LMFDB - Global number field search results

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Results (displaying all 26 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.28344976000000000000.4	x¹⁶ - 10x¹⁴ + 38x¹² - 70x¹⁰ + 59x⁸ + 40x⁶ - 163x⁴ + 55x² + 121	$ 2^{16}\cdot 5^{12}\cdot 11^{6} $	$C_2^4.C_2^3.C_2$ (as 16T646)	Trivial
16.0.28344976000000000000.5	x¹⁶ + 10x¹⁴ + 38x¹² + 70x¹⁰ + 59x⁸ - 40x⁶ - 163x⁴ - 55x² + 121	$ 2^{16}\cdot 5^{12}\cdot 11^{6} $	$C_2^4.C_2^3.C_2$ (as 16T646)	Trivial
16.4.3429742096000000000000.5	x¹⁶ - 3x¹⁴ - 5x¹² + 27x¹⁰ - 6x⁸ - 57x⁶ + 35x⁴ - 12x² + 1	$ 2^{16}\cdot 5^{12}\cdot 11^{8} $	$C_2^4.C_2^3.C_2$ (as 16T646)	Trivial (GRH)
16.4.3429742096000000000000.6	x¹⁶ - x¹⁴ - 8x¹² - 23x¹⁰ + 15x⁸ + 23x⁶ - 8x⁴ + x² + 1	$ 2^{16}\cdot 5^{12}\cdot 11^{8} $	$C_2^4.C_2^3.C_2$ (as 16T646)	Trivial (GRH)
16.8.33910015523872734969856.4	x¹⁶ - 8x¹⁵ + 24x¹⁴ - 16x¹³ - 80x¹² + 192x¹¹ - 56x¹⁰ - 280x⁹ + 182x⁸ + 392x⁷ - 456x⁶ - 48x⁵ + 280x⁴ - 176x³ + 24x² + 40x - 17	$ 2^{58}\cdot 7^{6} $	$C_2^4.C_2^3.C_2$ (as 16T646)	Trivial
16.8.33910015523872734969856.5	x¹⁶ - 8x¹⁵ + 32x¹⁴ - 80x¹³ + 100x¹² + 136x¹¹ - 1008x¹⁰ + 2768x⁹ - 5328x⁸ + 7808x⁷ - 8048x⁶ + 4784x⁵ - 648x⁴ - 1008x³ + 608x² - 112x + 2	$ 2^{58}\cdot 7^{6} $	$C_2^4.C_2^3.C_2$ (as 16T646)	Trivial (GRH)
16.4.825241970563213134765625.1	x¹⁶ - 2x¹⁵ + 2x¹⁴ + 17x¹³ - 53x¹² + 160x¹¹ - 567x¹⁰ + 1306x⁹ - 3585x⁸ + 6949x⁷ - 7552x⁶ + 9035x⁵ - 11178x⁴ + 4713x³ + 2747x² - 2323x + 691	$ 5^{12}\cdot 11^{10}\cdot 19^{4} $	$C_2^4.C_2^3.C_2$ (as 16T646)	$[2]$ (GRH)
16.4.825241970563213134765625.2	x¹⁶ - 3x¹⁵ - 2x¹⁴ + 5x¹³ + 10x¹² - 2x¹¹ - 571x¹⁰ + 610x⁹ + 204x⁸ - 1275x⁷ - 2514x⁶ - 3254x⁵ + 8945x⁴ - 2220x³ + 3512x² - 8726x + 1181	$ 5^{12}\cdot 11^{10}\cdot 19^{4} $	$C_2^4.C_2^3.C_2$ (as 16T646)	$[2]$ (GRH)
16.0.1112740419079696000000000000.1	x¹⁶ + 67x¹⁴ + 2149x¹² + 47378x¹⁰ + 785991x⁸ + 9245500x⁶ + 70680940x⁴ + 313783250x² + 615288025	$ 2^{16}\cdot 5^{12}\cdot 11^{4}\cdot 41^{6} $	$C_2^4.C_2^3.C_2$ (as 16T646)	$[2, 2]$ (GRH)
16.0.1112740419079696000000000000.2	x¹⁶ + 78x¹⁴ + 2954x¹² + 70302x¹⁰ + 1134091x⁸ + 12348600x⁶ + 86292965x⁴ + 347890125x² + 615288025	$ 2^{16}\cdot 5^{12}\cdot 11^{4}\cdot 41^{6} $	$C_2^4.C_2^3.C_2$ (as 16T646)	$[2, 2]$ (GRH)
