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Results (displaying all 22 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.8861338240000000000.1	x¹⁶ - 3x¹⁴ - 4x¹³ + 10x¹² + 28x¹¹ + 14x¹⁰ - 56x⁹ - 99x⁸ - 78x⁷ + 18x⁶ + 166x⁵ + 274x⁴ + 250x³ + 135x² + 40x + 5	$ 2^{16}\cdot 5^{10}\cdot 61^{4} $	$C_2^4.C_2^3$ (as 16T210)	Trivial
16.0.36665447040000000000.1	x¹⁶ - 4x¹⁵ + 6x¹⁴ - 8x¹³ + 23x¹² - 28x¹¹ + 12x¹⁰ - 24x⁹ + 17x⁸ + 24x⁷ + 12x⁶ + 28x⁵ + 23x⁴ + 8x³ + 6x² + 4x + 1	$ 2^{16}\cdot 3^{4}\cdot 5^{10}\cdot 29^{4} $	$C_2^4.C_2^3$ (as 16T210)	Trivial
16.4.472769874482845188096.1	x¹⁶ - 4x¹² + 16x¹⁰ - 42x⁸ + 160x⁶ - 132x⁴ + 16x² + 1	$ 2^{56}\cdot 3^{8} $	$C_2^4.C_2^3$ (as 16T210)	Trivial (GRH)
16.8.472769874482845188096.1	x¹⁶ - 8x¹⁴ + 16x¹² - 16x¹⁰ + 66x⁸ - 8x⁶ - 32x⁴ - 16x² + 1	$ 2^{56}\cdot 3^{8} $	$C_2^4.C_2^3$ (as 16T210)	Trivial (GRH)
16.4.472769874482845188096.2	x¹⁶ - 4x¹² - 16x¹⁰ - 42x⁸ - 160x⁶ - 132x⁴ - 16x² + 1	$ 2^{56}\cdot 3^{8} $	$C_2^4.C_2^3$ (as 16T210)	Trivial (GRH)
16.0.472769874482845188096.5	x¹⁶ + 8x¹⁴ + 16x¹² + 16x¹⁰ + 66x⁸ + 8x⁶ - 32x⁴ + 16x² + 1	$ 2^{56}\cdot 3^{8} $	$C_2^4.C_2^3$ (as 16T210)	$[2]$
16.0.1759218604441600000000.1	x¹⁶ + 4x¹⁴ + 10x¹² + 16x¹⁰ + 15x⁸ + 88x⁶ - 122x⁴ + 76x² + 1	$ 2^{52}\cdot 5^{8} $	$C_2^4.C_2^3$ (as 16T210)	Trivial
16.8.1759218604441600000000.1	x¹⁶ - 4x¹⁴ - 14x¹² + 40x¹⁰ - 85x⁸ + 120x⁶ - 54x⁴ + 4x² + 1	$ 2^{52}\cdot 5^{8} $	$C_2^4.C_2^3$ (as 16T210)	Trivial (GRH)
16.8.11574317056000000000000.1	x¹⁶ - 2x¹⁵ - 13x¹⁴ + 14x¹³ + 63x¹² + 10x¹¹ - 184x¹⁰ - 188x⁹ + 343x⁸ + 294x⁷ - 356x⁶ - 68x⁵ + 328x⁴ - 12x³ - 142x² - 8x + 1	$ 2^{24}\cdot 5^{12}\cdot 41^{4} $	$C_2^4.C_2^3$ (as 16T210)	Trivial (GRH)
16.0.140857138691308837890625.2	x¹⁶ - 6x¹⁵ + 31x¹⁴ - 99x¹³ + 260x¹² - 480x¹¹ + 725x¹⁰ - 732x⁹ + 857x⁸ - 522x⁷ + 763x⁶ - 60x⁵ + 442x⁴ + 198x³ + 216x² + 81x + 81	$ 5^{12}\cdot 13^{8}\cdot 29^{4} $	$C_2^4.C_2^3$ (as 16T210)	$[14]$ (GRH)
