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Results (displaying all 26 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.8861338240000000000.2	x¹⁶ - 6x¹⁵ + 13x¹⁴ - 2x¹³ - 41x¹² + 68x¹¹ - 126x⁹ + 143x⁸ + 10x⁷ - 134x⁶ + 46x⁵ + 144x⁴ - 210x³ + 130x² - 40x + 5	$ 2^{16}\cdot 5^{10}\cdot 61^{4} $	$C_2^4.C_2^3$ (as 16T217)	Trivial
16.4.118192468620711297024.3	x¹⁶ - 4x¹⁴ + 4x¹⁰ - 10x⁸ + 4x⁶ - 4x² + 1	$ 2^{54}\cdot 3^{8} $	$C_2^4.C_2^3$ (as 16T217)	Trivial (GRH)
16.8.118192468620711297024.3	x¹⁶ - 4x¹⁴ - 4x¹⁰ + 54x⁸ - 76x⁶ + 32x⁴ - 12x² + 1	$ 2^{54}\cdot 3^{8} $	$C_2^4.C_2^3$ (as 16T217)	Trivial (GRH)
16.4.118192468620711297024.4	x¹⁶ + 4x¹⁴ - 4x¹⁰ - 10x⁸ - 4x⁶ + 4x² + 1	$ 2^{54}\cdot 3^{8} $	$C_2^4.C_2^3$ (as 16T217)	Trivial (GRH)
16.0.118192468620711297024.17	x¹⁶ + 4x¹⁴ + 4x¹⁰ + 54x⁸ + 76x⁶ + 32x⁴ + 12x² + 1	$ 2^{54}\cdot 3^{8} $	$C_2^4.C_2^3$ (as 16T217)	$[2]$
16.0.221533456000000000000.2	x¹⁶ - 2x¹⁵ + 2x¹⁴ - 24x¹³ + 8x¹² + 34x¹¹ + 134x¹⁰ + 98x⁹ - 67x⁸ - 214x⁷ - 124x⁶ + 102x⁵ + 173x⁴ + 92x³ + 23x² + 4x + 1	$ 2^{16}\cdot 5^{12}\cdot 61^{4} $	$C_2^4.C_2^3$ (as 16T217)	$[2]$
16.0.1512914374440000000000.1	x¹⁶ - x¹⁵ + 7x¹⁴ + 10x¹³ + 29x¹² + 38x¹¹ + 28x¹⁰ + 28x⁹ - 56x⁸ + 55x⁷ - 49x⁶ - 60x⁵ + 285x⁴ - 460x³ + 370x² - 150x + 25	$ 2^{12}\cdot 3^{8}\cdot 5^{10}\cdot 7^{8} $	$C_2^4.C_2^3$ (as 16T217)	$[2]$
16.8.1512914374440000000000.1	x¹⁶ - 3x¹⁴ - 9x¹² + 27x¹⁰ - 16x⁸ + 27x⁶ - 9x⁴ - 3x² + 1	$ 2^{12}\cdot 3^{8}\cdot 5^{10}\cdot 7^{8} $	$C_2^4.C_2^3$ (as 16T217)	Trivial (GRH)
16.8.11574317056000000000000.2	x¹⁶ - 2x¹⁵ - 9x¹⁴ + 2x¹³ + 49x¹² + 102x¹¹ - 138x¹⁰ - 624x⁹ - 79x⁸ + 1750x⁷ + 1132x⁶ - 2464x⁵ - 1806x⁴ + 1320x³ + 780x² - 64x + 1	$ 2^{24}\cdot 5^{12}\cdot 41^{4} $	$C_2^4.C_2^3$ (as 16T217)	Trivial (GRH)
16.0.11574317056000000000000.4	x¹⁶ - 4x¹⁵ + 4x¹⁴ - 4x¹³ + 24x¹² - 36x¹¹ + 18x¹⁰ - 82x⁹ + 111x⁸ + 140x⁷ + 628x⁶ + 798x⁵ + 1479x⁴ + 1370x³ + 1285x² + 798x + 751	$ 2^{24}\cdot 5^{12}\cdot 41^{4} $	$C_2^4.C_2^3$ (as 16T217)	$[4]$