16.0.2229454910146816000000000000.3	x¹⁶ - 79x¹⁴ + 2940x¹² - 61956x¹⁰ + 777889x⁸ - 6088896x⁶ + 32389280x⁴ - 113326664x² + 197009296	$ 2^{20}\cdot 5^{12}\cdot 11^{4}\cdot 29^{6} $	$C_2^4.C_2^3.C_2$ (as 16T646)	$[2, 2]$ (GRH)
16.0.2229454910146816000000000000.4	x¹⁶ + 11x¹⁴ - 500x¹² - 2266x¹⁰ + 255549x⁸ + 4668774x⁶ + 35436060x⁴ + 130619016x² + 197009296	$ 2^{20}\cdot 5^{12}\cdot 11^{4}\cdot 29^{6} $	$C_2^4.C_2^3.C_2$ (as 16T646)	$[2, 2]$ (GRH)
16.0.26893256677956496000000000000.6	x¹⁶ + 64x¹⁴ + 3069x¹² + 86088x¹⁰ + 1843044x⁸ + 25996296x⁶ + 254177286x⁴ + 1275176342x² + 2376465001	$ 2^{16}\cdot 5^{12}\cdot 29^{6}\cdot 41^{4} $	$C_2^4.C_2^3.C_2$ (as 16T646)	$[2, 2]$ (GRH)
16.0.27818510476992400000000000000.1	x¹⁶ + 160x¹⁴ + 11810x¹² + 518865x¹⁰ + 14726560x⁸ + 275025300x⁶ + 3296657100x⁴ + 23237696075x² + 74449851025	$ 2^{16}\cdot 5^{14}\cdot 11^{4}\cdot 41^{6} $	$C_2^4.C_2^3.C_2$ (as 16T646)	$[2, 2, 2]$ (GRH)
16.0.45315174505109995158677487616.1	x¹⁶ - 8x¹⁵ + 40x¹⁴ - 24x¹³ - 528x¹² + 3224x¹¹ - 5672x¹⁰ - 10936x⁹ + 65694x⁸ - 110584x⁷ + 34688x⁶ + 155224x⁵ - 233104x⁴ + 70808x³ + 129552x² - 137400x + 42191	$ 2^{62}\cdot 7^{6}\cdot 17^{4} $	$C_2^4.C_2^3.C_2$ (as 16T646)	$[2, 2]$ (GRH)
16.0.45315174505109995158677487616.2	x¹⁶ - 8x¹⁵ + 40x¹⁴ - 88x¹³ + 208x¹² - 8x¹¹ - 2584x¹⁰ + 1672x⁹ + 12974x⁸ + 26120x⁷ + 2320x⁶ - 45224x⁵ + 82448x⁴ - 58952x³ + 25392x² - 5656x + 479	$ 2^{62}\cdot 7^{6}\cdot 17^{4} $	$C_2^4.C_2^3.C_2$ (as 16T646)	$[2, 2]$ (GRH)
16.0.672331416948912400000000000000.1	x¹⁶ - 4x¹⁵ - 10x¹⁴ - 100x¹³ + 2815x¹² - 2902x¹¹ - 73287x¹⁰ + 31830x⁹ + 1885080x⁸ - 1034380x⁷ - 29643917x⁶ + 22108018x⁵ + 239383365x⁴ - 156467770x³ - 1002864095x² + 378955036x + 1903906301	$ 2^{16}\cdot 5^{14}\cdot 29^{6}\cdot 41^{4} $	$C_2^4.C_2^3.C_2$ (as 16T646)	$[2, 2, 2, 4]$ (GRH)
16.16.672331416948912400000000000000.1	x¹⁶ - 8x¹⁵ - 45x¹⁴ + 390x¹³ + 915x¹² - 7344x¹¹ - 11793x¹⁰ + 66050x⁹ + 101540x⁸ - 278030x⁷ - 507873x⁶ + 401424x⁵ + 1140855x⁴ + 229470x³ - 726420x² - 502312x - 87719	$ 2^{16}\cdot 5^{14}\cdot 29^{6}\cdot 41^{4} $	$C_2^4.C_2^3.C_2$ (as 16T646)	Trivial (GRH)
16.0.672331416948912400000000000000.2	x¹⁶ - 2x¹⁵ + 49x¹⁴ + 18x¹³ + 1033x¹² + 1768x¹¹ + 16241x¹⁰ + 34754x⁹ + 169508x⁸ + 362188x⁷ + 1138799x⁶ + 2001274x⁵ + 4821683x⁴ + 7255146x³ + 12306656x² + 10628644x + 8643461	$ 2^{16}\cdot 5^{14}\cdot 29^{6}\cdot 41^{4} $	$C_2^4.C_2^3.C_2$ (as 16T646)	$[2, 2, 2, 2, 792]$ (GRH)
