LMFDB - Global number field search results

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Results (displaying all 26 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.758989440000000000.1	x¹⁶ - 4x¹⁴ - 8x¹³ + 7x¹² + 24x¹¹ + 15x¹⁰ - 38x⁹ - 40x⁸ + 22x⁷ + 59x⁶ - 24x⁵ - 41x⁴ + 14x³ + 35x² - 30x + 9	$ 2^{16}\cdot 3^{4}\cdot 5^{10}\cdot 11^{4} $	$C_2^4.C_2^4$ (as 16T459)	Trivial
16.0.6003725062500000000.2	x¹⁶ - 6x¹⁴ + 14x¹² - 2x¹⁰ - 6x⁸ - 14x⁶ + 81x⁴ - 68x² + 16	$ 2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 11^{4} $	$C_2^4.C_2^4$ (as 16T459)	$[2]$
16.0.717768397440000000000.3	x¹⁶ - 8x¹⁵ + 31x¹⁴ - 72x¹³ + 109x¹² - 118x¹¹ + 100x¹⁰ + 32x⁹ - 497x⁸ + 1140x⁷ - 1042x⁶ - 336x⁵ + 1876x⁴ - 2100x³ + 1200x² - 360x + 45	$ 2^{16}\cdot 3^{4}\cdot 5^{10}\cdot 61^{4} $	$C_2^4.C_2^4$ (as 16T459)	$[2]$
16.0.5677660175062500000000.2	x¹⁶ - 2x¹⁴ - 30x¹² - 2x¹⁰ + 354x⁸ + 982x⁶ + 1145x⁴ + 432x² + 256	$ 2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 61^{4} $	$C_2^4.C_2^4$ (as 16T459)	$[4]$
16.0.7407562915840000000000.4	x¹⁶ - 18x¹⁴ + 142x¹² - 624x¹⁰ + 1699x⁸ - 3000x⁶ + 3430x⁴ - 2250x² + 625	$ 2^{28}\cdot 5^{10}\cdot 41^{4} $	$C_2^4.C_2^4$ (as 16T459)	Trivial (GRH)
16.0.14013832946090262921216.1	x¹⁶ - 8x¹⁵ + 44x¹⁴ - 160x¹³ + 440x¹² - 944x¹¹ + 1672x¹⁰ - 2520x⁹ + 3342x⁸ - 3808x⁷ + 3768x⁶ - 3056x⁵ + 2100x⁴ - 1120x³ + 496x² - 144x + 34	$ 2^{56}\cdot 3^{4}\cdot 7^{4} $	$C_2^4.C_2^4$ (as 16T459)	$[2]$
16.4.21743271936000000000000.1	x¹⁶ - 16x¹³ - 24x¹² + 40x¹¹ + 76x¹⁰ - 72x⁹ - 324x⁸ - 336x⁷ + 208x⁶ + 1192x⁵ + 1872x⁴ + 1656x³ + 876x² + 256x + 31	$ 2^{40}\cdot 3^{4}\cdot 5^{12} $	$C_2^4.C_2^4$ (as 16T459)	Trivial (GRH)
16.0.21743271936000000000000.2	x¹⁶ + 8x¹⁴ + 10x¹² + 168x¹⁰ + 1079x⁸ + 1992x⁶ + 1350x⁴ + 432x² + 81	$ 2^{40}\cdot 3^{4}\cdot 5^{12} $	$C_2^4.C_2^4$ (as 16T459)	$[2]$ (GRH)
16.4.21743271936000000000000.2	x¹⁶ - 8x¹⁴ - 16x¹³ - 4x¹² + 56x¹¹ + 92x¹⁰ - 96x⁹ - 130x⁸ + 128x⁷ - 32x⁶ + 104x⁵ - 452x⁴ + 576x³ - 272x² + 48x - 4	$ 2^{40}\cdot 3^{4}\cdot 5^{12} $	$C_2^4.C_2^4$ (as 16T459)	Trivial (GRH)
