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Results (displaying all 20 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.17417174684532736.2	x¹⁶ + 3x¹⁴ + 11x¹² + 21x¹⁰ + 28x⁸ + 21x⁶ + 11x⁴ + 3x² + 1	$ 2^{20}\cdot 359^{4} $	$C_2\times C_2^3:S_4$ (as 16T747)	Trivial
16.0.18297527052795904.1	x¹⁶ - 4x¹⁵ + 8x¹⁴ - 12x¹³ + 14x¹² - 6x¹¹ - 16x¹⁰ + 46x⁹ - 67x⁸ + 62x⁷ - 22x⁶ - 36x⁵ + 77x⁴ - 78x³ + 50x² - 20x + 4	$ 2^{22}\cdot 257^{4} $	$C_2\times C_2^3:S_4$ (as 16T747)	Trivial (GRH)
16.0.36859674750877696.2	x¹⁶ - x¹⁴ - x¹² + x¹⁰ + 4x⁸ + x⁶ - x⁴ - x² + 1	$ 2^{20}\cdot 433^{4} $	$C_2\times C_2^3:S_4$ (as 16T747)	Trivial
16.0.42144634461229056.2	x¹⁶ - x¹⁴ - 3x¹² + x¹⁰ + 5x⁸ + x⁶ - 3x⁴ - x² + 1	$ 2^{12}\cdot 3^{8}\cdot 199^{4} $	$C_2\times C_2^3:S_4$ (as 16T747)	Trivial
16.0.278674794952523776.1	x¹⁶ - 4x¹⁵ + 8x¹⁴ - 10x¹³ + 15x¹² - 28x¹¹ + 42x¹⁰ - 48x⁹ + 49x⁸ - 48x⁷ + 42x⁶ - 28x⁵ + 15x⁴ - 10x³ + 8x² - 4x + 1	$ 2^{24}\cdot 359^{4} $	$C_2\times C_2^3:S_4$ (as 16T747)	Trivial
16.0.384165447630585856.2	x¹⁶ + 4x¹⁴ + 2x¹² - 4x¹⁰ - 5x⁸ - 4x⁶ + 2x⁴ + 4x² + 1	$ 2^{24}\cdot 389^{4} $	$C_2\times C_2^3:S_4$ (as 16T747)	Trivial
16.0.767656345600000000.3	x¹⁶ - 2x¹⁴ + 4x¹² - 10x¹⁰ + 15x⁸ - 10x⁶ + 4x⁴ - 2x² + 1	$ 2^{20}\cdot 5^{8}\cdot 37^{4} $	$C_2\times C_2^3:S_4$ (as 16T747)	Trivial
16.0.2409821569600000000.3	x¹⁶ + x¹⁴ + 3x¹² + 3x¹⁰ + 9x⁸ + 3x⁶ + 3x⁴ + x² + 1	$ 2^{12}\cdot 5^{8}\cdot 197^{4} $	$C_2\times C_2^3:S_4$ (as 16T747)	Trivial
16.0.6350601601600000000.1	x¹⁶ + 4x¹⁴ - 4x¹² - 26x¹⁰ + 14x⁸ + 76x⁶ + 58x⁴ + 15x² + 1	$ 2^{12}\cdot 5^{8}\cdot 251^{4} $	$C_2\times C_2^3:S_4$ (as 16T747)	Trivial
16.8.10621340052971585536.1	x¹⁶ - 10x¹⁴ + 31x¹² - 32x¹⁰ + 21x⁸ - 32x⁶ + 31x⁴ - 10x² + 1	$ 2^{32}\cdot 223^{4} $	$C_2\times C_2^3:S_4$ (as 16T747)	Trivial (GRH)
16.0.27548985049130991616.3	x¹⁶ + 6x¹⁴ + 8x¹² - 6x¹⁰ - 2x⁸ - 6x⁶ + 8x⁴ + 6x² + 1	$ 2^{32}\cdot 283^{4} $	$C_2\times C_2^3:S_4$ (as 16T747)	Trivial (GRH)
16.8.27548985049130991616.3	x¹⁶ - 8x¹⁴ + 31x¹² - 74x¹⁰ + 117x⁸ - 124x⁶ + 79x⁴ - 22x² + 1	$ 2^{32}\cdot 283^{4} $	$C_2\times C_2^3:S_4$ (as 16T747)	Trivial (GRH)
16.8.51555124070544572416.1	x¹⁶ - 8x¹⁴ + 23x¹² - 26x¹⁰ + 5x⁸ + 4x⁶ + 7x⁴ - 6x² + 1	$ 2^{32}\cdot 331^{4} $	$C_2\times C_2^3:S_4$ (as 16T747)	Trivial (GRH)
16.8.71340747507846086656.1	x¹⁶ - 6x¹⁴ + 11x¹² - 6x¹⁰ + x⁸ - 6x⁶ + 11x⁴ - 6x² + 1	$ 2^{32}\cdot 359^{4} $	$C_2\times C_2^3:S_4$ (as 16T747)	Trivial (GRH)
