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Results (displaying all 22 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.1367766797119140625.1	x¹⁶ - 6x¹⁵ + 13x¹⁴ - 5x¹³ - 20x¹² + 7x¹¹ + 85x¹⁰ - 161x⁹ + 91x⁸ + 60x⁷ - 95x⁶ - 9x⁵ + 98x⁴ - 91x³ + 42x² - 10x + 1	$ 5^{12}\cdot 29^{4}\cdot 89^{2} $	$C_2^2.C_2^5.C_2$ (as 16T610)	Trivial
16.0.12882379072509765625.1	x¹⁶ - 4x¹⁵ + 2x¹⁴ + 2x¹³ + 27x¹² - 65x¹¹ + 53x¹⁰ - 76x⁹ + 195x⁸ - 289x⁷ + 288x⁶ - 225x⁵ + 137x⁴ - 62x³ + 22x² - 6x + 1	$ 5^{12}\cdot 29^{2}\cdot 89^{4} $	$C_2^2.C_2^5.C_2$ (as 16T610)	Trivial
16.0.88284816000000000000.1	x¹⁶ - 8x¹⁵ + 34x¹⁴ - 96x¹³ + 196x¹² - 314x¹¹ + 410x¹⁰ - 420x⁹ + 317x⁸ - 160x⁷ + 15x⁶ + 72x⁵ - 54x⁴ - 8x³ + 11x² + 4x + 1	$ 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 29^{2} $	$C_2^2.C_2^5.C_2$ (as 16T610)	$[2]$
16.0.88284816000000000000.2	x¹⁶ + 11x¹⁴ - 16x¹³ + 49x¹² - 112x¹¹ + 173x¹⁰ - 304x⁹ + 437x⁸ - 498x⁷ + 534x⁶ - 482x⁵ + 313x⁴ - 140x³ + 42x² - 8x + 1	$ 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 29^{2} $	$C_2^2.C_2^5.C_2$ (as 16T610)	$[2]$
16.8.88284816000000000000.2	x¹⁶ - 4x¹⁵ - 5x¹⁴ + 52x¹³ - 88x¹² - 24x¹¹ + 265x¹⁰ - 386x⁹ + 271x⁸ - 86x⁷ - 4x⁶ + 8x⁵ - 14x⁴ + 24x³ - 6x² - 4x + 1	$ 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 29^{2} $	$C_2^2.C_2^5.C_2$ (as 16T610)	Trivial (GRH)
16.8.88284816000000000000.3	x¹⁶ - 6x¹⁴ - 2x¹³ - 2x¹² + 34x¹¹ + 34x¹⁰ - 114x⁹ - 41x⁸ + 164x⁷ + 3x⁶ - 110x⁵ + 22x⁴ + 32x³ - 11x² - 4x + 1	$ 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 29^{2} $	$C_2^2.C_2^5.C_2$ (as 16T610)	Trivial (GRH)
16.12.290029415062500000000.1	x¹⁶ - 28x¹² + 119x⁸ - 150x⁶ + 73x⁴ - 15x² + 1	$ 2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 29^{4} $	$C_2^2.C_2^5.C_2$ (as 16T610)	Trivial (GRH)
16.4.290029415062500000000.1	x¹⁶ + 11x¹⁴ + 39x¹² + 42x¹⁰ - 21x⁸ - 46x⁶ - 4x⁴ + 8x² + 1	$ 2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 29^{4} $	$C_2^2.C_2^5.C_2$ (as 16T610)	Trivial
16.12.290029415062500000000.2	x¹⁶ - 13x¹⁴ + 56x¹² - 64x¹⁰ - 141x⁸ + 348x⁶ - 156x⁴ - x² + 1	$ 2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 29^{4} $	$C_2^2.C_2^5.C_2$ (as 16T610)	Trivial (GRH)