16.8.21743271936000000000000.3	x¹⁶ - 8x¹⁴ + 10x¹² - 168x¹⁰ + 1079x⁸ - 1992x⁶ + 1350x⁴ - 432x² + 81	$ 2^{40}\cdot 3^{4}\cdot 5^{12} $	$C_2^4.C_2^4$ (as 16T459)	Trivial (GRH)
16.0.70448201072640000000000.1	x¹⁶ + 8x¹⁴ - 38x¹² - 56x¹⁰ + 399x⁸ + 1160x⁶ + 1150x⁴ + 400x² + 25	$ 2^{40}\cdot 3^{8}\cdot 5^{10} $	$C_2^4.C_2^4$ (as 16T459)	$[2]$ (GRH)
16.8.70448201072640000000000.2	x¹⁶ - 8x¹⁴ - 38x¹² + 56x¹⁰ + 399x⁸ - 1160x⁶ + 1150x⁴ - 400x² + 25	$ 2^{40}\cdot 3^{8}\cdot 5^{10} $	$C_2^4.C_2^4$ (as 16T459)	Trivial (GRH)
16.8.2963025166336000000000000.7	x¹⁶ - 12x¹⁴ - 16x¹³ + 2x¹² + 184x¹¹ + 336x¹⁰ - 548x⁹ - 915x⁸ + 912x⁷ + 908x⁶ - 1108x⁵ - 648x⁴ + 584x³ + 188x² - 228x - 89	$ 2^{32}\cdot 5^{12}\cdot 41^{4} $	$C_2^4.C_2^4$ (as 16T459)	Trivial (GRH)
16.8.4540481874533245186473984.1	x¹⁶ - 8x¹⁴ - 92x¹² + 440x¹⁰ - 186x⁸ - 440x⁶ - 92x⁴ + 8x² + 1	$ 2^{58}\cdot 3^{8}\cdot 7^{4} $	$C_2^4.C_2^4$ (as 16T459)	Trivial (GRH)
16.0.318343244414976000000000000.1	x¹⁶ - 12x¹⁴ + 90x¹² - 80x¹¹ - 172x¹⁰ + 820x⁹ + 799x⁸ - 1440x⁷ + 3532x⁶ + 5380x⁵ - 2120x⁴ + 2920x³ + 17932x² - 12180x + 11521	$ 2^{40}\cdot 3^{4}\cdot 5^{12}\cdot 11^{4} $	$C_2^4.C_2^4$ (as 16T459)	$[2, 8]$ (GRH)
16.8.342134593410406809600000000.1	x¹⁶ - 8x¹⁴ - 180x¹² - 200x¹⁰ + 1958x⁸ - 600x⁶ - 1620x⁴ - 216x² + 81	$ 2^{52}\cdot 3^{4}\cdot 5^{8}\cdot 7^{4} $	$C_2^4.C_2^4$ (as 16T459)	Trivial (GRH)
16.0.709450292895819560386560000.1	x¹⁶ - 8x¹⁵ + 8x¹⁴ + 72x¹³ - 56x¹² - 376x¹¹ - 272x¹⁰ + 1832x⁹ + 1230x⁸ - 752x⁷ - 720x⁶ - 12592x⁵ + 10724x⁴ - 15248x³ + 26480x² - 9504x + 17902	$ 2^{56}\cdot 3^{8}\cdot 5^{4}\cdot 7^{4} $	$C_2^4.C_2^4$ (as 16T459)	$[4, 4]$ (GRH)
16.8.1031432111904522240000000000.1	x¹⁶ - 4x¹⁵ + 20x¹⁴ - 68x¹³ + 50x¹² - 144x¹¹ - 360x¹⁰ + 1376x⁹ + 951x⁸ - 5456x⁷ - 9072x⁶ + 4104x⁵ + 9364x⁴ + 3052x³ - 84x² - 100x - 5	$ 2^{40}\cdot 3^{8}\cdot 5^{10}\cdot 11^{4} $	$C_2^4.C_2^4$ (as 16T459)	Trivial (GRH)