16.8.725042792081759922538839801856.1	x¹⁶ + 16x¹⁴ - 144x¹³ - 480x¹² - 3472x¹¹ - 6408x¹⁰ - 5152x⁹ + 13414x⁸ + 178864x⁷ + 77032x⁶ + 700720x⁵ - 357176x⁴ - 2773584x³ - 664992x² + 390096x - 32481	$ 2^{66}\cdot 7^{6}\cdot 17^{4} $	$C_2^4.C_2^3.C_2$ (as 16T646)	Trivial (GRH)
16.8.725042792081759922538839801856.2	x¹⁶ - 48x¹⁴ - 64x¹³ + 544x¹² + 2512x¹¹ + 3736x¹⁰ - 23632x⁹ - 89178x⁸ + 33296x⁷ + 227816x⁶ - 426976x⁵ - 625800x⁴ + 2369616x³ + 9936896x² + 19567936x + 14353967	$ 2^{66}\cdot 7^{6}\cdot 17^{4} $	$C_2^4.C_2^3.C_2$ (as 16T646)	$[2]$ (GRH)
16.0.4414801218324694314062500000000.1	x¹⁶ - 7x¹⁵ - 26x¹⁴ + 198x¹³ + 1238x¹² - 7747x¹¹ - 17774x¹⁰ + 172969x⁹ - 70297x⁸ - 1752687x⁷ + 4428414x⁶ - 2245971x⁵ + 1841738x⁴ - 22015584x³ + 35345376x² - 11444301x + 1185921	$ 2^{8}\cdot 5^{14}\cdot 29^{6}\cdot 41^{6} $	$C_2^4.C_2^3.C_2$ (as 16T646)	$[2, 2, 2, 8]$ (GRH)
16.8.13096085431976788600857793921024.1	x¹⁶ + 8x¹⁴ - 508x¹² - 2840x¹⁰ + 65942x⁸ + 146872x⁶ - 2196828x⁴ + 545496x² + 14161	$ 2^{62}\cdot 7^{6}\cdot 17^{6} $	$C_2^4.C_2^3.C_2$ (as 16T646)	$[2]$ (GRH)
16.8.13096085431976788600857793921024.2	x¹⁶ + 8x¹⁴ - 764x¹² - 3096x¹⁰ + 45974x⁸ - 14920x⁶ - 274012x⁴ - 94248x² + 14161	$ 2^{62}\cdot 7^{6}\cdot 17^{6} $	$C_2^4.C_2^3.C_2$ (as 16T646)	$[2]$ (GRH)
16.0.90361374415646880016000000000000.1	x¹⁶ - 6x¹⁵ + 21x¹⁴ - 68x¹³ + 578x¹² - 1782x¹¹ + 3296x¹⁰ - 12586x⁹ + 51409x⁸ - 114122x⁷ + 191292x⁶ - 254338x⁵ + 369314x⁴ - 809504x³ + 671241x² + 674734x + 904681	$ 2^{16}\cdot 5^{12}\cdot 29^{4}\cdot 41^{8} $	$C_2^4.C_2^3.C_2$ (as 16T646)	$[2, 4, 652]$ (GRH)
16.16.90361374415646880016000000000000.1	x¹⁶ - 6x¹⁵ - 47x¹⁴ + 394x¹³ - 99x¹² - 5198x¹¹ + 10255x¹⁰ + 19300x⁹ - 73824x⁸ + 13230x⁷ + 174825x⁶ - 172326x⁵ - 89901x⁴ + 208654x³ - 93950x² + 8432x + 1021	$ 2^{16}\cdot 5^{12}\cdot 29^{4}\cdot 41^{8} $	$C_2^4.C_2^3.C_2$ (as 16T646)	$[2]$ (GRH)

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Results (displaying all 26 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	Polynomial	Discriminant	Galois group	Class group
