LMFDB - Global number field search results

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Results (displaying all 22 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.19778044112006091964416.1	x¹⁶ - 53x¹² + 1836x⁸ - 7553x⁴ + 8281	$ 2^{16}\cdot 3^{12}\cdot 7^{6}\cdot 13^{6} $	16T868	$[2]$ (GRH)
16.0.19778044112006091964416.2	x¹⁶ + 5x¹⁴ - 11x¹² + 62x¹⁰ + 1549x⁸ - 1792x⁶ - 5348x⁴ + 1274x² + 8281	$ 2^{16}\cdot 3^{12}\cdot 7^{6}\cdot 13^{6} $	16T868	Trivial (GRH)
16.4.2133622988550169600000000.1	x¹⁶ - 22x¹² - 597x⁸ + 7258x⁴ + 43681	$ 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 19^{6} $	16T868	$[2]$ (GRH)
16.4.2133622988550169600000000.2	x¹⁶ - 3x¹⁴ - 119x¹² - 618x¹⁰ + 2099x⁸ + 22572x⁶ + 65626x⁴ + 87362x² + 43681	$ 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 19^{6} $	16T868	Trivial (GRH)
16.4.2133622988550169600000000.3	x¹⁶ + 47x¹² - 452x⁸ - 6973x⁴ + 43681	$ 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 19^{6} $	16T868	Trivial (GRH)
16.0.2133622988550169600000000.7	x¹⁶ - 13x¹² + 108x⁸ - 4433x⁴ + 43681	$ 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 19^{6} $	16T868	$[2]$ (GRH)
16.0.2133622988550169600000000.8	x¹⁶ - 62x¹² + 883x⁸ + 3058x⁴ + 43681	$ 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 19^{6} $	16T868	$[2]$ (GRH)
16.0.258168381614570521600000000.1	x¹⁶ - 7x¹⁴ + 214x¹² - 1672x¹⁰ + 15763x⁸ - 110594x⁶ + 667436x⁴ - 2503611x² + 5285401	$ 2^{16}\cdot 5^{8}\cdot 11^{8}\cdot 19^{6} $	16T868	$[2]$ (GRH)
16.4.258168381614570521600000000.1	x¹⁶ + 44x¹⁴ + 763x¹² + 5654x¹⁰ - 16137x⁸ - 330814x⁶ - 28677x⁴ + 1112716x² + 5285401	$ 2^{16}\cdot 5^{8}\cdot 11^{8}\cdot 19^{6} $	16T868	$[2]$ (GRH)
16.0.258168381614570521600000000.2	x¹⁶ - 22x¹⁴ + 324x¹² - 2607x¹⁰ + 16368x⁸ - 83974x⁶ + 414546x⁴ - 733381x² + 5285401	$ 2^{16}\cdot 5^{8}\cdot 11^{8}\cdot 19^{6} $	16T868	$[2]$ (GRH)
16.8.546207485068843417600000000.2	x¹⁶ - 8x¹⁵ + 22x¹⁴ + 42x¹³ - 587x¹² + 2002x¹¹ - 3040x¹⁰ - 630x⁹ + 17936x⁸ - 53100x⁷ + 61900x⁶ + 55282x⁵ - 228247x⁴ + 181342x³ + 119082x² - 223458x + 73961	$ 2^{24}\cdot 5^{8}\cdot 11^{6}\cdot 19^{6} $	16T868	Trivial (GRH)
16.0.770237898866611225600000000.1	x¹⁶ + 29x¹⁴ + 341x¹² + 1824x¹⁰ + 11039x⁸ + 117686x⁶ + 450528x⁴ + 15768841	$ 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 19^{8} $	16T868	$[2, 2]$ (GRH)