16.0.81495870570233856000000000000.2	x¹⁶ + 36x¹⁴ + 470x¹² + 2764x¹⁰ + 7679x⁸ + 9804x⁶ + 5580x⁴ + 1296x² + 81	$ 2^{48}\cdot 3^{4}\cdot 5^{12}\cdot 11^{4} $	$C_2^4.C_2^4$ (as 16T459)	$[2, 2, 174]$ (GRH)
16.16.81495870570233856000000000000.2	x¹⁶ - 36x¹⁴ + 470x¹² - 2764x¹⁰ + 7679x⁸ - 9804x⁶ + 5580x⁴ - 1296x² + 81	$ 2^{48}\cdot 3^{4}\cdot 5^{12}\cdot 11^{4} $	$C_2^4.C_2^4$ (as 16T459)	Trivial (GRH)
16.0.83993647724363776000000000000.1	x¹⁶ + 64x¹⁴ + 1450x¹² + 15556x¹⁰ + 84439x⁸ + 223076x⁶ + 251370x⁴ + 78204x² + 2401	$ 2^{40}\cdot 5^{12}\cdot 7^{4}\cdot 19^{4} $	$C_2^4.C_2^4$ (as 16T459)	$[2, 2, 110]$ (GRH)
16.16.83993647724363776000000000000.1	x¹⁶ - 8x¹⁵ - 32x¹⁴ + 320x¹³ + 210x¹² - 3592x¹¹ - 1256x¹⁰ + 17280x⁹ + 9144x⁸ - 34600x⁷ - 25264x⁶ + 22256x⁵ + 15770x⁴ - 7320x³ - 2888x² + 1264x - 89	$ 2^{40}\cdot 5^{12}\cdot 7^{4}\cdot 19^{4} $	$C_2^4.C_2^4$ (as 16T459)	Trivial (GRH)
16.0.263471075369680896000000000000.1	x¹⁶ + 8x¹⁴ + 154x¹² - 560x¹¹ + 2612x¹⁰ - 5160x⁹ + 19376x⁸ - 26560x⁷ + 146320x⁶ - 187680x⁵ + 763220x⁴ - 576800x³ + 1760200x² - 463200x + 2052900	$ 2^{40}\cdot 3^{4}\cdot 5^{12}\cdot 59^{4} $	$C_2^4.C_2^4$ (as 16T459)	$[2, 48]$ (GRH)
16.0.263471075369680896000000000000.2	x¹⁶ + 16x¹⁴ - 40x¹³ + 230x¹² + 40x¹¹ + 3464x¹⁰ + 1040x⁹ + 15534x⁸ + 1280x⁷ + 137584x⁶ + 255520x⁵ + 887830x⁴ + 934120x³ + 1811136x² + 1211320x + 2722361	$ 2^{40}\cdot 3^{4}\cdot 5^{12}\cdot 59^{4} $	$C_2^4.C_2^4$ (as 16T459)	$[2, 48]$ (GRH)
16.8.263471075369680896000000000000.2	x¹⁶ - 366x¹² - 520x¹¹ - 360x¹⁰ - 1120x⁹ + 15526x⁸ - 1760x⁷ - 33120x⁶ + 50200x⁵ - 65286x⁴ + 76280x³ - 81360x² + 56840x - 15239	$ 2^{40}\cdot 3^{4}\cdot 5^{12}\cdot 59^{4} $	$C_2^4.C_2^4$ (as 16T459)	$[2]$ (GRH)
16.8.853646284197766103040000000000.1	x¹⁶ - 12x¹⁴ - 544x¹² - 2440x¹⁰ + 12300x⁸ + 71600x⁶ + 39600x⁴ - 88000x² + 10000	$ 2^{40}\cdot 3^{8}\cdot 5^{10}\cdot 59^{4} $	$C_2^4.C_2^4$ (as 16T459)	$[2]$ (GRH)