16.0.28344976000000000000.4	x¹⁶ - 10x¹⁴ + 38x¹² - 70x¹⁰ + 59x⁸ + 40x⁶ - 163x⁴ + 55x² + 121	\( 2^{16}\cdot 5^{12}\cdot 11^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T646)	Trivial
16.0.28344976000000000000.5	x¹⁶ + 10x¹⁴ + 38x¹² + 70x¹⁰ + 59x⁸ - 40x⁶ - 163x⁴ - 55x² + 121	\( 2^{16}\cdot 5^{12}\cdot 11^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T646)	Trivial
16.4.3429742096000000000000.5	x¹⁶ - 3x¹⁴ - 5x¹² + 27x¹⁰ - 6x⁸ - 57x⁶ + 35x⁴ - 12x² + 1	\( 2^{16}\cdot 5^{12}\cdot 11^{8} \)	$C_2^4.C_2^3.C_2$ (as 16T646)	Trivial (GRH)
16.4.3429742096000000000000.6	x¹⁶ - x¹⁴ - 8x¹² - 23x¹⁰ + 15x⁸ + 23x⁶ - 8x⁴ + x² + 1	\( 2^{16}\cdot 5^{12}\cdot 11^{8} \)	$C_2^4.C_2^3.C_2$ (as 16T646)	Trivial (GRH)
16.8.33910015523872734969856.4	x¹⁶ - 8x¹⁵ + 24x¹⁴ - 16x¹³ - 80x¹² + 192x¹¹ - 56x¹⁰ - 280x⁹ + 182x⁸ + 392x⁷ - 456x⁶ - 48x⁵ + 280x⁴ - 176x³ + 24x² + 40x - 17	\( 2^{58}\cdot 7^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T646)	Trivial
16.8.33910015523872734969856.5	x¹⁶ - 8x¹⁵ + 32x¹⁴ - 80x¹³ + 100x¹² + 136x¹¹ - 1008x¹⁰ + 2768x⁹ - 5328x⁸ + 7808x⁷ - 8048x⁶ + 4784x⁵ - 648x⁴ - 1008x³ + 608x² - 112x + 2	\( 2^{58}\cdot 7^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T646)	Trivial (GRH)
16.4.825241970563213134765625.1	x¹⁶ - 2x¹⁵ + 2x¹⁴ + 17x¹³ - 53x¹² + 160x¹¹ - 567x¹⁰ + 1306x⁹ - 3585x⁸ + 6949x⁷ - 7552x⁶ + 9035x⁵ - 11178x⁴ + 4713x³ + 2747x² - 2323x + 691	\( 5^{12}\cdot 11^{10}\cdot 19^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T646)	$[2]$ (GRH)
16.4.825241970563213134765625.2	x¹⁶ - 3x¹⁵ - 2x¹⁴ + 5x¹³ + 10x¹² - 2x¹¹ - 571x¹⁰ + 610x⁹ + 204x⁸ - 1275x⁷ - 2514x⁶ - 3254x⁵ + 8945x⁴ - 2220x³ + 3512x² - 8726x + 1181	\( 5^{12}\cdot 11^{10}\cdot 19^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T646)	$[2]$ (GRH)
16.0.1112740419079696000000000000.1	x¹⁶ + 67x¹⁴ + 2149x¹² + 47378x¹⁰ + 785991x⁸ + 9245500x⁶ + 70680940x⁴ + 313783250x² + 615288025	\( 2^{16}\cdot 5^{12}\cdot 11^{4}\cdot 41^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T646)	$[2, 2]$ (GRH)
16.0.1112740419079696000000000000.2	x¹⁶ + 78x¹⁴ + 2954x¹² + 70302x¹⁰ + 1134091x⁸ + 12348600x⁶ + 86292965x⁴ + 347890125x² + 615288025	\( 2^{16}\cdot 5^{12}\cdot 11^{4}\cdot 41^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T646)	$[2, 2]$ (GRH)