16.0.256992219136000000000000.1	x¹⁶ - 6x¹⁵ + 37x¹⁴ - 128x¹³ + 398x¹² - 798x¹¹ + 1482x¹⁰ - 1784x⁹ + 2635x⁸ - 2088x⁷ + 2818x⁶ - 448x⁵ + 1016x⁴ + 112x³ + 128x² + 16	$ 2^{24}\cdot 5^{12}\cdot 89^{4} $	$C_2^4.C_2^3$ (as 16T210)	$[14]$ (GRH)
16.0.760294709821440000000000.1	x¹⁶ - 8x¹⁵ + 34x¹⁴ - 84x¹³ + 144x¹² - 284x¹¹ + 824x¹⁰ - 1694x⁹ + 1969x⁸ - 2084x⁷ + 5062x⁶ - 8238x⁵ + 5501x⁴ - 1826x³ + 1231x² - 182x + 139	$ 2^{24}\cdot 3^{8}\cdot 5^{10}\cdot 29^{4} $	$C_2^4.C_2^3$ (as 16T210)	$[6]$ (GRH)
16.0.760294709821440000000000.2	x¹⁶ - 4x¹⁵ + 4x¹⁴ + 16x¹³ - 32x¹² - 8x¹¹ + 116x¹⁰ - 412x⁹ + 1002x⁸ - 784x⁷ - 724x⁶ + 1024x⁵ + 1459x⁴ - 3764x³ + 3748x² - 1840x + 529	$ 2^{24}\cdot 3^{8}\cdot 5^{10}\cdot 29^{4} $	$C_2^4.C_2^3$ (as 16T210)	$[6]$ (GRH)
16.8.2963025166336000000000000.1	x¹⁶ + 8x¹⁴ - 40x¹² - 262x¹⁰ + 434x⁸ + 1952x⁶ - 1015x⁴ + 122x² + 1	$ 2^{32}\cdot 5^{12}\cdot 41^{4} $	$C_2^4.C_2^3$ (as 16T210)	Trivial (GRH)
16.0.20723941878730254150390625.1	x¹⁶ - 2x¹⁵ + 7x¹⁴ - 11x¹³ + 28x¹² + 30x¹¹ + 186x¹⁰ - 103x⁹ + 833x⁸ + 1344x⁷ + 1809x⁶ - 978x⁵ + 5088x⁴ + 3448x³ + 3088x² + 512x + 256	$ 5^{12}\cdot 13^{8}\cdot 101^{4} $	$C_2^4.C_2^3$ (as 16T210)	$[48]$ (GRH)
16.16.27789935251456000000000000.1	x¹⁶ - 2x¹⁵ - 45x¹⁴ + 74x¹³ + 807x¹² - 1002x¹¹ - 7340x¹⁰ + 5828x⁹ + 35651x⁸ - 11638x⁷ - 88466x⁶ - 7124x⁵ + 92696x⁴ + 28972x³ - 28444x² - 10968x - 639	$ 2^{24}\cdot 5^{12}\cdot 7^{4}\cdot 41^{4} $	$C_2^4.C_2^3$ (as 16T210)	Trivial (GRH)
16.0.65790008098816000000000000.1	x¹⁶ + 4x¹⁴ - 12x¹³ + 94x¹² - 216x¹¹ + 652x¹⁰ - 1148x⁹ + 4132x⁸ - 9824x⁷ + 27006x⁶ - 43844x⁵ + 59523x⁴ - 54320x³ + 37368x² - 14976x + 5351	$ 2^{32}\cdot 5^{12}\cdot 89^{4} $	$C_2^4.C_2^3$ (as 16T210)	$[2, 56]$ (GRH)
16.8.65790008098816000000000000.1	x¹⁶ - 8x¹⁵ + 8x¹⁴ + 36x¹³ + 160x¹² - 528x¹¹ - 2268x¹⁰ + 2904x⁹ + 20920x⁸ - 15616x⁷ - 96624x⁶ + 67856x⁵ + 167864x⁴ - 81408x³ - 48816x² + 864x + 1296	$ 2^{32}\cdot 5^{12}\cdot 89^{4} $	$C_2^4.C_2^3$ (as 16T210)	$[2]$ (GRH)
