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Results (displaying all 24 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.3673508889600000000.1	x¹⁶ + 6x¹⁴ + 21x¹² + 46x¹⁰ + 64x⁸ + 59x⁶ + 33x⁴ + 10x² + 1	$ 2^{16}\cdot 3^{4}\cdot 5^{8}\cdot 11^{6} $	$C_2\times D_4:D_4$ (as 16T265)	Trivial
16.0.23048663854325760000.1	x¹⁶ + 9x¹⁴ + 36x¹² + 78x¹⁰ + 96x⁸ + 45x⁶ - 18x⁴ - 27x² + 9	$ 2^{16}\cdot 3^{14}\cdot 5^{4}\cdot 7^{6} $	$C_2\times D_4:D_4$ (as 16T265)	Trivial
16.0.42511207857918050304.2	x¹⁶ - 2x¹⁵ + 3x¹⁴ - 6x¹³ + 7x¹² - 8x¹¹ + 4x¹⁰ - 2x⁸ + 4x⁶ + 8x⁵ + 7x⁴ + 6x³ + 3x² + 2x + 1	$ 2^{28}\cdot 3^{8}\cdot 17^{6} $	$C_2\times D_4:D_4$ (as 16T265)	Trivial
16.0.93572113180734849024.1	x¹⁶ + 2x¹⁴ + 3x¹² + 4x¹⁰ + x⁸ + 13x⁶ - 27x⁴ + 11x² + 1	$ 2^{16}\cdot 3^{6}\cdot 7^{4}\cdot 13^{8} $	$C_2\times D_4:D_4$ (as 16T265)	Trivial
16.0.136016004388491362304.9	x¹⁶ + 2x¹⁴ + 5x¹² + 12x¹⁰ - 10x⁸ - 24x⁶ + 32x⁴ - 10x² + 1	$ 2^{32}\cdot 3^{8}\cdot 13^{6} $	$C_2\times D_4:D_4$ (as 16T265)	Trivial (GRH)
16.0.142158742435915628544.3	x¹⁶ - 4x¹⁵ - x¹⁴ + 12x¹³ + 29x¹² - 104x¹¹ + 94x¹⁰ - 72x⁹ + 106x⁸ - 48x⁷ - 14x⁶ - 16x⁵ - 31x⁴ + 84x³ + 71x² - 260x + 169	$ 2^{24}\cdot 3^{14}\cdot 11^{6} $	$C_2\times D_4:D_4$ (as 16T265)	$[2]$
16.4.197382268518400000000.3	x¹⁶ - 6x¹⁴ - 3x¹² - 88x¹¹ - 138x¹⁰ - 52x⁹ + 66x⁸ + 96x⁷ - 4x⁶ - 48x⁵ - 25x⁴ + 8x² - 4x + 1	$ 2^{32}\cdot 5^{8}\cdot 7^{6} $	$C_2\times D_4:D_4$ (as 16T265)	Trivial
16.4.297554220057600000000.3	x¹⁶ - x¹⁴ + 3x¹² - 8x¹⁰ - x⁸ - 8x⁶ + 3x⁴ - x² + 1	$ 2^{16}\cdot 3^{8}\cdot 5^{8}\cdot 11^{6} $	$C_2\times D_4:D_4$ (as 16T265)	Trivial (GRH)
16.8.680179325726688804864.2	x¹⁶ - 10x¹⁴ - 12x¹³ + 19x¹² + 72x¹¹ + 88x¹⁰ - 8x⁹ - 169x⁸ - 272x⁷ - 230x⁶ - 24x⁵ + 226x⁴ + 344x³ + 228x² + 56x + 4	$ 2^{32}\cdot 3^{8}\cdot 17^{6} $	$C_2\times D_4:D_4$ (as 16T265)	Trivial (GRH)
16.0.680179325726688804864.7	x¹⁶ - 4x¹⁵ + 12x¹⁴ - 16x¹³ + 17x¹² - 8x¹¹ + 12x¹⁰ - 20x⁹ + 16x⁸ - 20x⁷ + 12x⁶ - 8x⁵ + 17x⁴ - 16x³ + 12x² - 4x + 1	$ 2^{32}\cdot 3^{8}\cdot 17^{6} $	$C_2\times D_4:D_4$ (as 16T265)	$[2]$
