LMFDB - Global number field search results

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Results (displaying all 24 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.9659566875244140625.1	x¹⁶ - 4x¹⁵ + 12x¹⁴ - 27x¹³ + 49x¹² - 75x¹¹ + 82x¹⁰ - 66x⁹ + 42x⁸ + 11x⁷ + 30x⁶ + 57x⁵ + 10x⁴ - 59x³ + 36x² - 5x + 1	$ 5^{12}\cdot 19^{6}\cdot 29^{2} $	$C_2^4.C_2^3.C_2$ (as 16T707)	$[2]$
16.0.9659566875244140625.2	x¹⁶ + 7x¹⁴ + 12x¹² + 10x¹⁰ + 86x⁸ + 155x⁶ - 12x⁴ - 4x² + 1	$ 5^{12}\cdot 19^{6}\cdot 29^{2} $	$C_2^4.C_2^3.C_2$ (as 16T707)	$[2]$
16.4.9942664589466402816.1	x¹⁶ - 8x¹⁴ + 16x¹² + 16x¹⁰ - 80x⁸ + 88x⁶ - 56x⁴ + 16x² + 4	$ 2^{34}\cdot 3^{14}\cdot 11^{2} $	$C_2^4.C_2^3.C_2$ (as 16T707)	Trivial
16.4.9942664589466402816.2	x¹⁶ + 8x¹⁴ + 16x¹² - 16x¹⁰ - 80x⁸ - 88x⁶ - 56x⁴ - 16x² + 4	$ 2^{34}\cdot 3^{14}\cdot 11^{2} $	$C_2^4.C_2^3.C_2$ (as 16T707)	Trivial
16.12.31358383355156494140625.1	x¹⁶ - 4x¹⁵ - 9x¹⁴ + 45x¹³ + 19x¹² - 138x¹¹ - 153x¹⁰ + 423x⁹ + 506x⁸ - 1251x⁷ - 299x⁶ + 1705x⁵ - 554x⁴ - 695x³ + 520x² - 110x + 5	$ 5^{12}\cdot 11^{2}\cdot 101^{6} $	$C_2^4.C_2^3.C_2$ (as 16T707)	Trivial (GRH)
16.4.31358383355156494140625.1	x¹⁶ - x¹⁵ + 6x¹⁴ - 20x¹³ - 20x¹² - 4x¹¹ - 20x¹⁰ + 325x⁹ + 161x⁸ - 995x⁷ - 185x⁶ + 896x⁵ - 155x⁴ - 170x³ + 66x² - 31x + 1	$ 5^{12}\cdot 11^{2}\cdot 101^{6} $	$C_2^4.C_2^3.C_2$ (as 16T707)	$[2]$ (GRH)
16.12.31358383355156494140625.2	x¹⁶ - 2x¹⁵ - 12x¹⁴ + 11x¹³ + 66x¹² + 12x¹¹ - 282x¹⁰ + 83x⁹ + 892x⁸ - 710x⁷ - 1583x⁶ + 579x⁵ + 1107x⁴ + 117x³ - 89x² + 1	$ 5^{12}\cdot 11^{2}\cdot 101^{6} $	$C_2^4.C_2^3.C_2$ (as 16T707)	Trivial (GRH)
16.4.31358383355156494140625.2	x¹⁶ - 8x¹⁵ + 18x¹⁴ + 14x¹³ - 91x¹² + 273x¹⁰ - 78x⁹ - 203x⁸ - 1008x⁷ + 845x⁶ + 3086x⁵ - 1590x⁴ - 4208x³ + 679x² + 2270x + 191	$ 5^{12}\cdot 11^{2}\cdot 101^{6} $	$C_2^4.C_2^3.C_2$ (as 16T707)	$[2]$ (GRH)
16.8.964335078219316650390625.3	x¹⁶ - 8x¹⁵ + 18x¹⁴ + 14x¹³ - 95x¹² + 24x¹¹ + 223x¹⁰ - 48x⁹ - 34x⁸ - 1600x⁷ + 205x⁶ + 6940x⁵ - 4490x⁴ - 5450x³ + 3650x² + 650x + 25	$ 5^{12}\cdot 61^{2}\cdot 101^{6} $	$C_2^4.C_2^3.C_2$ (as 16T707)	Trivial (GRH)