16.8.140857138691308837890625.1	x¹⁶ - 5x¹⁴ - 58x¹² + 195x¹⁰ + 494x⁸ - 585x⁶ - 1207x⁴ - 220x² + 16	$ 5^{12}\cdot 13^{8}\cdot 29^{4} $	$C_2^4.C_2^3$ (as 16T217)	Trivial (GRH)
16.8.140857138691308837890625.2	x¹⁶ - 4x¹⁵ - 10x¹³ - 18x¹² + 232x¹¹ - 50x¹⁰ - 30x⁹ - 571x⁸ - 374x⁷ + 148x⁶ + 366x⁵ + 453x⁴ + 16x³ - 113x² - 66x - 9	$ 5^{12}\cdot 13^{8}\cdot 29^{4} $	$C_2^4.C_2^3$ (as 16T217)	Trivial (GRH)
16.8.760294709821440000000000.1	x¹⁶ - 6x¹⁵ + 9x¹⁴ - 10x¹³ + 10x¹² + 216x¹¹ - 331x¹⁰ - 756x⁹ + 525x⁸ + 700x⁷ + 439x⁶ + 1236x⁵ - 424x⁴ - 1910x³ - 715x² + 50x + 25	$ 2^{24}\cdot 3^{8}\cdot 5^{10}\cdot 29^{4} $	$C_2^4.C_2^3$ (as 16T217)	Trivial (GRH)
16.8.760294709821440000000000.2	x¹⁶ - 4x¹⁵ + 20x¹³ - 68x¹² + 92x¹¹ + 40x¹⁰ - 300x⁹ + 866x⁸ - 1188x⁷ - 196x⁶ + 2528x⁵ - 3045x⁴ + 1416x³ - 640x² + 808x - 311	$ 2^{24}\cdot 3^{8}\cdot 5^{10}\cdot 29^{4} $	$C_2^4.C_2^3$ (as 16T217)	Trivial (GRH)
16.0.2963025166336000000000000.1	x¹⁶ - 8x¹⁵ + 28x¹⁴ - 52x¹³ + 88x¹² - 288x¹¹ + 1034x¹⁰ - 2596x⁹ + 5193x⁸ - 8408x⁷ + 12686x⁶ - 16660x⁵ + 22768x⁴ - 22416x³ + 25462x² - 14312x + 10721	$ 2^{32}\cdot 5^{12}\cdot 41^{4} $	$C_2^4.C_2^3$ (as 16T217)	$[2, 2, 4]$ (GRH)
16.0.2963025166336000000000000.2	x¹⁶ + 2x¹⁴ - 8x¹³ + 27x¹² + 8x¹¹ + 224x¹⁰ + 36x⁹ + 660x⁸ - 416x⁷ + 1252x⁶ - 904x⁵ + 2842x⁴ + 488x³ + 4042x² + 1476x + 1791	$ 2^{32}\cdot 5^{12}\cdot 41^{4} $	$C_2^4.C_2^3$ (as 16T217)	$[2, 4]$ (GRH)
16.8.2963025166336000000000000.2	x¹⁶ - 10x¹⁴ - 24x¹³ - 33x¹² + 136x¹⁰ + 604x⁹ + 1104x⁸ - 24x⁷ - 1744x⁶ - 828x⁵ + 704x⁴ + 288x³ - 126x² - 8x + 1	$ 2^{32}\cdot 5^{12}\cdot 41^{4} $	$C_2^4.C_2^3$ (as 16T217)	$[2]$ (GRH)
16.0.2963025166336000000000000.3	x¹⁶ - 10x¹⁴ - 16x¹³ + 27x¹² + 80x¹¹ + 176x¹⁰ + 316x⁹ + 684x⁸ + 984x⁷ + 1756x⁶ + 1988x⁵ + 2584x⁴ + 2272x³ + 2254x² + 1128x + 801	$ 2^{32}\cdot 5^{12}\cdot 41^{4} $	$C_2^4.C_2^3$ (as 16T217)	$[2, 4]$ (GRH)
