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Results (displaying all 20 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.3212471548762914816.1	x¹⁶ - 7x¹⁴ + 23x¹² - 49x¹⁰ + 79x⁸ - 98x⁶ + 92x⁴ - 56x² + 16	$ 2^{20}\cdot 3^{12}\cdot 7^{8} $	$C_2^4.C_2^3$ (as 16T329)	Trivial
16.0.34789235097600000000.6	x¹⁶ - 10x¹⁴ + 46x¹² - 130x¹⁰ + 262x⁸ - 390x⁶ + 414x⁴ - 270x² + 81	$ 2^{40}\cdot 3^{4}\cdot 5^{8} $	$C_2^4.C_2^3$ (as 16T329)	Trivial (GRH)
16.0.128353931059122929664.1	x¹⁶ - 4x¹⁴ + 16x¹² - 100x¹⁰ + 385x⁸ - 864x⁶ + 1170x⁴ - 864x² + 324	$ 2^{38}\cdot 3^{4}\cdot 7^{8} $	$C_2^4.C_2^3$ (as 16T329)	Trivial
16.0.194301296640000000000.1	x¹⁶ - 2x¹⁵ + 2x¹⁴ - 4x¹³ + 5x¹² + 36x¹¹ + 54x¹⁰ - 216x⁹ - 93x⁸ + 500x⁷ + 776x⁶ - 470x⁵ - 1299x⁴ - 672x³ + 610x² + 772x + 349	$ 2^{24}\cdot 3^{4}\cdot 5^{10}\cdot 11^{4} $	$C_2^4.C_2^3$ (as 16T329)	Trivial (GRH)
16.8.231260683111582301945856.1	x¹⁶ - 15x¹⁴ - 16x¹³ + 83x¹² + 150x¹¹ - 231x¹⁰ - 480x⁹ + 456x⁸ + 812x⁷ - 657x⁶ - 888x⁵ + 915x⁴ + 406x³ - 921x² + 472x - 83	$ 2^{24}\cdot 3^{12}\cdot 11^{10} $	$C_2^4.C_2^3$ (as 16T329)	Trivial (GRH)
16.0.231260683111582301945856.2	x¹⁶ - 2x¹⁵ - 4x¹⁴ + 20x¹³ - 49x¹² + 38x¹¹ + 225x¹⁰ - 426x⁹ + 1078x⁸ - 624x⁷ + 555x⁶ - 130x⁵ - 160x⁴ - 616x³ - 550x² + 484x + 484	$ 2^{24}\cdot 3^{12}\cdot 11^{10} $	$C_2^4.C_2^3$ (as 16T329)	$[4]$ (GRH)
16.0.287742083309962730143744.6	x¹⁶ - 2x¹⁵ + 5x¹⁴ - 20x¹³ + 40x¹² - 48x¹¹ + 274x¹⁰ + 44x⁹ + 703x⁸ + 142x⁷ + 591x⁶ - 120x⁵ + 412x⁴ - 20x³ + 706x² - 56x + 196	$ 2^{34}\cdot 7^{4}\cdot 17^{8} $	$C_2^4.C_2^3$ (as 16T329)	$[2]$ (GRH)
16.8.547527072574775633117184.1	x¹⁶ - 4x¹⁵ - 4x¹⁴ + 44x¹³ - 74x¹² - 44x¹¹ + 332x¹⁰ - 404x⁹ - 164x⁸ + 756x⁷ - 144x⁶ - 612x⁵ - 198x⁴ + 756x³ - 324x + 81	$ 2^{46}\cdot 3^{12}\cdot 11^{4} $	$C_2^4.C_2^3$ (as 16T329)	Trivial (GRH)
16.8.732410773216200100000000.1	x¹⁶ - x¹⁴ - 88x¹² + 15x¹⁰ + 1721x⁸ + 165x⁶ - 10648x⁴ - 1331x² + 14641	$ 2^{8}\cdot 5^{8}\cdot 11^{4}\cdot 29^{8} $	$C_2^4.C_2^3$ (as 16T329)	Trivial (GRH)
16.8.8470319941522177744961536.1	x¹⁶ - 8x¹⁵ + 16x¹⁴ - 12x¹³ + 86x¹² - 28x¹¹ - 952x¹⁰ + 2264x⁹ - 2803x⁸ + 3860x⁷ - 4812x⁶ + 3992x⁵ - 3060x⁴ + 2068x³ - 864x² + 428x - 167	$ 2^{44}\cdot 7^{8}\cdot 17^{4} $	$C_2^4.C_2^3$ (as 16T329)	Trivial (GRH)
16.8.8570160209533064970240000.3	x¹⁶ - 2x¹⁵ - 8x¹⁴ + 12x¹³ + 26x¹² + 64x¹¹ - 240x¹⁰ - 296x⁹ + 1136x⁸ - 872x⁷ - 816x⁶ + 3088x⁵ - 2680x⁴ - 96x³ + 832x² - 224x + 16	$ 2^{24}\cdot 3^{10}\cdot 5^{4}\cdot 7^{12} $	$C_2^4.C_2^3$ (as 16T329)	Trivial (GRH)