16.8.964335078219316650390625.4	x¹⁶ - 4x¹⁵ - 7x¹⁴ + 52x¹³ - 24x¹² - 174x¹¹ + 30x¹⁰ + 256x⁹ + 889x⁸ - 618x⁷ - 2730x⁶ + 1163x⁵ + 5906x⁴ - 6736x³ - 2103x² + 6583x - 2459	$ 5^{12}\cdot 61^{2}\cdot 101^{6} $	$C_2^4.C_2^3.C_2$ (as 16T707)	$[2]$ (GRH)
16.0.1333092859011603841941504.1	x¹⁶ + 8x¹⁴ - 14x¹² - 64x¹⁰ + 343x⁸ + 896x⁶ + 466x⁴ + 56x² + 1	$ 2^{32}\cdot 3^{12}\cdot 11^{2}\cdot 13^{6} $	$C_2^4.C_2^3.C_2$ (as 16T707)	$[2, 2]$ (GRH)
16.0.1333092859011603841941504.2	x¹⁶ + 16x¹⁴ + 10x¹² + 16x¹⁰ + 31x⁸ + 16x⁶ + 10x⁴ + 16x² + 1	$ 2^{32}\cdot 3^{12}\cdot 11^{2}\cdot 13^{6} $	$C_2^4.C_2^3.C_2$ (as 16T707)	$[2, 4]$ (GRH)
16.16.87569778018689765869140625.1	x¹⁶ - 35x¹⁴ + 459x¹² - 2890x¹⁰ + 8951x⁸ - 11630x⁶ + 2514x⁴ - 100x² + 1	$ 5^{12}\cdot 101^{2}\cdot 181^{6} $	$C_2^4.C_2^3.C_2$ (as 16T707)	Trivial (GRH)
16.16.87569778018689765869140625.2	x¹⁶ - 4x¹⁵ - 30x¹⁴ + 140x¹³ + 209x¹² - 1444x¹¹ + 232x¹⁰ + 4725x⁹ - 2799x⁸ - 5034x⁷ + 2187x⁶ + 2572x⁵ - 136x⁴ - 443x³ - 79x² + 3x + 1	$ 5^{12}\cdot 101^{2}\cdot 181^{6} $	$C_2^4.C_2^3.C_2$ (as 16T707)	Trivial (GRH)
16.0.103661741408596533461385216.3	x¹⁶ + 36x¹⁴ + 502x¹² + 3456x¹⁰ + 12399x⁸ + 21864x⁶ + 17410x⁴ + 19500x² + 28561	$ 2^{32}\cdot 3^{12}\cdot 13^{6}\cdot 97^{2} $	$C_2^4.C_2^3.C_2$ (as 16T707)	$[2, 4]$ (GRH)
16.0.103661741408596533461385216.4	x¹⁶ - 4x¹⁵ + 16x¹⁴ - 8x¹³ + 44x¹² + 284x¹¹ - 232x¹⁰ + 1432x⁹ + 1282x⁸ + 1804x⁷ + 13424x⁶ - 7528x⁵ + 44492x⁴ - 18644x³ + 61096x² - 22552x + 12409	$ 2^{32}\cdot 3^{12}\cdot 13^{6}\cdot 97^{2} $	$C_2^4.C_2^3.C_2$ (as 16T707)	$[2, 2, 20]$ (GRH)
16.0.103661741408596533461385216.5	x¹⁶ - 8x¹⁵ + 32x¹⁴ - 68x¹³ + 100x¹² - 124x¹¹ - 40x¹⁰ + 872x⁹ + 226x⁸ - 3456x⁷ + 2592x⁶ + 2052x⁵ + 8388x⁴ + 26028x³ + 17496x² - 14256x + 9801	$ 2^{32}\cdot 3^{12}\cdot 13^{6}\cdot 97^{2} $	$C_2^4.C_2^3.C_2$ (as 16T707)	$[2, 4]$ (GRH)