16.0.20723941878730254150390625.2	x¹⁶ - 3x¹⁵ + 14x¹⁴ - 37x¹³ + 104x¹² - 213x¹¹ + 706x¹⁰ - 909x⁹ + 2674x⁸ - 3351x⁷ + 6741x⁶ - 7810x⁵ + 11552x⁴ - 10664x³ + 6320x² - 1920x + 256	$ 5^{12}\cdot 13^{8}\cdot 101^{4} $	$C_2^4.C_2^3$ (as 16T217)	$[4, 8]$ (GRH)
16.0.20723941878730254150390625.3	x¹⁶ - 4x¹⁵ - 8x¹⁴ + 38x¹³ + 72x¹² - 204x¹¹ - 468x¹⁰ + 194x⁹ + 2370x⁸ + 1166x⁷ - 3236x⁶ - 4242x⁵ + 1467x⁴ + 10922x³ + 19072x² + 24330x + 20341	$ 5^{12}\cdot 13^{8}\cdot 101^{4} $	$C_2^4.C_2^3$ (as 16T217)	$[2, 8]$ (GRH)
16.16.27789935251456000000000000.2	x¹⁶ - 2x¹⁵ - 31x¹⁴ + 60x¹³ + 358x¹² - 710x¹¹ - 1934x¹⁰ + 4102x⁹ + 4883x⁸ - 11758x⁷ - 4774x⁶ + 15250x⁵ + 1088x⁴ - 7680x³ - 601x² + 1438x + 311	$ 2^{24}\cdot 5^{12}\cdot 7^{4}\cdot 41^{4} $	$C_2^4.C_2^3$ (as 16T217)	Trivial (GRH)
16.16.65790008098816000000000000.1	x¹⁶ - 34x¹⁴ + 379x¹² - 1768x¹⁰ + 3669x⁸ - 3036x⁶ + 591x⁴ - 42x² + 1	$ 2^{32}\cdot 5^{12}\cdot 89^{4} $	$C_2^4.C_2^3$ (as 16T217)	Trivial (GRH)
16.0.65790008098816000000000000.2	x¹⁶ - 4x¹⁵ + 22x¹⁴ - 92x¹³ + 213x¹² - 532x¹¹ + 912x¹⁰ - 356x⁹ - 1015x⁸ - 5232x⁷ + 16098x⁶ + 69508x⁵ + 245011x⁴ + 294708x³ + 304498x² + 317500x + 657121	$ 2^{32}\cdot 5^{12}\cdot 89^{4} $	$C_2^4.C_2^3$ (as 16T217)	$[2, 52]$ (GRH)
16.0.65790008098816000000000000.3	x¹⁶ + 34x¹⁴ + 439x¹² + 2808x¹⁰ + 9469x⁸ + 16216x⁶ + 12271x⁴ + 3402x² + 81	$ 2^{32}\cdot 5^{12}\cdot 89^{4} $	$C_2^4.C_2^3$ (as 16T217)	$[2, 8]$ (GRH)
16.0.65790008098816000000000000.4	x¹⁶ - 8x¹⁵ + 58x¹⁴ - 244x¹³ + 1015x¹² - 3068x¹¹ + 9712x¹⁰ - 22856x⁹ + 55650x⁸ - 95716x⁷ + 182566x⁶ - 220324x⁵ + 312484x⁴ - 112808x³ + 52714x² + 12464x + 1681	$ 2^{32}\cdot 5^{12}\cdot 89^{4} $	$C_2^4.C_2^3$ (as 16T217)	$[2, 6, 6]$ (GRH)
16.0.65790008098816000000000000.5	x¹⁶ + 34x¹⁴ + 379x¹² + 1768x¹⁰ + 3669x⁸ + 3036x⁶ + 591x⁴ + 42x² + 1	$ 2^{32}\cdot 5^{12}\cdot 89^{4} $	$C_2^4.C_2^3$ (as 16T217)	$[2, 8]$ (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