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Results (displaying all 26 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
16.0.758989440000000000.1	x¹⁶ - 4x¹⁴ - 8x¹³ + 7x¹² + 24x¹¹ + 15x¹⁰ - 38x⁹ - 40x⁸ + 22x⁷ + 59x⁶ - 24x⁵ - 41x⁴ + 14x³ + 35x² - 30x + 9	\( 2^{16}\cdot 3^{4}\cdot 5^{10}\cdot 11^{4} \)	$C_2^4.C_2^4$ (as 16T459)	Trivial
16.0.6003725062500000000.2	x¹⁶ - 6x¹⁴ + 14x¹² - 2x¹⁰ - 6x⁸ - 14x⁶ + 81x⁴ - 68x² + 16	\( 2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 11^{4} \)	$C_2^4.C_2^4$ (as 16T459)	$[2]$
16.0.717768397440000000000.3	x¹⁶ - 8x¹⁵ + 31x¹⁴ - 72x¹³ + 109x¹² - 118x¹¹ + 100x¹⁰ + 32x⁹ - 497x⁸ + 1140x⁷ - 1042x⁶ - 336x⁵ + 1876x⁴ - 2100x³ + 1200x² - 360x + 45	\( 2^{16}\cdot 3^{4}\cdot 5^{10}\cdot 61^{4} \)	$C_2^4.C_2^4$ (as 16T459)	$[2]$
16.0.5677660175062500000000.2	x¹⁶ - 2x¹⁴ - 30x¹² - 2x¹⁰ + 354x⁸ + 982x⁶ + 1145x⁴ + 432x² + 256	\( 2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 61^{4} \)	$C_2^4.C_2^4$ (as 16T459)	$[4]$
16.0.7407562915840000000000.4	x¹⁶ - 18x¹⁴ + 142x¹² - 624x¹⁰ + 1699x⁸ - 3000x⁶ + 3430x⁴ - 2250x² + 625	\( 2^{28}\cdot 5^{10}\cdot 41^{4} \)	$C_2^4.C_2^4$ (as 16T459)	Trivial (GRH)
16.0.14013832946090262921216.1	x¹⁶ - 8x¹⁵ + 44x¹⁴ - 160x¹³ + 440x¹² - 944x¹¹ + 1672x¹⁰ - 2520x⁹ + 3342x⁸ - 3808x⁷ + 3768x⁶ - 3056x⁵ + 2100x⁴ - 1120x³ + 496x² - 144x + 34	\( 2^{56}\cdot 3^{4}\cdot 7^{4} \)	$C_2^4.C_2^4$ (as 16T459)	$[2]$
16.4.21743271936000000000000.1	x¹⁶ - 16x¹³ - 24x¹² + 40x¹¹ + 76x¹⁰ - 72x⁹ - 324x⁸ - 336x⁷ + 208x⁶ + 1192x⁵ + 1872x⁴ + 1656x³ + 876x² + 256x + 31	\( 2^{40}\cdot 3^{4}\cdot 5^{12} \)	$C_2^4.C_2^4$ (as 16T459)	Trivial (GRH)
16.0.21743271936000000000000.2	x¹⁶ + 8x¹⁴ + 10x¹² + 168x¹⁰ + 1079x⁸ + 1992x⁶ + 1350x⁴ + 432x² + 81	\( 2^{40}\cdot 3^{4}\cdot 5^{12} \)	$C_2^4.C_2^4$ (as 16T459)	$[2]$ (GRH)
16.4.21743271936000000000000.2	x¹⁶ - 8x¹⁴ - 16x¹³ - 4x¹² + 56x¹¹ + 92x¹⁰ - 96x⁹ - 130x⁸ + 128x⁷ - 32x⁶ + 104x⁵ - 452x⁴ + 576x³ - 272x² + 48x - 4	\( 2^{40}\cdot 3^{4}\cdot 5^{12} \)	$C_2^4.C_2^4$ (as 16T459)	Trivial (GRH)