16.0.103661741408596533461385216.6	x¹⁶ - 8x¹⁵ + 40x¹⁴ - 140x¹³ + 488x¹² - 1472x¹¹ + 3694x¹⁰ - 7360x⁹ + 15655x⁸ - 30648x⁷ + 54430x⁶ - 74928x⁵ + 100450x⁴ - 103040x³ + 69862x² - 27024x + 6133	$ 2^{32}\cdot 3^{12}\cdot 13^{6}\cdot 97^{2} $	$C_2^4.C_2^3.C_2$ (as 16T707)	$[2, 2, 36]$ (GRH)
16.0.414646965634386133845540864.1	x¹⁶ - 4x¹⁵ + 10x¹⁴ - 40x¹³ + 122x¹² - 64x¹¹ + 112x¹⁰ - 752x⁹ + 478x⁸ + 2400x⁷ + 1636x⁶ + 4020x⁵ + 4324x⁴ + 2660x³ + 3244x² + 1944x + 358	$ 2^{34}\cdot 3^{12}\cdot 13^{6}\cdot 97^{2} $	$C_2^4.C_2^3.C_2$ (as 16T707)	$[2, 2, 4]$ (GRH)
16.0.414646965634386133845540864.2	x¹⁶ - 8x¹⁵ + 36x¹⁴ - 76x¹³ + 24x¹² + 480x¹¹ - 1148x¹⁰ + 488x⁹ + 5028x⁸ - 8168x⁷ - 2120x⁶ + 20160x⁵ - 14280x⁴ - 42800x³ + 104064x² - 92368x + 32056	$ 2^{34}\cdot 3^{12}\cdot 13^{6}\cdot 97^{2} $	$C_2^4.C_2^3.C_2$ (as 16T707)	$[2, 2, 4]$ (GRH)
16.0.71594983564208250058837890625.1	x¹⁶ - 6x¹⁵ + 32x¹⁴ - 104x¹³ + 554x¹² - 1276x¹¹ + 4718x¹⁰ - 10281x⁹ + 38308x⁸ - 56734x⁷ + 238958x⁶ - 202907x⁵ + 1117415x⁴ - 373248x³ + 3038941x² - 234427x + 3248561	$ 5^{12}\cdot 11^{2}\cdot 101^{6}\cdot 1511^{2} $	$C_2^4.C_2^3.C_2$ (as 16T707)	$[2, 2, 560]$ (GRH)
16.0.71594983564208250058837890625.2	x¹⁶ - 6x¹⁵ + 32x¹⁴ - 152x¹³ + 698x¹² - 2332x¹¹ + 8548x¹⁰ - 23117x⁹ + 62333x⁸ - 128672x⁷ + 348382x⁶ - 437821x⁵ + 1300506x⁴ - 919720x³ + 3251335x² - 576065x + 4954805	$ 5^{12}\cdot 11^{2}\cdot 101^{6}\cdot 1511^{2} $	$C_2^4.C_2^3.C_2$ (as 16T707)	$[2, 2, 620]$ (GRH)
16.8.621253507360730723174072265625.1	x¹⁶ - 4x¹⁵ - 18x¹⁴ + 119x¹³ - 156x¹² - 794x¹¹ + 2738x¹⁰ - 1404x⁹ - 8222x⁸ + 64964x⁷ + 398x⁶ - 385678x⁵ + 354290x⁴ + 427733x³ - 1780634x² + 1831867x + 241811	$ 5^{12}\cdot 11^{2}\cdot 101^{6}\cdot 4451^{2} $	$C_2^4.C_2^3.C_2$ (as 16T707)	$[2, 2]$ (GRH)
16.8.621253507360730723174072265625.2	x¹⁶ - 28x¹⁴ - 101x¹³ - 21x¹² + 466x¹¹ + 239x¹⁰ + 5663x⁹ - 12728x⁸ - 11743x⁷ + 63109x⁶ - 25123x⁵ + 59511x⁴ - 307720x³ + 32825x² + 20300x - 1795	$ 5^{12}\cdot 11^{2}\cdot 101^{6}\cdot 4451^{2} $	$C_2^4.C_2^3.C_2$ (as 16T707)	$[2]$ (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