16.0.680179325726688804864.8	x¹⁶ + 14x¹⁴ + 75x¹² + 204x¹⁰ + 339x⁸ + 398x⁶ + 329x⁴ + 80x² + 64	$ 2^{32}\cdot 3^{8}\cdot 17^{6} $	$C_2\times D_4:D_4$ (as 16T265)	$[2]$
16.0.2531007555174400000000.2	x¹⁶ - 2x¹⁵ - x¹⁴ + 10x¹³ - x¹² - 36x¹¹ - 20x¹⁰ + 76x⁹ + 142x⁸ + 76x⁷ - 20x⁶ - 36x⁵ - x⁴ + 10x³ - x² - 2x + 1	$ 2^{28}\cdot 5^{8}\cdot 17^{6} $	$C_2\times D_4:D_4$ (as 16T265)	Trivial (GRH)
16.0.12750963979803688960000.1	x¹⁶ - 4x¹⁵ + 8x¹⁴ - 16x¹³ + 73x¹² - 240x¹¹ + 504x¹⁰ - 812x⁹ + 1456x⁸ - 2988x⁷ + 5304x⁶ - 6960x⁵ + 6313x⁴ - 3584x³ + 968x² + 44x + 1	$ 2^{32}\cdot 5^{4}\cdot 41^{6} $	$C_2\times D_4:D_4$ (as 16T265)	$[2]$
16.0.14264873087553647015625.3	x¹⁶ - 4x¹⁵ + 11x¹⁴ - 18x¹³ + 30x¹² - 62x¹¹ + 94x¹⁰ - 118x⁹ + 133x⁸ - 156x⁷ + 180x⁶ - 109x⁵ + 60x⁴ - 24x³ + 7x² - x + 1	$ 3^{8}\cdot 5^{6}\cdot 7^{8}\cdot 17^{6} $	$C_2\times D_4:D_4$ (as 16T265)	Trivial
16.8.34820097123453788749824.4	x¹⁶ - 4x¹⁴ - 4x¹² - 24x¹⁰ + 44x⁸ - 24x⁶ + 80x⁴ - 64x² + 4	$ 2^{40}\cdot 3^{8}\cdot 13^{6} $	$C_2\times D_4:D_4$ (as 16T265)	Trivial (GRH)
16.0.36392638063594400907264.4	x¹⁶ - 12x¹⁴ + 99x¹² - 408x¹⁰ + 1200x⁸ - 2178x⁶ + 2871x⁴ - 2178x² + 1089	$ 2^{32}\cdot 3^{14}\cdot 11^{6} $	$C_2\times D_4:D_4$ (as 16T265)	$[4]$
16.0.36392638063594400907264.5	x¹⁶ - 30x¹⁴ + 378x¹² - 2340x¹⁰ + 8031x⁸ - 15444x⁶ + 15642x⁴ - 6534x² + 1089	$ 2^{32}\cdot 3^{14}\cdot 11^{6} $	$C_2\times D_4:D_4$ (as 16T265)	$[2]$ (GRH)
16.0.287742083309962730143744.3	x¹⁶ - 8x¹⁵ + 32x¹⁴ - 60x¹³ - 25x¹² + 384x¹¹ - 782x¹⁰ + 404x⁹ + 1454x⁸ - 3616x⁷ + 4320x⁶ - 2128x⁵ - 1220x⁴ + 2368x³ - 184x² - 368x + 104	$ 2^{34}\cdot 7^{4}\cdot 17^{8} $	$C_2\times D_4:D_4$ (as 16T265)	$[2, 6]$ (GRH)
16.16.111337464601516441600000000.1	x¹⁶ - 2x¹⁵ - 37x¹⁴ + 66x¹³ + 499x¹² - 790x¹¹ - 2984x¹⁰ + 4078x⁹ + 8014x⁸ - 8104x⁷ - 10617x⁶ + 5338x⁵ + 7205x⁴ - 116x³ - 1725x² - 514x - 41	$ 2^{24}\cdot 5^{8}\cdot 13^{4}\cdot 29^{6} $	$C_2\times D_4:D_4$ (as 16T265)	Trivial (GRH)
16.0.2396072989114866073600000000.1	x¹⁶ + 24x¹⁴ + 321x¹² + 2564x¹⁰ + 14414x⁸ + 43426x⁶ + 83148x⁴ + 97620x² + 52441	$ 2^{32}\cdot 5^{8}\cdot 7^{4}\cdot 29^{6} $	$C_2\times D_4:D_4$ (as 16T265)	$[2, 2, 230]$ (GRH)