16.8.21743271936000000000000.3	x¹⁶ - 8x¹⁴ + 10x¹² - 168x¹⁰ + 1079x⁸ - 1992x⁶ + 1350x⁴ - 432x² + 81	\( 2^{40}\cdot 3^{4}\cdot 5^{12} \)	$C_2^4.C_2^4$ (as 16T459)	Trivial (GRH)
16.0.70448201072640000000000.1	x¹⁶ + 8x¹⁴ - 38x¹² - 56x¹⁰ + 399x⁸ + 1160x⁶ + 1150x⁴ + 400x² + 25	\( 2^{40}\cdot 3^{8}\cdot 5^{10} \)	$C_2^4.C_2^4$ (as 16T459)	$[2]$ (GRH)
16.8.70448201072640000000000.2	x¹⁶ - 8x¹⁴ - 38x¹² + 56x¹⁰ + 399x⁸ - 1160x⁶ + 1150x⁴ - 400x² + 25	\( 2^{40}\cdot 3^{8}\cdot 5^{10} \)	$C_2^4.C_2^4$ (as 16T459)	Trivial (GRH)
16.8.2963025166336000000000000.7	x¹⁶ - 12x¹⁴ - 16x¹³ + 2x¹² + 184x¹¹ + 336x¹⁰ - 548x⁹ - 915x⁸ + 912x⁷ + 908x⁶ - 1108x⁵ - 648x⁴ + 584x³ + 188x² - 228x - 89	\( 2^{32}\cdot 5^{12}\cdot 41^{4} \)	$C_2^4.C_2^4$ (as 16T459)	Trivial (GRH)
16.8.4540481874533245186473984.1	x¹⁶ - 8x¹⁴ - 92x¹² + 440x¹⁰ - 186x⁸ - 440x⁶ - 92x⁴ + 8x² + 1	\( 2^{58}\cdot 3^{8}\cdot 7^{4} \)	$C_2^4.C_2^4$ (as 16T459)	Trivial (GRH)
16.0.318343244414976000000000000.1	x¹⁶ - 12x¹⁴ + 90x¹² - 80x¹¹ - 172x¹⁰ + 820x⁹ + 799x⁸ - 1440x⁷ + 3532x⁶ + 5380x⁵ - 2120x⁴ + 2920x³ + 17932x² - 12180x + 11521	\( 2^{40}\cdot 3^{4}\cdot 5^{12}\cdot 11^{4} \)	$C_2^4.C_2^4$ (as 16T459)	$[2, 8]$ (GRH)
16.8.342134593410406809600000000.1	x¹⁶ - 8x¹⁴ - 180x¹² - 200x¹⁰ + 1958x⁸ - 600x⁶ - 1620x⁴ - 216x² + 81	\( 2^{52}\cdot 3^{4}\cdot 5^{8}\cdot 7^{4} \)	$C_2^4.C_2^4$ (as 16T459)	Trivial (GRH)
16.0.709450292895819560386560000.1	x¹⁶ - 8x¹⁵ + 8x¹⁴ + 72x¹³ - 56x¹² - 376x¹¹ - 272x¹⁰ + 1832x⁹ + 1230x⁸ - 752x⁷ - 720x⁶ - 12592x⁵ + 10724x⁴ - 15248x³ + 26480x² - 9504x + 17902	\( 2^{56}\cdot 3^{8}\cdot 5^{4}\cdot 7^{4} \)	$C_2^4.C_2^4$ (as 16T459)	$[4, 4]$ (GRH)
16.8.1031432111904522240000000000.1	x¹⁶ - 4x¹⁵ + 20x¹⁴ - 68x¹³ + 50x¹² - 144x¹¹ - 360x¹⁰ + 1376x⁹ + 951x⁸ - 5456x⁷ - 9072x⁶ + 4104x⁵ + 9364x⁴ + 3052x³ - 84x² - 100x - 5	\( 2^{40}\cdot 3^{8}\cdot 5^{10}\cdot 11^{4} \)	$C_2^4.C_2^4$ (as 16T459)	Trivial (GRH)