16.0.9659566875244140625.1	x¹⁶ - 4x¹⁵ + 12x¹⁴ - 27x¹³ + 49x¹² - 75x¹¹ + 82x¹⁰ - 66x⁹ + 42x⁸ + 11x⁷ + 30x⁶ + 57x⁵ + 10x⁴ - 59x³ + 36x² - 5x + 1	\( 5^{12}\cdot 19^{6}\cdot 29^{2} \)	$C_2^4.C_2^3.C_2$ (as 16T707)	$[2]$
16.0.9659566875244140625.2	x¹⁶ + 7x¹⁴ + 12x¹² + 10x¹⁰ + 86x⁸ + 155x⁶ - 12x⁴ - 4x² + 1	\( 5^{12}\cdot 19^{6}\cdot 29^{2} \)	$C_2^4.C_2^3.C_2$ (as 16T707)	$[2]$
16.4.9942664589466402816.1	x¹⁶ - 8x¹⁴ + 16x¹² + 16x¹⁰ - 80x⁸ + 88x⁶ - 56x⁴ + 16x² + 4	\( 2^{34}\cdot 3^{14}\cdot 11^{2} \)	$C_2^4.C_2^3.C_2$ (as 16T707)	Trivial
16.4.9942664589466402816.2	x¹⁶ + 8x¹⁴ + 16x¹² - 16x¹⁰ - 80x⁸ - 88x⁶ - 56x⁴ - 16x² + 4	\( 2^{34}\cdot 3^{14}\cdot 11^{2} \)	$C_2^4.C_2^3.C_2$ (as 16T707)	Trivial
16.12.31358383355156494140625.1	x¹⁶ - 4x¹⁵ - 9x¹⁴ + 45x¹³ + 19x¹² - 138x¹¹ - 153x¹⁰ + 423x⁹ + 506x⁸ - 1251x⁷ - 299x⁶ + 1705x⁵ - 554x⁴ - 695x³ + 520x² - 110x + 5	\( 5^{12}\cdot 11^{2}\cdot 101^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T707)	Trivial (GRH)
16.4.31358383355156494140625.1	x¹⁶ - x¹⁵ + 6x¹⁴ - 20x¹³ - 20x¹² - 4x¹¹ - 20x¹⁰ + 325x⁹ + 161x⁸ - 995x⁷ - 185x⁶ + 896x⁵ - 155x⁴ - 170x³ + 66x² - 31x + 1	\( 5^{12}\cdot 11^{2}\cdot 101^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T707)	$[2]$ (GRH)
16.12.31358383355156494140625.2	x¹⁶ - 2x¹⁵ - 12x¹⁴ + 11x¹³ + 66x¹² + 12x¹¹ - 282x¹⁰ + 83x⁹ + 892x⁸ - 710x⁷ - 1583x⁶ + 579x⁵ + 1107x⁴ + 117x³ - 89x² + 1	\( 5^{12}\cdot 11^{2}\cdot 101^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T707)	Trivial (GRH)
16.4.31358383355156494140625.2	x¹⁶ - 8x¹⁵ + 18x¹⁴ + 14x¹³ - 91x¹² + 273x¹⁰ - 78x⁹ - 203x⁸ - 1008x⁷ + 845x⁶ + 3086x⁵ - 1590x⁴ - 4208x³ + 679x² + 2270x + 191	\( 5^{12}\cdot 11^{2}\cdot 101^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T707)	$[2]$ (GRH)
16.8.964335078219316650390625.3	x¹⁶ - 8x¹⁵ + 18x¹⁴ + 14x¹³ - 95x¹² + 24x¹¹ + 223x¹⁰ - 48x⁹ - 34x⁸ - 1600x⁷ + 205x⁶ + 6940x⁵ - 4490x⁴ - 5450x³ + 3650x² + 650x + 25	\( 5^{12}\cdot 61^{2}\cdot 101^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T707)	Trivial (GRH)
