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Results (displaying all 28 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.99038527051792384.4	x¹⁶ - 3x¹⁴ + 5x¹² - x¹⁰ + 12x⁸ - x⁶ + 5x⁴ - 3x² + 1	$ 2^{34}\cdot 7^{8} $	$C_2^4.C_2^3.C_2$ (as 16T500)	Trivial
16.0.103670069459943424.4	x¹⁶ + 5x¹² - 2x¹⁰ + 9x⁸ - 2x⁶ + 5x⁴ + 1	$ 2^{32}\cdot 17^{6} $	$C_2^4.C_2^3.C_2$ (as 16T500)	Trivial
16.4.557879216297265625.1	x¹⁶ - 3x¹⁵ + 6x¹⁴ - 12x¹³ + 13x¹² - 2x¹¹ - 26x¹⁰ + 47x⁹ - 49x⁸ + 47x⁷ - 26x⁶ - 2x⁵ + 13x⁴ - 12x³ + 6x² - 3x + 1	$ 5^{8}\cdot 7^{4}\cdot 29^{6} $	$C_2^4.C_2^3.C_2$ (as 16T500)	Trivial
16.8.6636230027766015625.1	x¹⁶ - 5x¹⁵ + 6x¹⁴ + 13x¹³ - 43x¹² + 36x¹¹ - 19x¹⁰ + 123x⁹ - 266x⁸ + 72x⁷ + 421x⁶ - 556x⁵ + 197x⁴ + 52x³ - 34x² + 1	$ 5^{8}\cdot 13^{4}\cdot 29^{6} $	$C_2^4.C_2^3.C_2$ (as 16T500)	Trivial (GRH)
16.4.15227477017600000000.4	x¹⁶ - 6x¹⁴ + 6x¹² - 5x¹⁰ + 16x⁸ - 13x⁶ - 8x⁴ + 9x² + 1	$ 2^{16}\cdot 5^{8}\cdot 29^{6} $	$C_2^4.C_2^3.C_2$ (as 16T500)	Trivial (GRH)
16.8.20401542367685902336.2	x¹⁶ - 4x¹⁴ - 16x¹² + 42x¹⁰ + 34x⁸ - 112x⁶ + 37x⁴ + 18x² + 1	$ 2^{32}\cdot 41^{6} $	$C_2^4.C_2^3.C_2$ (as 16T500)	Trivial
16.0.49698129096100000000.1	x¹⁶ - 4x¹⁴ + 20x¹² - 46x¹⁰ + 100x⁸ - 128x⁶ + 133x⁴ - 76x² + 16	$ 2^{8}\cdot 5^{8}\cdot 89^{6} $	$C_2^4.C_2^3.C_2$ (as 16T500)	Trivial
16.0.326424677882974437376.1	x¹⁶ - 4x¹⁵ + 10x¹⁴ - 20x¹³ + 46x¹² - 136x¹¹ + 386x¹⁰ - 896x⁹ + 1654x⁸ - 2436x⁷ + 2878x⁶ - 2708x⁵ + 2014x⁴ - 1152x³ + 510x² - 168x + 49	$ 2^{36}\cdot 41^{6} $	$C_2^4.C_2^3.C_2$ (as 16T500)	$[2]$
16.8.424632604507928264704.1	x¹⁶ - 12x¹⁴ + 56x¹² - 132x¹⁰ + 190x⁸ - 212x⁶ + 152x⁴ - 28x² + 1	$ 2^{44}\cdot 17^{6} $	$C_2^4.C_2^3.C_2$ (as 16T500)	Trivial (GRH)
16.0.795170065537600000000.1	x¹⁶ - x¹⁴ + 19x¹² - 26x¹⁰ + 120x⁸ - 216x⁶ + 144x⁴ - 256x² + 256	$ 2^{12}\cdot 5^{8}\cdot 89^{6} $	$C_2^4.C_2^3.C_2$ (as 16T500)	Trivial
16.8.4147643767353759765625.1	x¹⁶ - 5x¹⁵ + 5x¹⁴ + 36x¹³ - 118x¹² + 70x¹¹ + 206x¹⁰ - 576x⁹ + 684x⁸ + 211x⁷ - 1129x⁶ - 163x⁵ + 2024x⁴ - 1707x³ + 459x² + 22x - 19	$ 5^{12}\cdot 13^{4}\cdot 29^{6} $	$C_2^4.C_2^3.C_2$ (as 16T500)	Trivial (GRH)
16.0.4147643767353759765625.3	x¹⁶ - 8x¹⁵ + 36x¹⁴ - 112x¹³ + 283x¹² - 606x¹¹ + 1106x¹⁰ - 1691x⁹ + 2381x⁸ - 3184x⁷ + 3856x⁶ - 3845x⁵ + 5215x⁴ - 6182x³ + 1642x² + 1108x + 1831	$ 5^{12}\cdot 13^{4}\cdot 29^{6} $	$C_2^4.C_2^3.C_2$ (as 16T500)	$[6]$