16.4.290029415062500000000.2	x¹⁶ - 32x¹² - 90x¹⁰ - 61x⁸ + 30x⁶ + 47x⁴ + 15x² + 1	$ 2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 29^{4} $	$C_2^2.C_2^5.C_2$ (as 16T610)	Trivial
16.4.486301730062500000000.1	x¹⁶ - 4x¹⁵ + 2x¹⁴ + 3x¹³ + 6x¹² + 4x¹¹ - 38x¹⁰ - 16x⁹ + 7x⁸ + 120x⁷ + 288x⁶ + 152x⁵ - 3x⁴ + 39x³ + 79x² + 20x + 1	$ 2^{8}\cdot 3^{12}\cdot 5^{12}\cdot 11^{4} $	$C_2^2.C_2^5.C_2$ (as 16T610)	Trivial
16.4.486301730062500000000.2	x¹⁶ - 5x¹⁵ + 17x¹⁴ - 51x¹³ + 99x¹² - 139x¹¹ + 139x¹⁰ - 17x⁹ - 143x⁸ + 252x⁷ - 246x⁶ + 82x⁵ + 51x⁴ - 45x³ - 5x² + 10x - 5	$ 2^{8}\cdot 3^{12}\cdot 5^{12}\cdot 11^{4} $	$C_2^2.C_2^5.C_2$ (as 16T610)	Trivial (GRH)
16.0.475575744400000000000000.1	x¹⁶ - 4x¹⁵ + 15x¹⁴ - 20x¹³ + 75x¹² - 82x¹¹ + 373x¹⁰ - 240x⁹ + 1425x⁸ - 910x⁷ + 2563x⁶ - 2792x⁵ + 1320x⁴ - 2830x³ - 10x² + 296x + 1181	$ 2^{16}\cdot 5^{14}\cdot 29^{4}\cdot 41^{2} $	$C_2^2.C_2^5.C_2$ (as 16T610)	$[2, 2, 2]$ (GRH)
16.16.475575744400000000000000.1	x¹⁶ - 6x¹⁵ - 9x¹⁴ + 116x¹³ - 97x¹² - 686x¹¹ + 1184x¹⁰ + 1368x⁹ - 3757x⁸ - 466x⁷ + 4646x⁶ - 892x⁵ - 2117x⁴ + 388x³ + 289x² - 42x + 1	$ 2^{16}\cdot 5^{14}\cdot 29^{4}\cdot 41^{2} $	$C_2^2.C_2^5.C_2$ (as 16T610)	Trivial (GRH)
16.0.950586000400000000000000.1	x¹⁶ - 3x¹⁴ - 10x¹³ + 8x¹² + 70x¹¹ - 16x¹⁰ - 60x⁹ - 195x⁸ + 300x⁷ + 349x⁶ - 1710x⁵ + 3053x⁴ - 1980x³ + 3267x² - 13310x + 14641	$ 2^{16}\cdot 5^{14}\cdot 29^{2}\cdot 41^{4} $	$C_2^2.C_2^5.C_2$ (as 16T610)	$[2, 2, 2]$ (GRH)
16.16.950586000400000000000000.1	x¹⁶ - 6x¹⁵ - 13x¹⁴ + 122x¹³ + 5x¹² - 882x¹¹ + 562x¹⁰ + 2656x⁹ - 2729x⁸ - 2830x⁷ + 4235x⁶ + 110x⁵ - 1855x⁴ + 550x³ + 140x² - 70x + 5	$ 2^{16}\cdot 5^{14}\cdot 29^{2}\cdot 41^{4} $	$C_2^2.C_2^5.C_2$ (as 16T610)	Trivial (GRH)
16.8.15998368041616000000000000.3	x¹⁶ - 2x¹⁵ + 13x¹⁴ - 52x¹³ + 168x¹² - 138x¹¹ - 793x¹⁰ + 938x⁹ + 944x⁸ + 2280x⁷ - 9790x⁶ - 8234x⁵ + 40322x⁴ + 8210x³ - 54815x² - 8112x + 18901	$ 2^{16}\cdot 5^{12}\cdot 29^{6}\cdot 41^{2} $	$C_2^2.C_2^5.C_2$ (as 16T610)	Trivial (GRH)
16.8.15998368041616000000000000.4	x¹⁶ - 5x¹⁴ - 52x¹³ - 59x¹² + 390x¹¹ + 684x¹⁰ + 906x⁹ - 3069x⁸ - 16768x⁷ + 17647x⁶ + 50334x⁵ - 81533x⁴ - 15322x³ + 117324x² - 94538x + 24421	$ 2^{16}\cdot 5^{12}\cdot 29^{6}\cdot 41^{2} $	$C_2^2.C_2^5.C_2$ (as 16T610)	Trivial (GRH)