16.0.770237898866611225600000000.2	x¹⁶ + 132x¹² - 418x¹⁰ + 11039x⁸ + 47652x⁶ - 379411x⁴ + 528143x² + 15768841	$ 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 19^{8} $	16T868	$[2, 2]$ (GRH)
16.0.8739319761101494681600000000.1	x¹⁶ - 6x¹⁵ + 56x¹⁴ - 236x¹³ + 1142x¹² - 3414x¹¹ + 11058x¹⁰ - 21298x⁹ + 56291x⁸ - 43862x⁷ + 166514x⁶ + 37678x⁵ + 259628x⁴ + 170956x³ + 140326x² + 31410x + 13781	$ 2^{28}\cdot 5^{8}\cdot 11^{6}\cdot 19^{6} $	16T868	$[2, 2, 2, 2]$ (GRH)
16.0.72332103161031791641600000000.1	x¹⁶ + 162x¹² - 6610x¹⁰ + 41318x⁸ - 368590x⁶ + 8944847x⁴ - 70686050x² + 171060241	$ 2^{16}\cdot 5^{8}\cdot 29^{6}\cdot 41^{6} $	16T868	$[2, 2]$ (GRH)
16.4.197180902109852473753600000000.1	x¹⁶ - 8x¹⁵ - 14x¹⁴ + 238x¹³ + 409x¹² - 2986x¹¹ - 15006x¹⁰ + 19436x⁹ + 170225x⁸ - 101524x⁷ - 649026x⁶ + 1009684x⁵ + 4669x⁴ - 816582x³ + 4315806x² - 8868558x + 6401861	$ 2^{24}\cdot 5^{8}\cdot 11^{6}\cdot 19^{8} $	16T868	$[2, 2]$ (GRH)
16.4.197180902109852473753600000000.2	x¹⁶ - 2x¹⁵ + 34x¹⁴ + 82x¹³ - 457x¹² + 7022x¹¹ - 28498x¹⁰ + 128536x⁹ - 325780x⁸ + 775396x⁷ - 1014698x⁶ + 731524x⁵ + 1033292x⁴ - 3711478x³ + 14964706x² - 11893530x + 2573195	$ 2^{24}\cdot 5^{8}\cdot 11^{6}\cdot 19^{8} $	16T868	$[2, 2]$ (GRH)
16.8.7567771186285806117913600000000.2	x¹⁶ + 20x¹⁴ - 938x¹² - 8910x¹⁰ + 157399x⁸ + 814900x⁶ - 5053047x⁴ - 7859145x² + 6661561	$ 2^{16}\cdot 5^{8}\cdot 29^{6}\cdot 89^{6} $	16T868	$[2]$ (GRH)
16.0.199875058073008840373089541044249600000000.1	x¹⁶ + 1736x¹⁴ + 1211156x¹² + 430086456x¹⁰ + 80387048099x⁸ + 7216691979704x⁶ + 230917087201933x⁴ + 2822816545662095x² + 10285190654933041	$ 2^{16}\cdot 5^{8}\cdot 29^{6}\cdot 139^{4}\cdot 181^{6} $	16T868	$[2, 2, 2, 2, 2, 4, 23100260]$ (GRH)
16.16.199875058073008840373089541044249600000000.1	x¹⁶ - 1736x¹⁴ + 1211156x¹² - 430086456x¹⁰ + 80387048099x⁸ - 7216691979704x⁶ + 230917087201933x⁴ - 2822816545662095x² + 10285190654933041	$ 2^{16}\cdot 5^{8}\cdot 29^{6}\cdot 139^{4}\cdot 181^{6} $	16T868	Trivial (GRH)
16.0.199875058073008840373089541044249600000000.2	x¹⁶ + 2000x¹⁴ + 1449212x¹² + 493166662x¹⁰ + 82609767019x⁸ + 6431469174712x⁶ + 205796436670039x⁴ + 2611054203786213x² + 10285190654933041	$ 2^{16}\cdot 5^{8}\cdot 29^{6}\cdot 139^{4}\cdot 181^{6} $	16T868	$[2, 2, 2, 2, 2, 4, 25540748]$ (GRH)
16.16.199875058073008840373089541044249600000000.2	x¹⁶ - 2000x¹⁴ + 1449212x¹² - 493166662x¹⁰ + 82609767019x⁸ - 6431469174712x⁶ + 205796436670039x⁴ - 2611054203786213x² + 10285190654933041	$ 2^{16}\cdot 5^{8}\cdot 29^{6}\cdot 139^{4}\cdot 181^{6} $	16T868	Trivial (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