16.0.758534442582016000000000000.1	x¹⁶ + 26x¹⁴ + 227x¹² + 848x¹⁰ + 1490x⁸ + 1202x⁶ + 392x⁴ + 44x² + 1	$ 2^{40}\cdot 5^{12}\cdot 41^{4} $	$C_2^4.C_2^3$ (as 16T210)	$[12, 12]$ (GRH)
16.16.758534442582016000000000000.1	x¹⁶ - 26x¹⁴ + 227x¹² - 848x¹⁰ + 1490x⁸ - 1202x⁶ + 392x⁴ - 44x² + 1	$ 2^{40}\cdot 5^{12}\cdot 41^{4} $	$C_2^4.C_2^3$ (as 16T210)	Trivial (GRH)
16.8.758534442582016000000000000.1	x¹⁶ + 8x¹⁴ - 72x¹² - 414x¹⁰ - 110x⁸ + 936x⁶ + 423x⁴ - 62x² + 1	$ 2^{40}\cdot 5^{12}\cdot 41^{4} $	$C_2^4.C_2^3$ (as 16T210)	Trivial (GRH)
16.0.1052640129581056000000000000.1	x¹⁶ - 8x¹⁵ + 24x¹⁴ + 16x¹³ - 220x¹² + 224x¹¹ + 1264x¹⁰ - 1920x⁹ - 3448x⁸ + 11584x⁷ + 18776x⁶ - 35792x⁵ - 37408x⁴ + 95920x³ + 266416x² + 211296x + 114876	$ 2^{36}\cdot 5^{12}\cdot 89^{4} $	$C_2^4.C_2^3$ (as 16T210)	$[2, 2, 4]$ (GRH)

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Results (displaying all 22 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
16.0.8861338240000000000.1	x¹⁶ - 3x¹⁴ - 4x¹³ + 10x¹² + 28x¹¹ + 14x¹⁰ - 56x⁹ - 99x⁸ - 78x⁷ + 18x⁶ + 166x⁵ + 274x⁴ + 250x³ + 135x² + 40x + 5	\( 2^{16}\cdot 5^{10}\cdot 61^{4} \)	$C_2^4.C_2^3$ (as 16T210)	Trivial
16.0.36665447040000000000.1	x¹⁶ - 4x¹⁵ + 6x¹⁴ - 8x¹³ + 23x¹² - 28x¹¹ + 12x¹⁰ - 24x⁹ + 17x⁸ + 24x⁷ + 12x⁶ + 28x⁵ + 23x⁴ + 8x³ + 6x² + 4x + 1	\( 2^{16}\cdot 3^{4}\cdot 5^{10}\cdot 29^{4} \)	$C_2^4.C_2^3$ (as 16T210)	Trivial
16.4.472769874482845188096.1	x¹⁶ - 4x¹² + 16x¹⁰ - 42x⁸ + 160x⁶ - 132x⁴ + 16x² + 1	\( 2^{56}\cdot 3^{8} \)	$C_2^4.C_2^3$ (as 16T210)	Trivial (GRH)
16.8.472769874482845188096.1	x¹⁶ - 8x¹⁴ + 16x¹² - 16x¹⁰ + 66x⁸ - 8x⁶ - 32x⁴ - 16x² + 1	\( 2^{56}\cdot 3^{8} \)	$C_2^4.C_2^3$ (as 16T210)	Trivial (GRH)
16.4.472769874482845188096.2	x¹⁶ - 4x¹² - 16x¹⁰ - 42x⁸ - 160x⁶ - 132x⁴ - 16x² + 1	\( 2^{56}\cdot 3^{8} \)	$C_2^4.C_2^3$ (as 16T210)	Trivial (GRH)