16.8.22947318992896000000000000.1	x¹⁶ - 4x¹⁵ + 10x¹⁴ + 10x¹³ - 253x¹² + 1052x¹¹ - 2410x¹⁰ + 2720x⁹ + 3734x⁸ - 21514x⁷ + 32948x⁶ - 7154x⁵ - 35572x⁴ + 34066x³ + 2012x² - 12706x + 3121	$ 2^{24}\cdot 5^{12}\cdot 29^{4}\cdot 89^{2} $	$C_2^2.C_2^5.C_2$ (as 16T610)	Trivial (GRH)
16.8.22947318992896000000000000.2	x¹⁶ - 4x¹⁵ - 10x¹⁴ + 10x¹³ + 7x¹² + 132x¹¹ + 970x¹⁰ + 2080x⁹ - 406x⁸ - 6234x⁷ - 3232x⁶ + 6666x⁵ + 3328x⁴ - 5214x³ - 1728x² + 2494x + 1061	$ 2^{24}\cdot 5^{12}\cdot 29^{4}\cdot 89^{2} $	$C_2^2.C_2^5.C_2$ (as 16T610)	Trivial (GRH)
16.0.26893256677956496000000000000.4	x¹⁶ - 4x¹⁵ + 30x¹⁴ - 94x¹³ + 424x¹² - 672x¹¹ - 44x¹⁰ + 1872x⁹ + 23261x⁸ + 65654x⁷ + 98909x⁶ + 20494x⁵ + 60204x⁴ - 18628x³ + 23185x² - 4592x + 1681	$ 2^{16}\cdot 5^{12}\cdot 29^{6}\cdot 41^{4} $	$C_2^2.C_2^5.C_2$ (as 16T610)	$[2, 4, 8]$ (GRH)
16.0.26893256677956496000000000000.5	x¹⁶ - 4x¹⁵ + 42x¹⁴ - 136x¹³ + 876x¹² - 1800x¹¹ + 9133x¹⁰ - 12190x⁹ + 44647x⁸ - 2460x⁷ + 83373x⁶ + 33150x⁵ + 13276x⁴ - 1926x³ + 462x² - 24x + 1	$ 2^{16}\cdot 5^{12}\cdot 29^{6}\cdot 41^{4} $	$C_2^2.C_2^5.C_2$ (as 16T610)	$[2, 4, 8]$ (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
16.0.1367766797119140625.1	x¹⁶ - 6x¹⁵ + 13x¹⁴ - 5x¹³ - 20x¹² + 7x¹¹ + 85x¹⁰ - 161x⁹ + 91x⁸ + 60x⁷ - 95x⁶ - 9x⁵ + 98x⁴ - 91x³ + 42x² - 10x + 1	\( 5^{12}\cdot 29^{4}\cdot 89^{2} \)	$C_2^2.C_2^5.C_2$ (as 16T610)	Trivial
16.0.12882379072509765625.1	x¹⁶ - 4x¹⁵ + 2x¹⁴ + 2x¹³ + 27x¹² - 65x¹¹ + 53x¹⁰ - 76x⁹ + 195x⁸ - 289x⁷ + 288x⁶ - 225x⁵ + 137x⁴ - 62x³ + 22x² - 6x + 1	\( 5^{12}\cdot 29^{2}\cdot 89^{4} \)	$C_2^2.C_2^5.C_2$ (as 16T610)	Trivial
16.0.88284816000000000000.1	x¹⁶ - 8x¹⁵ + 34x¹⁴ - 96x¹³ + 196x¹² - 314x¹¹ + 410x¹⁰ - 420x⁹ + 317x⁸ - 160x⁷ + 15x⁶ + 72x⁵ - 54x⁴ - 8x³ + 11x² + 4x + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 29^{2} \)	$C_2^2.C_2^5.C_2$ (as 16T610)	$[2]$
16.0.88284816000000000000.2	x¹⁶ + 11x¹⁴ - 16x¹³ + 49x¹² - 112x¹¹ + 173x¹⁰ - 304x⁹ + 437x⁸ - 498x⁷ + 534x⁶ - 482x⁵ + 313x⁴ - 140x³ + 42x² - 8x + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 29^{2} \)	$C_2^2.C_2^5.C_2$ (as 16T610)	$[2]$