16.0.4147643767353759765625.4	x¹⁶ - 8x¹⁵ + 28x¹⁴ - 56x¹³ + 83x¹² - 134x¹¹ + 223x¹⁰ - 268x⁹ + 335x⁸ - 634x⁷ + 1012x⁶ - 1051x⁵ + 1481x⁴ - 1859x³ + 1452x² - 605x + 1271	$ 5^{12}\cdot 13^{4}\cdot 29^{6} $	$C_2^4.C_2^3.C_2$ (as 16T500)	$[6]$
16.0.11842998836451234765625.5	x¹⁶ - 5x¹⁵ + 17x¹⁴ - 54x¹³ + 99x¹² - 131x¹¹ + 144x¹⁰ + 64x⁹ - 328x⁸ + 470x⁷ - 500x⁶ + 66x⁵ + 599x⁴ - 588x³ + 256x² + 370x + 145	$ 5^{8}\cdot 13^{4}\cdot 101^{6} $	$C_2^4.C_2^3.C_2$ (as 16T500)	Trivial
16.8.36561172319257600000000.5	x¹⁶ - 3x¹⁴ + 8x¹² - 303x¹⁰ + 653x⁸ + 1792x⁶ - 1078x⁴ - 3430x² + 2401	$ 2^{16}\cdot 5^{8}\cdot 7^{4}\cdot 29^{6} $	$C_2^4.C_2^3.C_2$ (as 16T500)	Trivial (GRH)
16.0.36561172319257600000000.7	x¹⁶ + 3x¹⁴ + 8x¹² + 303x¹⁰ + 653x⁸ - 1792x⁶ - 1078x⁴ + 3430x² + 2401	$ 2^{16}\cdot 5^{8}\cdot 7^{4}\cdot 29^{6} $	$C_2^4.C_2^3.C_2$ (as 16T500)	$[4]$
16.16.119590095763705692160000.1	x¹⁶ - 2x¹⁵ - 21x¹⁴ + 38x¹³ + 146x¹² - 260x¹¹ - 425x¹⁰ + 748x⁹ + 609x⁸ - 1016x⁷ - 447x⁶ + 644x⁵ + 154x⁴ - 162x³ - 19x² + 10x + 1	$ 2^{24}\cdot 5^{4}\cdot 7^{4}\cdot 41^{6} $	$C_2^4.C_2^3.C_2$ (as 16T500)	Trivial (GRH)
16.8.119590095763705692160000.1	x¹⁶ - 6x¹⁵ + x¹⁴ + 34x¹³ - 29x¹² - 106x¹¹ + 292x¹⁰ - 172x⁹ - 539x⁸ + 986x⁷ - 310x⁶ - 300x⁵ + 44x⁴ + 92x³ + 56x² - 44x + 1	$ 2^{24}\cdot 5^{4}\cdot 7^{4}\cdot 41^{6} $	$C_2^4.C_2^3.C_2$ (as 16T500)	$[2]$ (GRH)
16.0.203563536777625600000000.2	x¹⁶ + 3x¹⁴ + 11x¹² + 32x¹⁰ + 60x⁸ + 128x⁶ + 176x⁴ + 192x² + 256	$ 2^{20}\cdot 5^{8}\cdot 89^{6} $	$C_2^4.C_2^3.C_2$ (as 16T500)	$[2, 4]$ (GRH)
16.0.203563536777625600000000.3	x¹⁶ - 3x¹⁴ + 11x¹² - 32x¹⁰ + 60x⁸ - 128x⁶ + 176x⁴ - 192x² + 256	$ 2^{20}\cdot 5^{8}\cdot 89^{6} $	$C_2^4.C_2^3.C_2$ (as 16T500)	$[2]$ (GRH)
16.0.434911971099673600000000.1	x¹⁶ - 5x¹⁴ - 60x¹² + 208x¹⁰ + 2043x⁸ + 5220x⁶ + 9396x⁴ + 5887x² + 841	$ 2^{16}\cdot 5^{8}\cdot 13^{4}\cdot 29^{6} $	$C_2^4.C_2^3.C_2$ (as 16T500)	$[2, 2]$ (GRH)
16.16.434911971099673600000000.1	x¹⁶ - 17x¹⁴ + 111x¹² - 356x¹⁰ + 588x⁸ - 472x⁶ + 154x⁴ - 21x² + 1	$ 2^{16}\cdot 5^{8}\cdot 13^{4}\cdot 29^{6} $	$C_2^4.C_2^3.C_2$ (as 16T500)	Trivial (GRH)
16.0.434911971099673600000000.2	x¹⁶ + 17x¹⁴ + 111x¹² + 356x¹⁰ + 588x⁸ + 472x⁶ + 154x⁴ + 21x² + 1	$ 2^{16}\cdot 5^{8}\cdot 13^{4}\cdot 29^{6} $	$C_2^4.C_2^3.C_2$ (as 16T500)	$[16]$ (GRH)
16.8.434911971099673600000000.3	x¹⁶ + 5x¹⁴ - 60x¹² - 208x¹⁰ + 2043x⁸ - 5220x⁶ + 9396x⁴ - 5887x² + 841	$ 2^{16}\cdot 5^{8}\cdot 13^{4}\cdot 29^{6} $	$C_2^4.C_2^3.C_2$ (as 16T500)	$[2]$ (GRH)