16.8.2396072989114866073600000000.1	x¹⁶ - 10x¹⁴ - 73x¹² + 70x¹⁰ + 3693x⁸ - 25120x⁶ + 91047x⁴ - 148850x² + 78961	$ 2^{32}\cdot 5^{8}\cdot 7^{4}\cdot 29^{6} $	$C_2\times D_4:D_4$ (as 16T265)	Trivial (GRH)
16.8.2396072989114866073600000000.2	x¹⁶ - 6x¹⁴ - 117x¹² - 160x¹⁰ + 7741x⁸ - 3630x⁶ - 47493x⁴ - 37752x² + 14641	$ 2^{32}\cdot 5^{8}\cdot 7^{4}\cdot 29^{6} $	$C_2\times D_4:D_4$ (as 16T265)	$[6]$ (GRH)
16.16.23371568066647895270400000000.3	x¹⁶ - 42x¹⁴ + 688x¹² - 5727x¹⁰ + 26070x⁸ - 64464x⁶ + 80104x⁴ - 39015x² + 289	$ 2^{16}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8}\cdot 17^{6} $	$C_2\times D_4:D_4$ (as 16T265)	Trivial (GRH)
16.0.239324857002474447568896000000.1	x¹⁶ - 4x¹⁵ + 28x¹⁴ - 112x¹³ + 453x¹² - 1366x¹¹ + 3212x¹⁰ - 2362x⁹ - 13887x⁸ + 55526x⁷ - 74956x⁶ - 51670x⁵ + 354791x⁴ - 560202x³ + 439768x² - 181620x + 49869	$ 2^{24}\cdot 3^{8}\cdot 5^{6}\cdot 7^{8}\cdot 17^{6} $	$C_2\times D_4:D_4$ (as 16T265)	$[2, 2, 234]$ (GRH)

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Results (displaying all 24 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
16.0.3673508889600000000.1	x¹⁶ + 6x¹⁴ + 21x¹² + 46x¹⁰ + 64x⁸ + 59x⁶ + 33x⁴ + 10x² + 1	\( 2^{16}\cdot 3^{4}\cdot 5^{8}\cdot 11^{6} \)	$C_2\times D_4:D_4$ (as 16T265)	Trivial
16.0.23048663854325760000.1	x¹⁶ + 9x¹⁴ + 36x¹² + 78x¹⁰ + 96x⁸ + 45x⁶ - 18x⁴ - 27x² + 9	\( 2^{16}\cdot 3^{14}\cdot 5^{4}\cdot 7^{6} \)	$C_2\times D_4:D_4$ (as 16T265)	Trivial
16.0.42511207857918050304.2	x¹⁶ - 2x¹⁵ + 3x¹⁴ - 6x¹³ + 7x¹² - 8x¹¹ + 4x¹⁰ - 2x⁸ + 4x⁶ + 8x⁵ + 7x⁴ + 6x³ + 3x² + 2x + 1	\( 2^{28}\cdot 3^{8}\cdot 17^{6} \)	$C_2\times D_4:D_4$ (as 16T265)	Trivial
16.0.93572113180734849024.1	x¹⁶ + 2x¹⁴ + 3x¹² + 4x¹⁰ + x⁸ + 13x⁶ - 27x⁴ + 11x² + 1	\( 2^{16}\cdot 3^{6}\cdot 7^{4}\cdot 13^{8} \)	$C_2\times D_4:D_4$ (as 16T265)	Trivial
16.0.136016004388491362304.9	x¹⁶ + 2x¹⁴ + 5x¹² + 12x¹⁰ - 10x⁸ - 24x⁶ + 32x⁴ - 10x² + 1	\( 2^{32}\cdot 3^{8}\cdot 13^{6} \)	$C_2\times D_4:D_4$ (as 16T265)	Trivial (GRH)