16.0.472769874482845188096.5	x¹⁶ + 8x¹⁴ + 16x¹² + 16x¹⁰ + 66x⁸ + 8x⁶ - 32x⁴ + 16x² + 1	\( 2^{56}\cdot 3^{8} \)	$C_2^4.C_2^3$ (as 16T210)	$[2]$
16.0.1759218604441600000000.1	x¹⁶ + 4x¹⁴ + 10x¹² + 16x¹⁰ + 15x⁸ + 88x⁶ - 122x⁴ + 76x² + 1	\( 2^{52}\cdot 5^{8} \)	$C_2^4.C_2^3$ (as 16T210)	Trivial
16.8.1759218604441600000000.1	x¹⁶ - 4x¹⁴ - 14x¹² + 40x¹⁰ - 85x⁸ + 120x⁶ - 54x⁴ + 4x² + 1	\( 2^{52}\cdot 5^{8} \)	$C_2^4.C_2^3$ (as 16T210)	Trivial (GRH)
16.8.11574317056000000000000.1	x¹⁶ - 2x¹⁵ - 13x¹⁴ + 14x¹³ + 63x¹² + 10x¹¹ - 184x¹⁰ - 188x⁹ + 343x⁸ + 294x⁷ - 356x⁶ - 68x⁵ + 328x⁴ - 12x³ - 142x² - 8x + 1	\( 2^{24}\cdot 5^{12}\cdot 41^{4} \)	$C_2^4.C_2^3$ (as 16T210)	Trivial (GRH)
16.0.140857138691308837890625.2	x¹⁶ - 6x¹⁵ + 31x¹⁴ - 99x¹³ + 260x¹² - 480x¹¹ + 725x¹⁰ - 732x⁹ + 857x⁸ - 522x⁷ + 763x⁶ - 60x⁵ + 442x⁴ + 198x³ + 216x² + 81x + 81	\( 5^{12}\cdot 13^{8}\cdot 29^{4} \)	$C_2^4.C_2^3$ (as 16T210)	$[14]$ (GRH)
16.0.256992219136000000000000.1	x¹⁶ - 6x¹⁵ + 37x¹⁴ - 128x¹³ + 398x¹² - 798x¹¹ + 1482x¹⁰ - 1784x⁹ + 2635x⁸ - 2088x⁷ + 2818x⁶ - 448x⁵ + 1016x⁴ + 112x³ + 128x² + 16	\( 2^{24}\cdot 5^{12}\cdot 89^{4} \)	$C_2^4.C_2^3$ (as 16T210)	$[14]$ (GRH)
16.0.760294709821440000000000.1	x¹⁶ - 8x¹⁵ + 34x¹⁴ - 84x¹³ + 144x¹² - 284x¹¹ + 824x¹⁰ - 1694x⁹ + 1969x⁸ - 2084x⁷ + 5062x⁶ - 8238x⁵ + 5501x⁴ - 1826x³ + 1231x² - 182x + 139	\( 2^{24}\cdot 3^{8}\cdot 5^{10}\cdot 29^{4} \)	$C_2^4.C_2^3$ (as 16T210)	$[6]$ (GRH)
16.0.760294709821440000000000.2	x¹⁶ - 4x¹⁵ + 4x¹⁴ + 16x¹³ - 32x¹² - 8x¹¹ + 116x¹⁰ - 412x⁹ + 1002x⁸ - 784x⁷ - 724x⁶ + 1024x⁵ + 1459x⁴ - 3764x³ + 3748x² - 1840x + 529	\( 2^{24}\cdot 3^{8}\cdot 5^{10}\cdot 29^{4} \)	$C_2^4.C_2^3$ (as 16T210)	$[6]$ (GRH)
16.8.2963025166336000000000000.1	x¹⁶ + 8x¹⁴ - 40x¹² - 262x¹⁰ + 434x⁸ + 1952x⁶ - 1015x⁴ + 122x² + 1	\( 2^{32}\cdot 5^{12}\cdot 41^{4} \)	$C_2^4.C_2^3$ (as 16T210)	Trivial (GRH)