16.8.496981290961000000000000.1	x¹⁶ + 13x¹⁴ - 39x¹² - 491x¹⁰ + 689x⁸ + 4672x⁶ - 4816x⁴ - 7384x² + 5776	$ 2^{12}\cdot 5^{12}\cdot 89^{6} $	$C_2^4.C_2^3.C_2$ (as 16T500)	Trivial (GRH)
16.0.3264246778829744373760000.1	x¹⁶ + 26x¹⁴ + 273x¹² + 1504x¹⁰ + 4729x⁸ + 8620x⁶ + 8725x⁴ + 4250x² + 625	$ 2^{40}\cdot 5^{4}\cdot 41^{6} $	$C_2^4.C_2^3.C_2$ (as 16T500)	$[96]$ (GRH)
16.0.9359660113729945600000000.2	x¹⁶ - 6x¹⁵ + 28x¹⁴ - 94x¹³ + 308x¹² - 882x¹¹ + 2342x¹⁰ - 5730x⁹ + 12818x⁸ - 23940x⁷ + 38440x⁶ - 62248x⁵ + 95069x⁴ - 109534x³ + 82038x² - 34940x + 6691	$ 2^{24}\cdot 5^{8}\cdot 7^{4}\cdot 29^{6} $	$C_2^4.C_2^3.C_2$ (as 16T500)	$[2, 10]$ (GRH)
16.0.9359660113729945600000000.3	x¹⁶ - 6x¹⁵ + 32x¹⁴ - 80x¹³ + 161x¹² - 14x¹¹ - 410x¹⁰ + 1738x⁹ - 1715x⁸ + 1874x⁷ + 6254x⁶ - 4340x⁵ + 17345x⁴ + 5770x³ + 11202x² + 11468x + 6281	$ 2^{24}\cdot 5^{8}\cdot 7^{4}\cdot 29^{6} $	$C_2^4.C_2^3.C_2$ (as 16T500)	$[2, 20]$ (GRH)

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Results (displaying all 28 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
16.0.99038527051792384.4	x¹⁶ - 3x¹⁴ + 5x¹² - x¹⁰ + 12x⁸ - x⁶ + 5x⁴ - 3x² + 1	\( 2^{34}\cdot 7^{8} \)	$C_2^4.C_2^3.C_2$ (as 16T500)	Trivial
16.0.103670069459943424.4	x¹⁶ + 5x¹² - 2x¹⁰ + 9x⁸ - 2x⁶ + 5x⁴ + 1	\( 2^{32}\cdot 17^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T500)	Trivial
16.4.557879216297265625.1	x¹⁶ - 3x¹⁵ + 6x¹⁴ - 12x¹³ + 13x¹² - 2x¹¹ - 26x¹⁰ + 47x⁹ - 49x⁸ + 47x⁷ - 26x⁶ - 2x⁵ + 13x⁴ - 12x³ + 6x² - 3x + 1	\( 5^{8}\cdot 7^{4}\cdot 29^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T500)	Trivial
16.8.6636230027766015625.1	x¹⁶ - 5x¹⁵ + 6x¹⁴ + 13x¹³ - 43x¹² + 36x¹¹ - 19x¹⁰ + 123x⁹ - 266x⁸ + 72x⁷ + 421x⁶ - 556x⁵ + 197x⁴ + 52x³ - 34x² + 1	\( 5^{8}\cdot 13^{4}\cdot 29^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T500)	Trivial (GRH)
16.4.15227477017600000000.4	x¹⁶ - 6x¹⁴ + 6x¹² - 5x¹⁰ + 16x⁸ - 13x⁶ - 8x⁴ + 9x² + 1	\( 2^{16}\cdot 5^{8}\cdot 29^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T500)	Trivial (GRH)
16.8.20401542367685902336.2	x¹⁶ - 4x¹⁴ - 16x¹² + 42x¹⁰ + 34x⁸ - 112x⁶ + 37x⁴ + 18x² + 1	\( 2^{32}\cdot 41^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T500)	Trivial
16.0.49698129096100000000.1	x¹⁶ - 4x¹⁴ + 20x¹² - 46x¹⁰ + 100x⁸ - 128x⁶ + 133x⁴ - 76x² + 16	\( 2^{8}\cdot 5^{8}\cdot 89^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T500)	Trivial