16.0.81495870570233856000000000000.2	x¹⁶ + 36x¹⁴ + 470x¹² + 2764x¹⁰ + 7679x⁸ + 9804x⁶ + 5580x⁴ + 1296x² + 81	\( 2^{48}\cdot 3^{4}\cdot 5^{12}\cdot 11^{4} \)	$C_2^4.C_2^4$ (as 16T459)	$[2, 2, 174]$ (GRH)
16.16.81495870570233856000000000000.2	x¹⁶ - 36x¹⁴ + 470x¹² - 2764x¹⁰ + 7679x⁸ - 9804x⁶ + 5580x⁴ - 1296x² + 81	\( 2^{48}\cdot 3^{4}\cdot 5^{12}\cdot 11^{4} \)	$C_2^4.C_2^4$ (as 16T459)	Trivial (GRH)
16.0.83993647724363776000000000000.1	x¹⁶ + 64x¹⁴ + 1450x¹² + 15556x¹⁰ + 84439x⁸ + 223076x⁶ + 251370x⁴ + 78204x² + 2401	\( 2^{40}\cdot 5^{12}\cdot 7^{4}\cdot 19^{4} \)	$C_2^4.C_2^4$ (as 16T459)	$[2, 2, 110]$ (GRH)
16.16.83993647724363776000000000000.1	x¹⁶ - 8x¹⁵ - 32x¹⁴ + 320x¹³ + 210x¹² - 3592x¹¹ - 1256x¹⁰ + 17280x⁹ + 9144x⁸ - 34600x⁷ - 25264x⁶ + 22256x⁵ + 15770x⁴ - 7320x³ - 2888x² + 1264x - 89	\( 2^{40}\cdot 5^{12}\cdot 7^{4}\cdot 19^{4} \)	$C_2^4.C_2^4$ (as 16T459)	Trivial (GRH)
16.0.263471075369680896000000000000.1	x¹⁶ + 8x¹⁴ + 154x¹² - 560x¹¹ + 2612x¹⁰ - 5160x⁹ + 19376x⁸ - 26560x⁷ + 146320x⁶ - 187680x⁵ + 763220x⁴ - 576800x³ + 1760200x² - 463200x + 2052900	\( 2^{40}\cdot 3^{4}\cdot 5^{12}\cdot 59^{4} \)	$C_2^4.C_2^4$ (as 16T459)	$[2, 48]$ (GRH)
16.0.263471075369680896000000000000.2	x¹⁶ + 16x¹⁴ - 40x¹³ + 230x¹² + 40x¹¹ + 3464x¹⁰ + 1040x⁹ + 15534x⁸ + 1280x⁷ + 137584x⁶ + 255520x⁵ + 887830x⁴ + 934120x³ + 1811136x² + 1211320x + 2722361	\( 2^{40}\cdot 3^{4}\cdot 5^{12}\cdot 59^{4} \)	$C_2^4.C_2^4$ (as 16T459)	$[2, 48]$ (GRH)
16.8.263471075369680896000000000000.2	x¹⁶ - 366x¹² - 520x¹¹ - 360x¹⁰ - 1120x⁹ + 15526x⁸ - 1760x⁷ - 33120x⁶ + 50200x⁵ - 65286x⁴ + 76280x³ - 81360x² + 56840x - 15239	\( 2^{40}\cdot 3^{4}\cdot 5^{12}\cdot 59^{4} \)	$C_2^4.C_2^4$ (as 16T459)	$[2]$ (GRH)
16.8.853646284197766103040000000000.1	x¹⁶ - 12x¹⁴ - 544x¹² - 2440x¹⁰ + 12300x⁸ + 71600x⁶ + 39600x⁴ - 88000x² + 10000	\( 2^{40}\cdot 3^{8}\cdot 5^{10}\cdot 59^{4} \)	$C_2^4.C_2^4$ (as 16T459)	$[2]$ (GRH)