16.0.19778044112006091964416.1	x¹⁶ - 53x¹² + 1836x⁸ - 7553x⁴ + 8281	\( 2^{16}\cdot 3^{12}\cdot 7^{6}\cdot 13^{6} \)	16T868	$[2]$ (GRH)
16.0.19778044112006091964416.2	x¹⁶ + 5x¹⁴ - 11x¹² + 62x¹⁰ + 1549x⁸ - 1792x⁶ - 5348x⁴ + 1274x² + 8281	\( 2^{16}\cdot 3^{12}\cdot 7^{6}\cdot 13^{6} \)	16T868	Trivial (GRH)
16.4.2133622988550169600000000.1	x¹⁶ - 22x¹² - 597x⁸ + 7258x⁴ + 43681	\( 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 19^{6} \)	16T868	$[2]$ (GRH)
16.4.2133622988550169600000000.2	x¹⁶ - 3x¹⁴ - 119x¹² - 618x¹⁰ + 2099x⁸ + 22572x⁶ + 65626x⁴ + 87362x² + 43681	\( 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 19^{6} \)	16T868	Trivial (GRH)
16.4.2133622988550169600000000.3	x¹⁶ + 47x¹² - 452x⁸ - 6973x⁴ + 43681	\( 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 19^{6} \)	16T868	Trivial (GRH)
16.0.2133622988550169600000000.7	x¹⁶ - 13x¹² + 108x⁸ - 4433x⁴ + 43681	\( 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 19^{6} \)	16T868	$[2]$ (GRH)
16.0.2133622988550169600000000.8	x¹⁶ - 62x¹² + 883x⁸ + 3058x⁴ + 43681	\( 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 19^{6} \)	16T868	$[2]$ (GRH)
16.0.258168381614570521600000000.1	x¹⁶ - 7x¹⁴ + 214x¹² - 1672x¹⁰ + 15763x⁸ - 110594x⁶ + 667436x⁴ - 2503611x² + 5285401	\( 2^{16}\cdot 5^{8}\cdot 11^{8}\cdot 19^{6} \)	16T868	$[2]$ (GRH)
16.4.258168381614570521600000000.1	x¹⁶ + 44x¹⁴ + 763x¹² + 5654x¹⁰ - 16137x⁸ - 330814x⁶ - 28677x⁴ + 1112716x² + 5285401	\( 2^{16}\cdot 5^{8}\cdot 11^{8}\cdot 19^{6} \)	16T868	$[2]$ (GRH)
16.0.258168381614570521600000000.2	x¹⁶ - 22x¹⁴ + 324x¹² - 2607x¹⁰ + 16368x⁸ - 83974x⁶ + 414546x⁴ - 733381x² + 5285401	\( 2^{16}\cdot 5^{8}\cdot 11^{8}\cdot 19^{6} \)	16T868	$[2]$ (GRH)
16.8.546207485068843417600000000.2	x¹⁶ - 8x¹⁵ + 22x¹⁴ + 42x¹³ - 587x¹² + 2002x¹¹ - 3040x¹⁰ - 630x⁹ + 17936x⁸ - 53100x⁷ + 61900x⁶ + 55282x⁵ - 228247x⁴ + 181342x³ + 119082x² - 223458x + 73961	\( 2^{24}\cdot 5^{8}\cdot 11^{6}\cdot 19^{6} \)	16T868	Trivial (GRH)
16.0.770237898866611225600000000.1	x¹⁶ + 29x¹⁴ + 341x¹² + 1824x¹⁰ + 11039x⁸ + 117686x⁶ + 450528x⁴ + 15768841	\( 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 19^{8} \)	16T868	$[2, 2]$ (GRH)
16.0.770237898866611225600000000.2	x¹⁶ + 132x¹² - 418x¹⁰ + 11039x⁸ + 47652x⁶ - 379411x⁴ + 528143x² + 15768841	\( 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 19^{8} \)	16T868	$[2, 2]$ (GRH)