16.0.326424677882974437376.1	x¹⁶ - 4x¹⁵ + 10x¹⁴ - 20x¹³ + 46x¹² - 136x¹¹ + 386x¹⁰ - 896x⁹ + 1654x⁸ - 2436x⁷ + 2878x⁶ - 2708x⁵ + 2014x⁴ - 1152x³ + 510x² - 168x + 49	\( 2^{36}\cdot 41^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T500)	$[2]$
16.8.424632604507928264704.1	x¹⁶ - 12x¹⁴ + 56x¹² - 132x¹⁰ + 190x⁸ - 212x⁶ + 152x⁴ - 28x² + 1	\( 2^{44}\cdot 17^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T500)	Trivial (GRH)
16.0.795170065537600000000.1	x¹⁶ - x¹⁴ + 19x¹² - 26x¹⁰ + 120x⁸ - 216x⁶ + 144x⁴ - 256x² + 256	\( 2^{12}\cdot 5^{8}\cdot 89^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T500)	Trivial
16.8.4147643767353759765625.1	x¹⁶ - 5x¹⁵ + 5x¹⁴ + 36x¹³ - 118x¹² + 70x¹¹ + 206x¹⁰ - 576x⁹ + 684x⁸ + 211x⁷ - 1129x⁶ - 163x⁵ + 2024x⁴ - 1707x³ + 459x² + 22x - 19	\( 5^{12}\cdot 13^{4}\cdot 29^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T500)	Trivial (GRH)
16.0.4147643767353759765625.3	x¹⁶ - 8x¹⁵ + 36x¹⁴ - 112x¹³ + 283x¹² - 606x¹¹ + 1106x¹⁰ - 1691x⁹ + 2381x⁸ - 3184x⁷ + 3856x⁶ - 3845x⁵ + 5215x⁴ - 6182x³ + 1642x² + 1108x + 1831	\( 5^{12}\cdot 13^{4}\cdot 29^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T500)	$[6]$
16.0.4147643767353759765625.4	x¹⁶ - 8x¹⁵ + 28x¹⁴ - 56x¹³ + 83x¹² - 134x¹¹ + 223x¹⁰ - 268x⁹ + 335x⁸ - 634x⁷ + 1012x⁶ - 1051x⁵ + 1481x⁴ - 1859x³ + 1452x² - 605x + 1271	\( 5^{12}\cdot 13^{4}\cdot 29^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T500)	$[6]$
16.0.11842998836451234765625.5	x¹⁶ - 5x¹⁵ + 17x¹⁴ - 54x¹³ + 99x¹² - 131x¹¹ + 144x¹⁰ + 64x⁹ - 328x⁸ + 470x⁷ - 500x⁶ + 66x⁵ + 599x⁴ - 588x³ + 256x² + 370x + 145	\( 5^{8}\cdot 13^{4}\cdot 101^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T500)	Trivial
16.8.36561172319257600000000.5	x¹⁶ - 3x¹⁴ + 8x¹² - 303x¹⁰ + 653x⁸ + 1792x⁶ - 1078x⁴ - 3430x² + 2401	\( 2^{16}\cdot 5^{8}\cdot 7^{4}\cdot 29^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T500)	Trivial (GRH)
16.0.36561172319257600000000.7	x¹⁶ + 3x¹⁴ + 8x¹² + 303x¹⁰ + 653x⁸ - 1792x⁶ - 1078x⁴ + 3430x² + 2401	\( 2^{16}\cdot 5^{8}\cdot 7^{4}\cdot 29^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T500)	$[4]$
16.16.119590095763705692160000.1	x¹⁶ - 2x¹⁵ - 21x¹⁴ + 38x¹³ + 146x¹² - 260x¹¹ - 425x¹⁰ + 748x⁹ + 609x⁸ - 1016x⁷ - 447x⁶ + 644x⁵ + 154x⁴ - 162x³ - 19x² + 10x + 1	\( 2^{24}\cdot 5^{4}\cdot 7^{4}\cdot 41^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T500)	Trivial (GRH)