16.0.20723941878730254150390625.1	x¹⁶ - 2x¹⁵ + 7x¹⁴ - 11x¹³ + 28x¹² + 30x¹¹ + 186x¹⁰ - 103x⁹ + 833x⁸ + 1344x⁷ + 1809x⁶ - 978x⁵ + 5088x⁴ + 3448x³ + 3088x² + 512x + 256	\( 5^{12}\cdot 13^{8}\cdot 101^{4} \)	$C_2^4.C_2^3$ (as 16T210)	$[48]$ (GRH)
16.16.27789935251456000000000000.1	x¹⁶ - 2x¹⁵ - 45x¹⁴ + 74x¹³ + 807x¹² - 1002x¹¹ - 7340x¹⁰ + 5828x⁹ + 35651x⁸ - 11638x⁷ - 88466x⁶ - 7124x⁵ + 92696x⁴ + 28972x³ - 28444x² - 10968x - 639	\( 2^{24}\cdot 5^{12}\cdot 7^{4}\cdot 41^{4} \)	$C_2^4.C_2^3$ (as 16T210)	Trivial (GRH)
16.0.65790008098816000000000000.1	x¹⁶ + 4x¹⁴ - 12x¹³ + 94x¹² - 216x¹¹ + 652x¹⁰ - 1148x⁹ + 4132x⁸ - 9824x⁷ + 27006x⁶ - 43844x⁵ + 59523x⁴ - 54320x³ + 37368x² - 14976x + 5351	\( 2^{32}\cdot 5^{12}\cdot 89^{4} \)	$C_2^4.C_2^3$ (as 16T210)	$[2, 56]$ (GRH)
16.8.65790008098816000000000000.1	x¹⁶ - 8x¹⁵ + 8x¹⁴ + 36x¹³ + 160x¹² - 528x¹¹ - 2268x¹⁰ + 2904x⁹ + 20920x⁸ - 15616x⁷ - 96624x⁶ + 67856x⁵ + 167864x⁴ - 81408x³ - 48816x² + 864x + 1296	\( 2^{32}\cdot 5^{12}\cdot 89^{4} \)	$C_2^4.C_2^3$ (as 16T210)	$[2]$ (GRH)
16.0.758534442582016000000000000.1	x¹⁶ + 26x¹⁴ + 227x¹² + 848x¹⁰ + 1490x⁸ + 1202x⁶ + 392x⁴ + 44x² + 1	\( 2^{40}\cdot 5^{12}\cdot 41^{4} \)	$C_2^4.C_2^3$ (as 16T210)	$[12, 12]$ (GRH)
16.16.758534442582016000000000000.1	x¹⁶ - 26x¹⁴ + 227x¹² - 848x¹⁰ + 1490x⁸ - 1202x⁶ + 392x⁴ - 44x² + 1	\( 2^{40}\cdot 5^{12}\cdot 41^{4} \)	$C_2^4.C_2^3$ (as 16T210)	Trivial (GRH)
16.8.758534442582016000000000000.1	x¹⁶ + 8x¹⁴ - 72x¹² - 414x¹⁰ - 110x⁸ + 936x⁶ + 423x⁴ - 62x² + 1	\( 2^{40}\cdot 5^{12}\cdot 41^{4} \)	$C_2^4.C_2^3$ (as 16T210)	Trivial (GRH)
16.0.1052640129581056000000000000.1	x¹⁶ - 8x¹⁵ + 24x¹⁴ + 16x¹³ - 220x¹² + 224x¹¹ + 1264x¹⁰ - 1920x⁹ - 3448x⁸ + 11584x⁷ + 18776x⁶ - 35792x⁵ - 37408x⁴ + 95920x³ + 266416x² + 211296x + 114876	\( 2^{36}\cdot 5^{12}\cdot 89^{4} \)	$C_2^4.C_2^3$ (as 16T210)	$[2, 2, 4]$ (GRH)