16.0.7029206082976827375616.2	x¹⁶ - 8x¹⁵ + 28x¹⁴ - 56x¹³ + 48x¹² + 76x¹¹ - 318x¹⁰ + 512x⁹ - 362x⁸ - 216x⁷ + 852x⁶ - 1068x⁵ + 833x⁴ - 452x³ + 178x² - 48x + 25	$ 2^{16}\cdot 18097^{4} $	$C_2\times C_2^3:S_4$ (as 16T747)	$[2]$
16.0.7029206082976827375616.3	x¹⁶ - 2x¹⁴ + 3x¹² - 6x¹⁰ + 9x⁸ - 24x⁶ + 48x⁴ - 128x² + 256	$ 2^{16}\cdot 18097^{4} $	$C_2\times C_2^3:S_4$ (as 16T747)	Trivial
16.0.1112902699252309005697024.1	x¹⁶ + 7x¹² - 158x¹⁰ + 803x⁸ - 1172x⁶ + 3089x⁴ + 1042x² + 196	$ 2^{34}\cdot 2837^{4} $	$C_2\times C_2^3:S_4$ (as 16T747)	$[6]$ (GRH)
16.16.4451610797009236022788096.1	x¹⁶ - 26x¹⁴ + 240x¹² - 998x¹⁰ + 1934x⁸ - 1654x⁶ + 512x⁴ - 42x² + 1	$ 2^{36}\cdot 2837^{4} $	$C_2\times C_2^3:S_4$ (as 16T747)	Trivial (GRH)
16.16.15095651501680439049846784.1	x¹⁶ - 20x¹⁴ + 146x¹² - 502x¹⁰ + 865x⁸ - 742x⁶ + 317x⁴ - 62x² + 4	$ 2^{30}\cdot 10889^{4} $	$C_2\times C_2^3:S_4$ (as 16T747)	Trivial (GRH)
16.0.25221297570561000000000000.1	x¹⁶ + 35x¹⁴ + 475x¹² + 3225x¹⁰ + 11775x⁸ + 22875x⁶ + 21250x⁴ + 6875x² + 625	$ 2^{12}\cdot 3^{12}\cdot 5^{12}\cdot 83^{4} $	$C_2\times C_2^3:S_4$ (as 16T747)	$[2, 2, 30]$ (GRH)

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Results (displaying all 20 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
16.0.17417174684532736.2	x¹⁶ + 3x¹⁴ + 11x¹² + 21x¹⁰ + 28x⁸ + 21x⁶ + 11x⁴ + 3x² + 1	\( 2^{20}\cdot 359^{4} \)	$C_2\times C_2^3:S_4$ (as 16T747)	Trivial
16.0.18297527052795904.1	x¹⁶ - 4x¹⁵ + 8x¹⁴ - 12x¹³ + 14x¹² - 6x¹¹ - 16x¹⁰ + 46x⁹ - 67x⁸ + 62x⁷ - 22x⁶ - 36x⁵ + 77x⁴ - 78x³ + 50x² - 20x + 4	\( 2^{22}\cdot 257^{4} \)	$C_2\times C_2^3:S_4$ (as 16T747)	Trivial (GRH)
16.0.36859674750877696.2	x¹⁶ - x¹⁴ - x¹² + x¹⁰ + 4x⁸ + x⁶ - x⁴ - x² + 1	\( 2^{20}\cdot 433^{4} \)	$C_2\times C_2^3:S_4$ (as 16T747)	Trivial
16.0.42144634461229056.2	x¹⁶ - x¹⁴ - 3x¹² + x¹⁰ + 5x⁸ + x⁶ - 3x⁴ - x² + 1	\( 2^{12}\cdot 3^{8}\cdot 199^{4} \)	$C_2\times C_2^3:S_4$ (as 16T747)	Trivial
16.0.278674794952523776.1	x¹⁶ - 4x¹⁵ + 8x¹⁴ - 10x¹³ + 15x¹² - 28x¹¹ + 42x¹⁰ - 48x⁹ + 49x⁸ - 48x⁷ + 42x⁶ - 28x⁵ + 15x⁴ - 10x³ + 8x² - 4x + 1	\( 2^{24}\cdot 359^{4} \)	$C_2\times C_2^3:S_4$ (as 16T747)	Trivial
16.0.384165447630585856.2	x¹⁶ + 4x¹⁴ + 2x¹² - 4x¹⁰ - 5x⁸ - 4x⁶ + 2x⁴ + 4x² + 1	\( 2^{24}\cdot 389^{4} \)	$C_2\times C_2^3:S_4$ (as 16T747)	Trivial