16.8.119590095763705692160000.1	x¹⁶ - 6x¹⁵ + x¹⁴ + 34x¹³ - 29x¹² - 106x¹¹ + 292x¹⁰ - 172x⁹ - 539x⁸ + 986x⁷ - 310x⁶ - 300x⁵ + 44x⁴ + 92x³ + 56x² - 44x + 1	\( 2^{24}\cdot 5^{4}\cdot 7^{4}\cdot 41^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T500)	$[2]$ (GRH)
16.0.203563536777625600000000.2	x¹⁶ + 3x¹⁴ + 11x¹² + 32x¹⁰ + 60x⁸ + 128x⁶ + 176x⁴ + 192x² + 256	\( 2^{20}\cdot 5^{8}\cdot 89^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T500)	$[2, 4]$ (GRH)
16.0.203563536777625600000000.3	x¹⁶ - 3x¹⁴ + 11x¹² - 32x¹⁰ + 60x⁸ - 128x⁶ + 176x⁴ - 192x² + 256	\( 2^{20}\cdot 5^{8}\cdot 89^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T500)	$[2]$ (GRH)
16.0.434911971099673600000000.1	x¹⁶ - 5x¹⁴ - 60x¹² + 208x¹⁰ + 2043x⁸ + 5220x⁶ + 9396x⁴ + 5887x² + 841	\( 2^{16}\cdot 5^{8}\cdot 13^{4}\cdot 29^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T500)	$[2, 2]$ (GRH)
16.16.434911971099673600000000.1	x¹⁶ - 17x¹⁴ + 111x¹² - 356x¹⁰ + 588x⁸ - 472x⁶ + 154x⁴ - 21x² + 1	\( 2^{16}\cdot 5^{8}\cdot 13^{4}\cdot 29^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T500)	Trivial (GRH)
16.0.434911971099673600000000.2	x¹⁶ + 17x¹⁴ + 111x¹² + 356x¹⁰ + 588x⁸ + 472x⁶ + 154x⁴ + 21x² + 1	\( 2^{16}\cdot 5^{8}\cdot 13^{4}\cdot 29^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T500)	$[16]$ (GRH)
16.8.434911971099673600000000.3	x¹⁶ + 5x¹⁴ - 60x¹² - 208x¹⁰ + 2043x⁸ - 5220x⁶ + 9396x⁴ - 5887x² + 841	\( 2^{16}\cdot 5^{8}\cdot 13^{4}\cdot 29^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T500)	$[2]$ (GRH)
16.8.496981290961000000000000.1	x¹⁶ + 13x¹⁴ - 39x¹² - 491x¹⁰ + 689x⁸ + 4672x⁶ - 4816x⁴ - 7384x² + 5776	\( 2^{12}\cdot 5^{12}\cdot 89^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T500)	Trivial (GRH)
16.0.3264246778829744373760000.1	x¹⁶ + 26x¹⁴ + 273x¹² + 1504x¹⁰ + 4729x⁸ + 8620x⁶ + 8725x⁴ + 4250x² + 625	\( 2^{40}\cdot 5^{4}\cdot 41^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T500)	$[96]$ (GRH)
16.0.9359660113729945600000000.2	x¹⁶ - 6x¹⁵ + 28x¹⁴ - 94x¹³ + 308x¹² - 882x¹¹ + 2342x¹⁰ - 5730x⁹ + 12818x⁸ - 23940x⁷ + 38440x⁶ - 62248x⁵ + 95069x⁴ - 109534x³ + 82038x² - 34940x + 6691	\( 2^{24}\cdot 5^{8}\cdot 7^{4}\cdot 29^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T500)	$[2, 10]$ (GRH)
16.0.9359660113729945600000000.3	x¹⁶ - 6x¹⁵ + 32x¹⁴ - 80x¹³ + 161x¹² - 14x¹¹ - 410x¹⁰ + 1738x⁹ - 1715x⁸ + 1874x⁷ + 6254x⁶ - 4340x⁵ + 17345x⁴ + 5770x³ + 11202x² + 11468x + 6281	\( 2^{24}\cdot 5^{8}\cdot 7^{4}\cdot 29^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T500)	$[2, 20]$ (GRH)