16.0.8861338240000000000.2	x¹⁶ - 6x¹⁵ + 13x¹⁴ - 2x¹³ - 41x¹² + 68x¹¹ - 126x⁹ + 143x⁸ + 10x⁷ - 134x⁶ + 46x⁵ + 144x⁴ - 210x³ + 130x² - 40x + 5	\( 2^{16}\cdot 5^{10}\cdot 61^{4} \)	$C_2^4.C_2^3$ (as 16T217)	Trivial
16.4.118192468620711297024.3	x¹⁶ - 4x¹⁴ + 4x¹⁰ - 10x⁸ + 4x⁶ - 4x² + 1	\( 2^{54}\cdot 3^{8} \)	$C_2^4.C_2^3$ (as 16T217)	Trivial (GRH)
16.8.118192468620711297024.3	x¹⁶ - 4x¹⁴ - 4x¹⁰ + 54x⁸ - 76x⁶ + 32x⁴ - 12x² + 1	\( 2^{54}\cdot 3^{8} \)	$C_2^4.C_2^3$ (as 16T217)	Trivial (GRH)
16.4.118192468620711297024.4	x¹⁶ + 4x¹⁴ - 4x¹⁰ - 10x⁸ - 4x⁶ + 4x² + 1	\( 2^{54}\cdot 3^{8} \)	$C_2^4.C_2^3$ (as 16T217)	Trivial (GRH)
16.0.118192468620711297024.17	x¹⁶ + 4x¹⁴ + 4x¹⁰ + 54x⁸ + 76x⁶ + 32x⁴ + 12x² + 1	\( 2^{54}\cdot 3^{8} \)	$C_2^4.C_2^3$ (as 16T217)	$[2]$
16.0.221533456000000000000.2	x¹⁶ - 2x¹⁵ + 2x¹⁴ - 24x¹³ + 8x¹² + 34x¹¹ + 134x¹⁰ + 98x⁹ - 67x⁸ - 214x⁷ - 124x⁶ + 102x⁵ + 173x⁴ + 92x³ + 23x² + 4x + 1	\( 2^{16}\cdot 5^{12}\cdot 61^{4} \)	$C_2^4.C_2^3$ (as 16T217)	$[2]$
16.0.1512914374440000000000.1	x¹⁶ - x¹⁵ + 7x¹⁴ + 10x¹³ + 29x¹² + 38x¹¹ + 28x¹⁰ + 28x⁹ - 56x⁸ + 55x⁷ - 49x⁶ - 60x⁵ + 285x⁴ - 460x³ + 370x² - 150x + 25	\( 2^{12}\cdot 3^{8}\cdot 5^{10}\cdot 7^{8} \)	$C_2^4.C_2^3$ (as 16T217)	$[2]$
16.8.1512914374440000000000.1	x¹⁶ - 3x¹⁴ - 9x¹² + 27x¹⁰ - 16x⁸ + 27x⁶ - 9x⁴ - 3x² + 1	\( 2^{12}\cdot 3^{8}\cdot 5^{10}\cdot 7^{8} \)	$C_2^4.C_2^3$ (as 16T217)	Trivial (GRH)
16.8.11574317056000000000000.2	x¹⁶ - 2x¹⁵ - 9x¹⁴ + 2x¹³ + 49x¹² + 102x¹¹ - 138x¹⁰ - 624x⁹ - 79x⁸ + 1750x⁷ + 1132x⁶ - 2464x⁵ - 1806x⁴ + 1320x³ + 780x² - 64x + 1	\( 2^{24}\cdot 5^{12}\cdot 41^{4} \)	$C_2^4.C_2^3$ (as 16T217)	Trivial (GRH)
16.0.11574317056000000000000.4	x¹⁶ - 4x¹⁵ + 4x¹⁴ - 4x¹³ + 24x¹² - 36x¹¹ + 18x¹⁰ - 82x⁹ + 111x⁸ + 140x⁷ + 628x⁶ + 798x⁵ + 1479x⁴ + 1370x³ + 1285x² + 798x + 751	\( 2^{24}\cdot 5^{12}\cdot 41^{4} \)	$C_2^4.C_2^3$ (as 16T217)	$[4]$