16.0.767656345600000000.3	x¹⁶ - 2x¹⁴ + 4x¹² - 10x¹⁰ + 15x⁸ - 10x⁶ + 4x⁴ - 2x² + 1	\( 2^{20}\cdot 5^{8}\cdot 37^{4} \)	$C_2\times C_2^3:S_4$ (as 16T747)	Trivial
16.0.2409821569600000000.3	x¹⁶ + x¹⁴ + 3x¹² + 3x¹⁰ + 9x⁸ + 3x⁶ + 3x⁴ + x² + 1	\( 2^{12}\cdot 5^{8}\cdot 197^{4} \)	$C_2\times C_2^3:S_4$ (as 16T747)	Trivial
16.0.6350601601600000000.1	x¹⁶ + 4x¹⁴ - 4x¹² - 26x¹⁰ + 14x⁸ + 76x⁶ + 58x⁴ + 15x² + 1	\( 2^{12}\cdot 5^{8}\cdot 251^{4} \)	$C_2\times C_2^3:S_4$ (as 16T747)	Trivial
16.8.10621340052971585536.1	x¹⁶ - 10x¹⁴ + 31x¹² - 32x¹⁰ + 21x⁸ - 32x⁶ + 31x⁴ - 10x² + 1	\( 2^{32}\cdot 223^{4} \)	$C_2\times C_2^3:S_4$ (as 16T747)	Trivial (GRH)
16.0.27548985049130991616.3	x¹⁶ + 6x¹⁴ + 8x¹² - 6x¹⁰ - 2x⁸ - 6x⁶ + 8x⁴ + 6x² + 1	\( 2^{32}\cdot 283^{4} \)	$C_2\times C_2^3:S_4$ (as 16T747)	Trivial (GRH)
16.8.27548985049130991616.3	x¹⁶ - 8x¹⁴ + 31x¹² - 74x¹⁰ + 117x⁸ - 124x⁶ + 79x⁴ - 22x² + 1	\( 2^{32}\cdot 283^{4} \)	$C_2\times C_2^3:S_4$ (as 16T747)	Trivial (GRH)
16.8.51555124070544572416.1	x¹⁶ - 8x¹⁴ + 23x¹² - 26x¹⁰ + 5x⁸ + 4x⁶ + 7x⁴ - 6x² + 1	\( 2^{32}\cdot 331^{4} \)	$C_2\times C_2^3:S_4$ (as 16T747)	Trivial (GRH)
16.8.71340747507846086656.1	x¹⁶ - 6x¹⁴ + 11x¹² - 6x¹⁰ + x⁸ - 6x⁶ + 11x⁴ - 6x² + 1	\( 2^{32}\cdot 359^{4} \)	$C_2\times C_2^3:S_4$ (as 16T747)	Trivial (GRH)
16.0.7029206082976827375616.2	x¹⁶ - 8x¹⁵ + 28x¹⁴ - 56x¹³ + 48x¹² + 76x¹¹ - 318x¹⁰ + 512x⁹ - 362x⁸ - 216x⁷ + 852x⁶ - 1068x⁵ + 833x⁴ - 452x³ + 178x² - 48x + 25	\( 2^{16}\cdot 18097^{4} \)	$C_2\times C_2^3:S_4$ (as 16T747)	$[2]$
16.0.7029206082976827375616.3	x¹⁶ - 2x¹⁴ + 3x¹² - 6x¹⁰ + 9x⁸ - 24x⁶ + 48x⁴ - 128x² + 256	\( 2^{16}\cdot 18097^{4} \)	$C_2\times C_2^3:S_4$ (as 16T747)	Trivial
16.0.1112902699252309005697024.1	x¹⁶ + 7x¹² - 158x¹⁰ + 803x⁸ - 1172x⁶ + 3089x⁴ + 1042x² + 196	\( 2^{34}\cdot 2837^{4} \)	$C_2\times C_2^3:S_4$ (as 16T747)	$[6]$ (GRH)
16.16.4451610797009236022788096.1	x¹⁶ - 26x¹⁴ + 240x¹² - 998x¹⁰ + 1934x⁸ - 1654x⁶ + 512x⁴ - 42x² + 1	\( 2^{36}\cdot 2837^{4} \)	$C_2\times C_2^3:S_4$ (as 16T747)	Trivial (GRH)
16.16.15095651501680439049846784.1	x¹⁶ - 20x¹⁴ + 146x¹² - 502x¹⁰ + 865x⁸ - 742x⁶ + 317x⁴ - 62x² + 4	\( 2^{30}\cdot 10889^{4} \)	$C_2\times C_2^3:S_4$ (as 16T747)	Trivial (GRH)
16.0.25221297570561000000000000.1	x¹⁶ + 35x¹⁴ + 475x¹² + 3225x¹⁰ + 11775x⁸ + 22875x⁶ + 21250x⁴ + 6875x² + 625	\( 2^{12}\cdot 3^{12}\cdot 5^{12}\cdot 83^{4} \)	$C_2\times C_2^3:S_4$ (as 16T747)	$[2, 2, 30]$ (GRH)