16.0.2229454910146816000000000000.3	x¹⁶ - 79x¹⁴ + 2940x¹² - 61956x¹⁰ + 777889x⁸ - 6088896x⁶ + 32389280x⁴ - 113326664x² + 197009296	\( 2^{20}\cdot 5^{12}\cdot 11^{4}\cdot 29^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T646)	$[2, 2]$ (GRH)
16.0.2229454910146816000000000000.4	x¹⁶ + 11x¹⁴ - 500x¹² - 2266x¹⁰ + 255549x⁸ + 4668774x⁶ + 35436060x⁴ + 130619016x² + 197009296	\( 2^{20}\cdot 5^{12}\cdot 11^{4}\cdot 29^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T646)	$[2, 2]$ (GRH)
16.0.26893256677956496000000000000.6	x¹⁶ + 64x¹⁴ + 3069x¹² + 86088x¹⁰ + 1843044x⁸ + 25996296x⁶ + 254177286x⁴ + 1275176342x² + 2376465001	\( 2^{16}\cdot 5^{12}\cdot 29^{6}\cdot 41^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T646)	$[2, 2]$ (GRH)
16.0.27818510476992400000000000000.1	x¹⁶ + 160x¹⁴ + 11810x¹² + 518865x¹⁰ + 14726560x⁸ + 275025300x⁶ + 3296657100x⁴ + 23237696075x² + 74449851025	\( 2^{16}\cdot 5^{14}\cdot 11^{4}\cdot 41^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T646)	$[2, 2, 2]$ (GRH)
16.0.45315174505109995158677487616.1	x¹⁶ - 8x¹⁵ + 40x¹⁴ - 24x¹³ - 528x¹² + 3224x¹¹ - 5672x¹⁰ - 10936x⁹ + 65694x⁸ - 110584x⁷ + 34688x⁶ + 155224x⁵ - 233104x⁴ + 70808x³ + 129552x² - 137400x + 42191	\( 2^{62}\cdot 7^{6}\cdot 17^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T646)	$[2, 2]$ (GRH)
16.0.45315174505109995158677487616.2	x¹⁶ - 8x¹⁵ + 40x¹⁴ - 88x¹³ + 208x¹² - 8x¹¹ - 2584x¹⁰ + 1672x⁹ + 12974x⁸ + 26120x⁷ + 2320x⁶ - 45224x⁵ + 82448x⁴ - 58952x³ + 25392x² - 5656x + 479	\( 2^{62}\cdot 7^{6}\cdot 17^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T646)	$[2, 2]$ (GRH)
16.0.672331416948912400000000000000.1	x¹⁶ - 4x¹⁵ - 10x¹⁴ - 100x¹³ + 2815x¹² - 2902x¹¹ - 73287x¹⁰ + 31830x⁹ + 1885080x⁸ - 1034380x⁷ - 29643917x⁶ + 22108018x⁵ + 239383365x⁴ - 156467770x³ - 1002864095x² + 378955036x + 1903906301	\( 2^{16}\cdot 5^{14}\cdot 29^{6}\cdot 41^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T646)	$[2, 2, 2, 4]$ (GRH)
16.16.672331416948912400000000000000.1	x¹⁶ - 8x¹⁵ - 45x¹⁴ + 390x¹³ + 915x¹² - 7344x¹¹ - 11793x¹⁰ + 66050x⁹ + 101540x⁸ - 278030x⁷ - 507873x⁶ + 401424x⁵ + 1140855x⁴ + 229470x³ - 726420x² - 502312x - 87719	\( 2^{16}\cdot 5^{14}\cdot 29^{6}\cdot 41^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T646)	Trivial (GRH)