16.8.964335078219316650390625.4	x¹⁶ - 4x¹⁵ - 7x¹⁴ + 52x¹³ - 24x¹² - 174x¹¹ + 30x¹⁰ + 256x⁹ + 889x⁸ - 618x⁷ - 2730x⁶ + 1163x⁵ + 5906x⁴ - 6736x³ - 2103x² + 6583x - 2459	\( 5^{12}\cdot 61^{2}\cdot 101^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T707)	$[2]$ (GRH)
16.0.1333092859011603841941504.1	x¹⁶ + 8x¹⁴ - 14x¹² - 64x¹⁰ + 343x⁸ + 896x⁶ + 466x⁴ + 56x² + 1	\( 2^{32}\cdot 3^{12}\cdot 11^{2}\cdot 13^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T707)	$[2, 2]$ (GRH)
16.0.1333092859011603841941504.2	x¹⁶ + 16x¹⁴ + 10x¹² + 16x¹⁰ + 31x⁸ + 16x⁶ + 10x⁴ + 16x² + 1	\( 2^{32}\cdot 3^{12}\cdot 11^{2}\cdot 13^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T707)	$[2, 4]$ (GRH)
16.16.87569778018689765869140625.1	x¹⁶ - 35x¹⁴ + 459x¹² - 2890x¹⁰ + 8951x⁸ - 11630x⁶ + 2514x⁴ - 100x² + 1	\( 5^{12}\cdot 101^{2}\cdot 181^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T707)	Trivial (GRH)
16.16.87569778018689765869140625.2	x¹⁶ - 4x¹⁵ - 30x¹⁴ + 140x¹³ + 209x¹² - 1444x¹¹ + 232x¹⁰ + 4725x⁹ - 2799x⁸ - 5034x⁷ + 2187x⁶ + 2572x⁵ - 136x⁴ - 443x³ - 79x² + 3x + 1	\( 5^{12}\cdot 101^{2}\cdot 181^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T707)	Trivial (GRH)
16.0.103661741408596533461385216.3	x¹⁶ + 36x¹⁴ + 502x¹² + 3456x¹⁰ + 12399x⁸ + 21864x⁶ + 17410x⁴ + 19500x² + 28561	\( 2^{32}\cdot 3^{12}\cdot 13^{6}\cdot 97^{2} \)	$C_2^4.C_2^3.C_2$ (as 16T707)	$[2, 4]$ (GRH)
16.0.103661741408596533461385216.4	x¹⁶ - 4x¹⁵ + 16x¹⁴ - 8x¹³ + 44x¹² + 284x¹¹ - 232x¹⁰ + 1432x⁹ + 1282x⁸ + 1804x⁷ + 13424x⁶ - 7528x⁵ + 44492x⁴ - 18644x³ + 61096x² - 22552x + 12409	\( 2^{32}\cdot 3^{12}\cdot 13^{6}\cdot 97^{2} \)	$C_2^4.C_2^3.C_2$ (as 16T707)	$[2, 2, 20]$ (GRH)
16.0.103661741408596533461385216.5	x¹⁶ - 8x¹⁵ + 32x¹⁴ - 68x¹³ + 100x¹² - 124x¹¹ - 40x¹⁰ + 872x⁹ + 226x⁸ - 3456x⁷ + 2592x⁶ + 2052x⁵ + 8388x⁴ + 26028x³ + 17496x² - 14256x + 9801	\( 2^{32}\cdot 3^{12}\cdot 13^{6}\cdot 97^{2} \)	$C_2^4.C_2^3.C_2$ (as 16T707)	$[2, 4]$ (GRH)