16.0.142158742435915628544.3	x¹⁶ - 4x¹⁵ - x¹⁴ + 12x¹³ + 29x¹² - 104x¹¹ + 94x¹⁰ - 72x⁹ + 106x⁸ - 48x⁷ - 14x⁶ - 16x⁵ - 31x⁴ + 84x³ + 71x² - 260x + 169	\( 2^{24}\cdot 3^{14}\cdot 11^{6} \)	$C_2\times D_4:D_4$ (as 16T265)	$[2]$
16.4.197382268518400000000.3	x¹⁶ - 6x¹⁴ - 3x¹² - 88x¹¹ - 138x¹⁰ - 52x⁹ + 66x⁸ + 96x⁷ - 4x⁶ - 48x⁵ - 25x⁴ + 8x² - 4x + 1	\( 2^{32}\cdot 5^{8}\cdot 7^{6} \)	$C_2\times D_4:D_4$ (as 16T265)	Trivial
16.4.297554220057600000000.3	x¹⁶ - x¹⁴ + 3x¹² - 8x¹⁰ - x⁸ - 8x⁶ + 3x⁴ - x² + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{8}\cdot 11^{6} \)	$C_2\times D_4:D_4$ (as 16T265)	Trivial (GRH)
16.8.680179325726688804864.2	x¹⁶ - 10x¹⁴ - 12x¹³ + 19x¹² + 72x¹¹ + 88x¹⁰ - 8x⁹ - 169x⁸ - 272x⁷ - 230x⁶ - 24x⁵ + 226x⁴ + 344x³ + 228x² + 56x + 4	\( 2^{32}\cdot 3^{8}\cdot 17^{6} \)	$C_2\times D_4:D_4$ (as 16T265)	Trivial (GRH)
16.0.680179325726688804864.7	x¹⁶ - 4x¹⁵ + 12x¹⁴ - 16x¹³ + 17x¹² - 8x¹¹ + 12x¹⁰ - 20x⁹ + 16x⁸ - 20x⁷ + 12x⁶ - 8x⁵ + 17x⁴ - 16x³ + 12x² - 4x + 1	\( 2^{32}\cdot 3^{8}\cdot 17^{6} \)	$C_2\times D_4:D_4$ (as 16T265)	$[2]$
16.0.680179325726688804864.8	x¹⁶ + 14x¹⁴ + 75x¹² + 204x¹⁰ + 339x⁸ + 398x⁶ + 329x⁴ + 80x² + 64	\( 2^{32}\cdot 3^{8}\cdot 17^{6} \)	$C_2\times D_4:D_4$ (as 16T265)	$[2]$
16.0.2531007555174400000000.2	x¹⁶ - 2x¹⁵ - x¹⁴ + 10x¹³ - x¹² - 36x¹¹ - 20x¹⁰ + 76x⁹ + 142x⁸ + 76x⁷ - 20x⁶ - 36x⁵ - x⁴ + 10x³ - x² - 2x + 1	\( 2^{28}\cdot 5^{8}\cdot 17^{6} \)	$C_2\times D_4:D_4$ (as 16T265)	Trivial (GRH)
16.0.12750963979803688960000.1	x¹⁶ - 4x¹⁵ + 8x¹⁴ - 16x¹³ + 73x¹² - 240x¹¹ + 504x¹⁰ - 812x⁹ + 1456x⁸ - 2988x⁷ + 5304x⁶ - 6960x⁵ + 6313x⁴ - 3584x³ + 968x² + 44x + 1	\( 2^{32}\cdot 5^{4}\cdot 41^{6} \)	$C_2\times D_4:D_4$ (as 16T265)	$[2]$
16.0.14264873087553647015625.3	x¹⁶ - 4x¹⁵ + 11x¹⁴ - 18x¹³ + 30x¹² - 62x¹¹ + 94x¹⁰ - 118x⁹ + 133x⁸ - 156x⁷ + 180x⁶ - 109x⁵ + 60x⁴ - 24x³ + 7x² - x + 1	\( 3^{8}\cdot 5^{6}\cdot 7^{8}\cdot 17^{6} \)	$C_2\times D_4:D_4$ (as 16T265)	Trivial
16.8.34820097123453788749824.4	x¹⁶ - 4x¹⁴ - 4x¹² - 24x¹⁰ + 44x⁸ - 24x⁶ + 80x⁴ - 64x² + 4	\( 2^{40}\cdot 3^{8}\cdot 13^{6} \)	$C_2\times D_4:D_4$ (as 16T265)	Trivial (GRH)