16.0.672331416948912400000000000000.2	x¹⁶ - 2x¹⁵ + 49x¹⁴ + 18x¹³ + 1033x¹² + 1768x¹¹ + 16241x¹⁰ + 34754x⁹ + 169508x⁸ + 362188x⁷ + 1138799x⁶ + 2001274x⁵ + 4821683x⁴ + 7255146x³ + 12306656x² + 10628644x + 8643461	\( 2^{16}\cdot 5^{14}\cdot 29^{6}\cdot 41^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T646)	$[2, 2, 2, 2, 792]$ (GRH)
16.8.725042792081759922538839801856.1	x¹⁶ + 16x¹⁴ - 144x¹³ - 480x¹² - 3472x¹¹ - 6408x¹⁰ - 5152x⁹ + 13414x⁸ + 178864x⁷ + 77032x⁶ + 700720x⁵ - 357176x⁴ - 2773584x³ - 664992x² + 390096x - 32481	\( 2^{66}\cdot 7^{6}\cdot 17^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T646)	Trivial (GRH)
16.8.725042792081759922538839801856.2	x¹⁶ - 48x¹⁴ - 64x¹³ + 544x¹² + 2512x¹¹ + 3736x¹⁰ - 23632x⁹ - 89178x⁸ + 33296x⁷ + 227816x⁶ - 426976x⁵ - 625800x⁴ + 2369616x³ + 9936896x² + 19567936x + 14353967	\( 2^{66}\cdot 7^{6}\cdot 17^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T646)	$[2]$ (GRH)
16.0.4414801218324694314062500000000.1	x¹⁶ - 7x¹⁵ - 26x¹⁴ + 198x¹³ + 1238x¹² - 7747x¹¹ - 17774x¹⁰ + 172969x⁹ - 70297x⁸ - 1752687x⁷ + 4428414x⁶ - 2245971x⁵ + 1841738x⁴ - 22015584x³ + 35345376x² - 11444301x + 1185921	\( 2^{8}\cdot 5^{14}\cdot 29^{6}\cdot 41^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T646)	$[2, 2, 2, 8]$ (GRH)
16.8.13096085431976788600857793921024.1	x¹⁶ + 8x¹⁴ - 508x¹² - 2840x¹⁰ + 65942x⁸ + 146872x⁶ - 2196828x⁴ + 545496x² + 14161	\( 2^{62}\cdot 7^{6}\cdot 17^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T646)	$[2]$ (GRH)
16.8.13096085431976788600857793921024.2	x¹⁶ + 8x¹⁴ - 764x¹² - 3096x¹⁰ + 45974x⁸ - 14920x⁶ - 274012x⁴ - 94248x² + 14161	\( 2^{62}\cdot 7^{6}\cdot 17^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T646)	$[2]$ (GRH)
16.0.90361374415646880016000000000000.1	x¹⁶ - 6x¹⁵ + 21x¹⁴ - 68x¹³ + 578x¹² - 1782x¹¹ + 3296x¹⁰ - 12586x⁹ + 51409x⁸ - 114122x⁷ + 191292x⁶ - 254338x⁵ + 369314x⁴ - 809504x³ + 671241x² + 674734x + 904681	\( 2^{16}\cdot 5^{12}\cdot 29^{4}\cdot 41^{8} \)	$C_2^4.C_2^3.C_2$ (as 16T646)	$[2, 4, 652]$ (GRH)
16.16.90361374415646880016000000000000.1	x¹⁶ - 6x¹⁵ - 47x¹⁴ + 394x¹³ - 99x¹² - 5198x¹¹ + 10255x¹⁰ + 19300x⁹ - 73824x⁸ + 13230x⁷ + 174825x⁶ - 172326x⁵ - 89901x⁴ + 208654x³ - 93950x² + 8432x + 1021	\( 2^{16}\cdot 5^{12}\cdot 29^{4}\cdot 41^{8} \)	$C_2^4.C_2^3.C_2$ (as 16T646)	$[2]$ (GRH)