16.8.140857138691308837890625.1	x¹⁶ - 5x¹⁴ - 58x¹² + 195x¹⁰ + 494x⁸ - 585x⁶ - 1207x⁴ - 220x² + 16	\( 5^{12}\cdot 13^{8}\cdot 29^{4} \)	$C_2^4.C_2^3$ (as 16T217)	Trivial (GRH)
16.8.140857138691308837890625.2	x¹⁶ - 4x¹⁵ - 10x¹³ - 18x¹² + 232x¹¹ - 50x¹⁰ - 30x⁹ - 571x⁸ - 374x⁷ + 148x⁶ + 366x⁵ + 453x⁴ + 16x³ - 113x² - 66x - 9	\( 5^{12}\cdot 13^{8}\cdot 29^{4} \)	$C_2^4.C_2^3$ (as 16T217)	Trivial (GRH)
16.8.760294709821440000000000.1	x¹⁶ - 6x¹⁵ + 9x¹⁴ - 10x¹³ + 10x¹² + 216x¹¹ - 331x¹⁰ - 756x⁹ + 525x⁸ + 700x⁷ + 439x⁶ + 1236x⁵ - 424x⁴ - 1910x³ - 715x² + 50x + 25	\( 2^{24}\cdot 3^{8}\cdot 5^{10}\cdot 29^{4} \)	$C_2^4.C_2^3$ (as 16T217)	Trivial (GRH)
16.8.760294709821440000000000.2	x¹⁶ - 4x¹⁵ + 20x¹³ - 68x¹² + 92x¹¹ + 40x¹⁰ - 300x⁹ + 866x⁸ - 1188x⁷ - 196x⁶ + 2528x⁵ - 3045x⁴ + 1416x³ - 640x² + 808x - 311	\( 2^{24}\cdot 3^{8}\cdot 5^{10}\cdot 29^{4} \)	$C_2^4.C_2^3$ (as 16T217)	Trivial (GRH)
16.0.2963025166336000000000000.1	x¹⁶ - 8x¹⁵ + 28x¹⁴ - 52x¹³ + 88x¹² - 288x¹¹ + 1034x¹⁰ - 2596x⁹ + 5193x⁸ - 8408x⁷ + 12686x⁶ - 16660x⁵ + 22768x⁴ - 22416x³ + 25462x² - 14312x + 10721	\( 2^{32}\cdot 5^{12}\cdot 41^{4} \)	$C_2^4.C_2^3$ (as 16T217)	$[2, 2, 4]$ (GRH)
16.0.2963025166336000000000000.2	x¹⁶ + 2x¹⁴ - 8x¹³ + 27x¹² + 8x¹¹ + 224x¹⁰ + 36x⁹ + 660x⁸ - 416x⁷ + 1252x⁶ - 904x⁵ + 2842x⁴ + 488x³ + 4042x² + 1476x + 1791	\( 2^{32}\cdot 5^{12}\cdot 41^{4} \)	$C_2^4.C_2^3$ (as 16T217)	$[2, 4]$ (GRH)
16.8.2963025166336000000000000.2	x¹⁶ - 10x¹⁴ - 24x¹³ - 33x¹² + 136x¹⁰ + 604x⁹ + 1104x⁸ - 24x⁷ - 1744x⁶ - 828x⁵ + 704x⁴ + 288x³ - 126x² - 8x + 1	\( 2^{32}\cdot 5^{12}\cdot 41^{4} \)	$C_2^4.C_2^3$ (as 16T217)	$[2]$ (GRH)
16.0.2963025166336000000000000.3	x¹⁶ - 10x¹⁴ - 16x¹³ + 27x¹² + 80x¹¹ + 176x¹⁰ + 316x⁹ + 684x⁸ + 984x⁷ + 1756x⁶ + 1988x⁵ + 2584x⁴ + 2272x³ + 2254x² + 1128x + 801	\( 2^{32}\cdot 5^{12}\cdot 41^{4} \)	$C_2^4.C_2^3$ (as 16T217)	$[2, 4]$ (GRH)