16.0.36392638063594400907264.4	x¹⁶ - 12x¹⁴ + 99x¹² - 408x¹⁰ + 1200x⁸ - 2178x⁶ + 2871x⁴ - 2178x² + 1089	\( 2^{32}\cdot 3^{14}\cdot 11^{6} \)	$C_2\times D_4:D_4$ (as 16T265)	$[4]$
16.0.36392638063594400907264.5	x¹⁶ - 30x¹⁴ + 378x¹² - 2340x¹⁰ + 8031x⁸ - 15444x⁶ + 15642x⁴ - 6534x² + 1089	\( 2^{32}\cdot 3^{14}\cdot 11^{6} \)	$C_2\times D_4:D_4$ (as 16T265)	$[2]$ (GRH)
16.0.287742083309962730143744.3	x¹⁶ - 8x¹⁵ + 32x¹⁴ - 60x¹³ - 25x¹² + 384x¹¹ - 782x¹⁰ + 404x⁹ + 1454x⁸ - 3616x⁷ + 4320x⁶ - 2128x⁵ - 1220x⁴ + 2368x³ - 184x² - 368x + 104	\( 2^{34}\cdot 7^{4}\cdot 17^{8} \)	$C_2\times D_4:D_4$ (as 16T265)	$[2, 6]$ (GRH)
16.16.111337464601516441600000000.1	x¹⁶ - 2x¹⁵ - 37x¹⁴ + 66x¹³ + 499x¹² - 790x¹¹ - 2984x¹⁰ + 4078x⁹ + 8014x⁸ - 8104x⁷ - 10617x⁶ + 5338x⁵ + 7205x⁴ - 116x³ - 1725x² - 514x - 41	\( 2^{24}\cdot 5^{8}\cdot 13^{4}\cdot 29^{6} \)	$C_2\times D_4:D_4$ (as 16T265)	Trivial (GRH)
16.0.2396072989114866073600000000.1	x¹⁶ + 24x¹⁴ + 321x¹² + 2564x¹⁰ + 14414x⁸ + 43426x⁶ + 83148x⁴ + 97620x² + 52441	\( 2^{32}\cdot 5^{8}\cdot 7^{4}\cdot 29^{6} \)	$C_2\times D_4:D_4$ (as 16T265)	$[2, 2, 230]$ (GRH)
16.8.2396072989114866073600000000.1	x¹⁶ - 10x¹⁴ - 73x¹² + 70x¹⁰ + 3693x⁸ - 25120x⁶ + 91047x⁴ - 148850x² + 78961	\( 2^{32}\cdot 5^{8}\cdot 7^{4}\cdot 29^{6} \)	$C_2\times D_4:D_4$ (as 16T265)	Trivial (GRH)
16.8.2396072989114866073600000000.2	x¹⁶ - 6x¹⁴ - 117x¹² - 160x¹⁰ + 7741x⁸ - 3630x⁶ - 47493x⁴ - 37752x² + 14641	\( 2^{32}\cdot 5^{8}\cdot 7^{4}\cdot 29^{6} \)	$C_2\times D_4:D_4$ (as 16T265)	$[6]$ (GRH)
16.16.23371568066647895270400000000.3	x¹⁶ - 42x¹⁴ + 688x¹² - 5727x¹⁰ + 26070x⁸ - 64464x⁶ + 80104x⁴ - 39015x² + 289	\( 2^{16}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8}\cdot 17^{6} \)	$C_2\times D_4:D_4$ (as 16T265)	Trivial (GRH)
16.0.239324857002474447568896000000.1	x¹⁶ - 4x¹⁵ + 28x¹⁴ - 112x¹³ + 453x¹² - 1366x¹¹ + 3212x¹⁰ - 2362x⁹ - 13887x⁸ + 55526x⁷ - 74956x⁶ - 51670x⁵ + 354791x⁴ - 560202x³ + 439768x² - 181620x + 49869	\( 2^{24}\cdot 3^{8}\cdot 5^{6}\cdot 7^{8}\cdot 17^{6} \)	$C_2\times D_4:D_4$ (as 16T265)	$[2, 2, 234]$ (GRH)