16.8.88284816000000000000.2	x¹⁶ - 4x¹⁵ - 5x¹⁴ + 52x¹³ - 88x¹² - 24x¹¹ + 265x¹⁰ - 386x⁹ + 271x⁸ - 86x⁷ - 4x⁶ + 8x⁵ - 14x⁴ + 24x³ - 6x² - 4x + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 29^{2} \)	$C_2^2.C_2^5.C_2$ (as 16T610)	Trivial (GRH)
16.8.88284816000000000000.3	x¹⁶ - 6x¹⁴ - 2x¹³ - 2x¹² + 34x¹¹ + 34x¹⁰ - 114x⁹ - 41x⁸ + 164x⁷ + 3x⁶ - 110x⁵ + 22x⁴ + 32x³ - 11x² - 4x + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 29^{2} \)	$C_2^2.C_2^5.C_2$ (as 16T610)	Trivial (GRH)
16.12.290029415062500000000.1	x¹⁶ - 28x¹² + 119x⁸ - 150x⁶ + 73x⁴ - 15x² + 1	\( 2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 29^{4} \)	$C_2^2.C_2^5.C_2$ (as 16T610)	Trivial (GRH)
16.4.290029415062500000000.1	x¹⁶ + 11x¹⁴ + 39x¹² + 42x¹⁰ - 21x⁸ - 46x⁶ - 4x⁴ + 8x² + 1	\( 2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 29^{4} \)	$C_2^2.C_2^5.C_2$ (as 16T610)	Trivial
16.12.290029415062500000000.2	x¹⁶ - 13x¹⁴ + 56x¹² - 64x¹⁰ - 141x⁸ + 348x⁶ - 156x⁴ - x² + 1	\( 2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 29^{4} \)	$C_2^2.C_2^5.C_2$ (as 16T610)	Trivial (GRH)
16.4.290029415062500000000.2	x¹⁶ - 32x¹² - 90x¹⁰ - 61x⁸ + 30x⁶ + 47x⁴ + 15x² + 1	\( 2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 29^{4} \)	$C_2^2.C_2^5.C_2$ (as 16T610)	Trivial
16.4.486301730062500000000.1	x¹⁶ - 4x¹⁵ + 2x¹⁴ + 3x¹³ + 6x¹² + 4x¹¹ - 38x¹⁰ - 16x⁹ + 7x⁸ + 120x⁷ + 288x⁶ + 152x⁵ - 3x⁴ + 39x³ + 79x² + 20x + 1	\( 2^{8}\cdot 3^{12}\cdot 5^{12}\cdot 11^{4} \)	$C_2^2.C_2^5.C_2$ (as 16T610)	Trivial
16.4.486301730062500000000.2	x¹⁶ - 5x¹⁵ + 17x¹⁴ - 51x¹³ + 99x¹² - 139x¹¹ + 139x¹⁰ - 17x⁹ - 143x⁸ + 252x⁷ - 246x⁶ + 82x⁵ + 51x⁴ - 45x³ - 5x² + 10x - 5	\( 2^{8}\cdot 3^{12}\cdot 5^{12}\cdot 11^{4} \)	$C_2^2.C_2^5.C_2$ (as 16T610)	Trivial (GRH)
16.0.475575744400000000000000.1	x¹⁶ - 4x¹⁵ + 15x¹⁴ - 20x¹³ + 75x¹² - 82x¹¹ + 373x¹⁰ - 240x⁹ + 1425x⁸ - 910x⁷ + 2563x⁶ - 2792x⁵ + 1320x⁴ - 2830x³ - 10x² + 296x + 1181	\( 2^{16}\cdot 5^{14}\cdot 29^{4}\cdot 41^{2} \)	$C_2^2.C_2^5.C_2$ (as 16T610)	$[2, 2, 2]$ (GRH)
16.16.475575744400000000000000.1	x¹⁶ - 6x¹⁵ - 9x¹⁴ + 116x¹³ - 97x¹² - 686x¹¹ + 1184x¹⁰ + 1368x⁹ - 3757x⁸ - 466x⁷ + 4646x⁶ - 892x⁵ - 2117x⁴ + 388x³ + 289x² - 42x + 1	\( 2^{16}\cdot 5^{14}\cdot 29^{4}\cdot 41^{2} \)	$C_2^2.C_2^5.C_2$ (as 16T610)	Trivial (GRH)