16.0.103661741408596533461385216.6	x¹⁶ - 8x¹⁵ + 40x¹⁴ - 140x¹³ + 488x¹² - 1472x¹¹ + 3694x¹⁰ - 7360x⁹ + 15655x⁸ - 30648x⁷ + 54430x⁶ - 74928x⁵ + 100450x⁴ - 103040x³ + 69862x² - 27024x + 6133	\( 2^{32}\cdot 3^{12}\cdot 13^{6}\cdot 97^{2} \)	$C_2^4.C_2^3.C_2$ (as 16T707)	$[2, 2, 36]$ (GRH)
16.0.414646965634386133845540864.1	x¹⁶ - 4x¹⁵ + 10x¹⁴ - 40x¹³ + 122x¹² - 64x¹¹ + 112x¹⁰ - 752x⁹ + 478x⁸ + 2400x⁷ + 1636x⁶ + 4020x⁵ + 4324x⁴ + 2660x³ + 3244x² + 1944x + 358	\( 2^{34}\cdot 3^{12}\cdot 13^{6}\cdot 97^{2} \)	$C_2^4.C_2^3.C_2$ (as 16T707)	$[2, 2, 4]$ (GRH)
16.0.414646965634386133845540864.2	x¹⁶ - 8x¹⁵ + 36x¹⁴ - 76x¹³ + 24x¹² + 480x¹¹ - 1148x¹⁰ + 488x⁹ + 5028x⁸ - 8168x⁷ - 2120x⁶ + 20160x⁵ - 14280x⁴ - 42800x³ + 104064x² - 92368x + 32056	\( 2^{34}\cdot 3^{12}\cdot 13^{6}\cdot 97^{2} \)	$C_2^4.C_2^3.C_2$ (as 16T707)	$[2, 2, 4]$ (GRH)
16.0.71594983564208250058837890625.1	x¹⁶ - 6x¹⁵ + 32x¹⁴ - 104x¹³ + 554x¹² - 1276x¹¹ + 4718x¹⁰ - 10281x⁹ + 38308x⁸ - 56734x⁷ + 238958x⁶ - 202907x⁵ + 1117415x⁴ - 373248x³ + 3038941x² - 234427x + 3248561	\( 5^{12}\cdot 11^{2}\cdot 101^{6}\cdot 1511^{2} \)	$C_2^4.C_2^3.C_2$ (as 16T707)	$[2, 2, 560]$ (GRH)
16.0.71594983564208250058837890625.2	x¹⁶ - 6x¹⁵ + 32x¹⁴ - 152x¹³ + 698x¹² - 2332x¹¹ + 8548x¹⁰ - 23117x⁹ + 62333x⁸ - 128672x⁷ + 348382x⁶ - 437821x⁵ + 1300506x⁴ - 919720x³ + 3251335x² - 576065x + 4954805	\( 5^{12}\cdot 11^{2}\cdot 101^{6}\cdot 1511^{2} \)	$C_2^4.C_2^3.C_2$ (as 16T707)	$[2, 2, 620]$ (GRH)
16.8.621253507360730723174072265625.1	x¹⁶ - 4x¹⁵ - 18x¹⁴ + 119x¹³ - 156x¹² - 794x¹¹ + 2738x¹⁰ - 1404x⁹ - 8222x⁸ + 64964x⁷ + 398x⁶ - 385678x⁵ + 354290x⁴ + 427733x³ - 1780634x² + 1831867x + 241811	\( 5^{12}\cdot 11^{2}\cdot 101^{6}\cdot 4451^{2} \)	$C_2^4.C_2^3.C_2$ (as 16T707)	$[2, 2]$ (GRH)
16.8.621253507360730723174072265625.2	x¹⁶ - 28x¹⁴ - 101x¹³ - 21x¹² + 466x¹¹ + 239x¹⁰ + 5663x⁹ - 12728x⁸ - 11743x⁷ + 63109x⁶ - 25123x⁵ + 59511x⁴ - 307720x³ + 32825x² + 20300x - 1795	\( 5^{12}\cdot 11^{2}\cdot 101^{6}\cdot 4451^{2} \)	$C_2^4.C_2^3.C_2$ (as 16T707)	$[2]$ (GRH)