16.0.20723941878730254150390625.2	x¹⁶ - 3x¹⁵ + 14x¹⁴ - 37x¹³ + 104x¹² - 213x¹¹ + 706x¹⁰ - 909x⁹ + 2674x⁸ - 3351x⁷ + 6741x⁶ - 7810x⁵ + 11552x⁴ - 10664x³ + 6320x² - 1920x + 256	\( 5^{12}\cdot 13^{8}\cdot 101^{4} \)	$C_2^4.C_2^3$ (as 16T217)	$[4, 8]$ (GRH)
16.0.20723941878730254150390625.3	x¹⁶ - 4x¹⁵ - 8x¹⁴ + 38x¹³ + 72x¹² - 204x¹¹ - 468x¹⁰ + 194x⁹ + 2370x⁸ + 1166x⁷ - 3236x⁶ - 4242x⁵ + 1467x⁴ + 10922x³ + 19072x² + 24330x + 20341	\( 5^{12}\cdot 13^{8}\cdot 101^{4} \)	$C_2^4.C_2^3$ (as 16T217)	$[2, 8]$ (GRH)
16.16.27789935251456000000000000.2	x¹⁶ - 2x¹⁵ - 31x¹⁴ + 60x¹³ + 358x¹² - 710x¹¹ - 1934x¹⁰ + 4102x⁹ + 4883x⁸ - 11758x⁷ - 4774x⁶ + 15250x⁵ + 1088x⁴ - 7680x³ - 601x² + 1438x + 311	\( 2^{24}\cdot 5^{12}\cdot 7^{4}\cdot 41^{4} \)	$C_2^4.C_2^3$ (as 16T217)	Trivial (GRH)
16.16.65790008098816000000000000.1	x¹⁶ - 34x¹⁴ + 379x¹² - 1768x¹⁰ + 3669x⁸ - 3036x⁶ + 591x⁴ - 42x² + 1	\( 2^{32}\cdot 5^{12}\cdot 89^{4} \)	$C_2^4.C_2^3$ (as 16T217)	Trivial (GRH)
16.0.65790008098816000000000000.2	x¹⁶ - 4x¹⁵ + 22x¹⁴ - 92x¹³ + 213x¹² - 532x¹¹ + 912x¹⁰ - 356x⁹ - 1015x⁸ - 5232x⁷ + 16098x⁶ + 69508x⁵ + 245011x⁴ + 294708x³ + 304498x² + 317500x + 657121	\( 2^{32}\cdot 5^{12}\cdot 89^{4} \)	$C_2^4.C_2^3$ (as 16T217)	$[2, 52]$ (GRH)
16.0.65790008098816000000000000.3	x¹⁶ + 34x¹⁴ + 439x¹² + 2808x¹⁰ + 9469x⁸ + 16216x⁶ + 12271x⁴ + 3402x² + 81	\( 2^{32}\cdot 5^{12}\cdot 89^{4} \)	$C_2^4.C_2^3$ (as 16T217)	$[2, 8]$ (GRH)
16.0.65790008098816000000000000.4	x¹⁶ - 8x¹⁵ + 58x¹⁴ - 244x¹³ + 1015x¹² - 3068x¹¹ + 9712x¹⁰ - 22856x⁹ + 55650x⁸ - 95716x⁷ + 182566x⁶ - 220324x⁵ + 312484x⁴ - 112808x³ + 52714x² + 12464x + 1681	\( 2^{32}\cdot 5^{12}\cdot 89^{4} \)	$C_2^4.C_2^3$ (as 16T217)	$[2, 6, 6]$ (GRH)
16.0.65790008098816000000000000.5	x¹⁶ + 34x¹⁴ + 379x¹² + 1768x¹⁰ + 3669x⁸ + 3036x⁶ + 591x⁴ + 42x² + 1	\( 2^{32}\cdot 5^{12}\cdot 89^{4} \)	$C_2^4.C_2^3$ (as 16T217)	$[2, 8]$ (GRH)