16.0.950586000400000000000000.1	x¹⁶ - 3x¹⁴ - 10x¹³ + 8x¹² + 70x¹¹ - 16x¹⁰ - 60x⁹ - 195x⁸ + 300x⁷ + 349x⁶ - 1710x⁵ + 3053x⁴ - 1980x³ + 3267x² - 13310x + 14641	\( 2^{16}\cdot 5^{14}\cdot 29^{2}\cdot 41^{4} \)	$C_2^2.C_2^5.C_2$ (as 16T610)	$[2, 2, 2]$ (GRH)
16.16.950586000400000000000000.1	x¹⁶ - 6x¹⁵ - 13x¹⁴ + 122x¹³ + 5x¹² - 882x¹¹ + 562x¹⁰ + 2656x⁹ - 2729x⁸ - 2830x⁷ + 4235x⁶ + 110x⁵ - 1855x⁴ + 550x³ + 140x² - 70x + 5	\( 2^{16}\cdot 5^{14}\cdot 29^{2}\cdot 41^{4} \)	$C_2^2.C_2^5.C_2$ (as 16T610)	Trivial (GRH)
16.8.15998368041616000000000000.3	x¹⁶ - 2x¹⁵ + 13x¹⁴ - 52x¹³ + 168x¹² - 138x¹¹ - 793x¹⁰ + 938x⁹ + 944x⁸ + 2280x⁷ - 9790x⁶ - 8234x⁵ + 40322x⁴ + 8210x³ - 54815x² - 8112x + 18901	\( 2^{16}\cdot 5^{12}\cdot 29^{6}\cdot 41^{2} \)	$C_2^2.C_2^5.C_2$ (as 16T610)	Trivial (GRH)
16.8.15998368041616000000000000.4	x¹⁶ - 5x¹⁴ - 52x¹³ - 59x¹² + 390x¹¹ + 684x¹⁰ + 906x⁹ - 3069x⁸ - 16768x⁷ + 17647x⁶ + 50334x⁵ - 81533x⁴ - 15322x³ + 117324x² - 94538x + 24421	\( 2^{16}\cdot 5^{12}\cdot 29^{6}\cdot 41^{2} \)	$C_2^2.C_2^5.C_2$ (as 16T610)	Trivial (GRH)
16.8.22947318992896000000000000.1	x¹⁶ - 4x¹⁵ + 10x¹⁴ + 10x¹³ - 253x¹² + 1052x¹¹ - 2410x¹⁰ + 2720x⁹ + 3734x⁸ - 21514x⁷ + 32948x⁶ - 7154x⁵ - 35572x⁴ + 34066x³ + 2012x² - 12706x + 3121	\( 2^{24}\cdot 5^{12}\cdot 29^{4}\cdot 89^{2} \)	$C_2^2.C_2^5.C_2$ (as 16T610)	Trivial (GRH)
16.8.22947318992896000000000000.2	x¹⁶ - 4x¹⁵ - 10x¹⁴ + 10x¹³ + 7x¹² + 132x¹¹ + 970x¹⁰ + 2080x⁹ - 406x⁸ - 6234x⁷ - 3232x⁶ + 6666x⁵ + 3328x⁴ - 5214x³ - 1728x² + 2494x + 1061	\( 2^{24}\cdot 5^{12}\cdot 29^{4}\cdot 89^{2} \)	$C_2^2.C_2^5.C_2$ (as 16T610)	Trivial (GRH)
16.0.26893256677956496000000000000.4	x¹⁶ - 4x¹⁵ + 30x¹⁴ - 94x¹³ + 424x¹² - 672x¹¹ - 44x¹⁰ + 1872x⁹ + 23261x⁸ + 65654x⁷ + 98909x⁶ + 20494x⁵ + 60204x⁴ - 18628x³ + 23185x² - 4592x + 1681	\( 2^{16}\cdot 5^{12}\cdot 29^{6}\cdot 41^{4} \)	$C_2^2.C_2^5.C_2$ (as 16T610)	$[2, 4, 8]$ (GRH)
16.0.26893256677956496000000000000.5	x¹⁶ - 4x¹⁵ + 42x¹⁴ - 136x¹³ + 876x¹² - 1800x¹¹ + 9133x¹⁰ - 12190x⁹ + 44647x⁸ - 2460x⁷ + 83373x⁶ + 33150x⁵ + 13276x⁴ - 1926x³ + 462x² - 24x + 1	\( 2^{16}\cdot 5^{12}\cdot 29^{6}\cdot 41^{4} \)	$C_2^2.C_2^5.C_2$ (as 16T610)	$[2, 4, 8]$ (GRH)