 55279x^2 + 22201	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 149^{4} \)	16T1744	$[2]$ (GRH)
16.4.8924358963806233600000000.1	x^16 - 82x^12 - 140x^10 + 1479x^8 + 14665x^6 - 82993x^4 + 98340x^2 + 22201	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 149^{4} \)	16T1744	Trivial (GRH)
16.8.8924358963806233600000000.1	x^16 - 28x^14 + 196x^12 - 372x^10 - 105x^8 - 1963x^6 + 17031x^4 - 35462x^2 + 22201	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 149^{4} \)	16T1744	Trivial (GRH)
16.0.8924358963806233600000000.2	x^16 + 22x^14 + 146x^12 + 358x^10 + 1200x^8 + 4772x^6 + 3131x^4 + 36058x^2 + 22201	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 149^{4} \)	16T1744	$[2]$ (GRH)
16.4.8924358963806233600000000.2	x^16 - 4x^14 - 63x^12 - 27x^10 + 531x^8 + 3370x^6 + 13261x^4 + 20711x^2 + 22201	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 149^{4} \)	16T1744	Trivial (GRH)
16.8.8924358963806233600000000.2	x^16 - 23x^14 + 169x^12 - 244x^10 - 1954x^8 + 5769x^6 + 7129x^4 - 34717x^2 + 22201	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 149^{4} \)	16T1744	Trivial (GRH)
16.0.3809203750059908108916883456.1	x^16 + 32x^14 + 388x^12 + 2288x^10 + 7670x^8 + 15936x^6 + 12836x^4 + 1904x^2 + 49	\( 2^{52}\cdot 7^{4}\cdot 137^{4} \)	16T1744	$[2]$ (GRH)
16.8.3809203750059908108916883456.1	x^16 - 32x^14 + 388x^12 - 2288x^10 + 7670x^8 - 15936x^6 + 12836x^4 - 1904x^2 + 49	\( 2^{52}\cdot 7^{4}\cdot 137^{4} \)	16T1744	$[2]$ (GRH)
16.0.3809203750059908108916883456.2	x^16 + 16x^14 + 136x^12 + 896x^10 + 3736x^8 + 8768x^6 + 13600x^4 + 12544x^2 + 784	\( 2^{52}\cdot 7^{4}\cdot 137^{4} \)	16T1744	$[6]$ (GRH)
16.8.3809203750059908108916883456.2	x^16 - 16x^14 + 136x^12 - 896x^10 + 3736x^8 - 8768x^6 + 13600x^4 - 12544x^2 + 784	\( 2^{52}\cdot 7^{4}\cdot 137^{4} \)	16T1744	$[2]$ (GRH)
16.0.27387862668182175769600000000.1	x^16 + 74x^14 + 2125x^12 + 30551x^10 + 237155x^8 + 1010173x^6 + 2331118x^4 + 2704851x^2 + 1229881	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 1109^{4} \)	16T1744	$[2, 3414]$ (GRH)
16.16.27387862668182175769600000000.1	x^16 - 74x^14 + 2125x^12 - 30551x^10 + 237155x^8 - 1010173x^6 + 2331118x^4 - 2704851x^2 + 1229881	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 1109^{4} \)	16T1744	Trivial (GRH)
16.0.17117414167613859856000000000000.1	x^16 + 180x^14 + 12415x^12 + 417875x^10 + 7355100x^8 + 69576750x^6 + 347255625x^4 + 844226250x^2 + 768675625	\( 2^{16}\cdot 5^{12}\cdot 29^{4}\cdot 1109^{4} \)	16T1744	$[2, 2, 30520]$ (GRH)
16.16.17117414167613859856000000000000.1	x^16 - 180x^14 + 12415x^12 - 417875x^10 + 7355100x^8 - 69576750x^6 + 347255625x^4 - 844226250x^2 + 768675625	\( 2^{16}\cdot 5^{12}\cdot 29^{4}\cdot 1109^{4} \)	16T1744	Trivial (GRH)