16.0.8739319761101494681600000000.1	x¹⁶ - 6x¹⁵ + 56x¹⁴ - 236x¹³ + 1142x¹² - 3414x¹¹ + 11058x¹⁰ - 21298x⁹ + 56291x⁸ - 43862x⁷ + 166514x⁶ + 37678x⁵ + 259628x⁴ + 170956x³ + 140326x² + 31410x + 13781	\( 2^{28}\cdot 5^{8}\cdot 11^{6}\cdot 19^{6} \)	16T868	$[2, 2, 2, 2]$ (GRH)
16.0.72332103161031791641600000000.1	x¹⁶ + 162x¹² - 6610x¹⁰ + 41318x⁸ - 368590x⁶ + 8944847x⁴ - 70686050x² + 171060241	\( 2^{16}\cdot 5^{8}\cdot 29^{6}\cdot 41^{6} \)	16T868	$[2, 2]$ (GRH)
16.4.197180902109852473753600000000.1	x¹⁶ - 8x¹⁵ - 14x¹⁴ + 238x¹³ + 409x¹² - 2986x¹¹ - 15006x¹⁰ + 19436x⁹ + 170225x⁸ - 101524x⁷ - 649026x⁶ + 1009684x⁵ + 4669x⁴ - 816582x³ + 4315806x² - 8868558x + 6401861	\( 2^{24}\cdot 5^{8}\cdot 11^{6}\cdot 19^{8} \)	16T868	$[2, 2]$ (GRH)
16.4.197180902109852473753600000000.2	x¹⁶ - 2x¹⁵ + 34x¹⁴ + 82x¹³ - 457x¹² + 7022x¹¹ - 28498x¹⁰ + 128536x⁹ - 325780x⁸ + 775396x⁷ - 1014698x⁶ + 731524x⁵ + 1033292x⁴ - 3711478x³ + 14964706x² - 11893530x + 2573195	\( 2^{24}\cdot 5^{8}\cdot 11^{6}\cdot 19^{8} \)	16T868	$[2, 2]$ (GRH)
16.8.7567771186285806117913600000000.2	x¹⁶ + 20x¹⁴ - 938x¹² - 8910x¹⁰ + 157399x⁸ + 814900x⁶ - 5053047x⁴ - 7859145x² + 6661561	\( 2^{16}\cdot 5^{8}\cdot 29^{6}\cdot 89^{6} \)	16T868	$[2]$ (GRH)
16.0.199875058073008840373089541044249600000000.1	x¹⁶ + 1736x¹⁴ + 1211156x¹² + 430086456x¹⁰ + 80387048099x⁸ + 7216691979704x⁶ + 230917087201933x⁴ + 2822816545662095x² + 10285190654933041	\( 2^{16}\cdot 5^{8}\cdot 29^{6}\cdot 139^{4}\cdot 181^{6} \)	16T868	$[2, 2, 2, 2, 2, 4, 23100260]$ (GRH)
16.16.199875058073008840373089541044249600000000.1	x¹⁶ - 1736x¹⁴ + 1211156x¹² - 430086456x¹⁰ + 80387048099x⁸ - 7216691979704x⁶ + 230917087201933x⁴ - 2822816545662095x² + 10285190654933041	\( 2^{16}\cdot 5^{8}\cdot 29^{6}\cdot 139^{4}\cdot 181^{6} \)	16T868	Trivial (GRH)
16.0.199875058073008840373089541044249600000000.2	x¹⁶ + 2000x¹⁴ + 1449212x¹² + 493166662x¹⁰ + 82609767019x⁸ + 6431469174712x⁶ + 205796436670039x⁴ + 2611054203786213x² + 10285190654933041	\( 2^{16}\cdot 5^{8}\cdot 29^{6}\cdot 139^{4}\cdot 181^{6} \)	16T868	$[2, 2, 2, 2, 2, 4, 25540748]$ (GRH)
16.16.199875058073008840373089541044249600000000.2	x¹⁶ - 2000x¹⁴ + 1449212x¹² - 493166662x¹⁰ + 82609767019x⁸ - 6431469174712x⁶ + 205796436670039x⁴ - 2611054203786213x² + 10285190654933041	\( 2^{16}\cdot 5^{8}\cdot 29^{6}\cdot 139^{4}\cdot 181^{6} \)	16T868	Trivial (GRH)