16.8.11769324018218625600000000.1	x¹⁶ - 5x¹⁴ - 52x¹² + 55x¹⁰ + 484x⁸ - 145x⁶ - 733x⁴ - 100x² + 16	$ 2^{12}\cdot 3^{12}\cdot 5^{8}\cdot 7^{12} $	$C_2^4.C_2^3$ (as 16T329)	$[2]$ (GRH)
16.0.35103376218247434118103040000.1	x¹⁶ + 52x¹⁴ + 890x¹² + 7088x¹⁰ + 30091x⁸ + 70800x⁶ + 88650x⁴ + 49500x² + 5625	$ 2^{36}\cdot 3^{10}\cdot 5^{4}\cdot 7^{12} $	$C_2^4.C_2^3$ (as 16T329)	$[2, 2, 2, 96]$ (GRH)
16.16.35103376218247434118103040000.1	x¹⁶ - 52x¹⁴ + 890x¹² - 7088x¹⁰ + 30091x⁸ - 70800x⁶ + 88650x⁴ - 49500x² + 5625	$ 2^{36}\cdot 3^{10}\cdot 5^{4}\cdot 7^{12} $	$C_2^4.C_2^3$ (as 16T329)	Trivial (GRH)
16.0.35103376218247434118103040000.2	x¹⁶ - 12x¹⁴ + 22x¹² - 408x¹⁰ + 5971x⁸ + 10320x⁶ + 116250x⁴ - 148500x² + 50625	$ 2^{36}\cdot 3^{10}\cdot 5^{4}\cdot 7^{12} $	$C_2^4.C_2^3$ (as 16T329)	$[2, 4, 4]$ (GRH)
16.0.35103376218247434118103040000.3	x¹⁶ + 12x¹⁴ + 22x¹² + 408x¹⁰ + 5971x⁸ - 10320x⁶ + 116250x⁴ + 148500x² + 50625	$ 2^{36}\cdot 3^{10}\cdot 5^{4}\cdot 7^{12} $	$C_2^4.C_2^3$ (as 16T329)	$[2, 4, 4]$ (GRH)
16.16.56543072165403532840000000000.1	x¹⁶ - 90x¹⁴ - 52x¹³ + 3017x¹² + 2658x¹¹ - 49046x¹⁰ - 49347x⁹ + 421718x⁸ + 421830x⁷ - 1949561x⁶ - 1743798x⁵ + 4584026x⁴ + 3252475x³ - 4442610x² - 1991175x + 483025	$ 2^{12}\cdot 5^{10}\cdot 29^{8}\cdot 41^{4} $	$C_2^4.C_2^3$ (as 16T329)	Trivial (GRH)
16.8.74998863177338890240000000000.1	x¹⁶ + 9x¹⁴ - 843x¹² - 14469x¹⁰ - 2679x⁸ + 853160x⁶ + 1398760x⁴ - 11446600x² + 5856400	$ 2^{20}\cdot 5^{10}\cdot 11^{4}\cdot 29^{8} $	$C_2^4.C_2^3$ (as 16T329)	$[2]$ (GRH)
16.8.74998863177338890240000000000.2	x¹⁶ + 6x¹⁴ - 938x¹² + 2544x¹⁰ + 199521x⁸ - 1425270x⁶ - 934120x⁴ + 11180400x² + 5856400	$ 2^{20}\cdot 5^{10}\cdot 11^{4}\cdot 29^{8} $	$C_2^4.C_2^3$ (as 16T329)	$[2]$ (GRH)
16.0.379681744835278131840000000000.1	x¹⁶ + 101x¹⁴ + 3757x¹² + 70889x¹⁰ + 762106x⁸ + 4851165x⁶ + 18017505x⁴ + 35937000x² + 29648025	$ 2^{16}\cdot 3^{4}\cdot 5^{10}\cdot 11^{4}\cdot 29^{8} $	$C_2^4.C_2^3$ (as 16T329)	$[2, 2, 2, 2, 1640]$ (GRH)

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Results (displaying all 20 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
16.0.3212471548762914816.1	x¹⁶ - 7x¹⁴ + 23x¹² - 49x¹⁰ + 79x⁸ - 98x⁶ + 92x⁴ - 56x² + 16	\( 2^{20}\cdot 3^{12}\cdot 7^{8} \)	$C_2^4.C_2^3$ (as 16T329)	Trivial
16.0.34789235097600000000.6	x¹⁶ - 10x¹⁴ + 46x¹² - 130x¹⁰ + 262x⁸ - 390x⁶ + 414x⁴ - 270x² + 81	\( 2^{40}\cdot 3^{4}\cdot 5^{8} \)	$C_2^4.C_2^3$ (as 16T329)	Trivial (GRH)
16.0.128353931059122929664.1	x¹⁶ - 4x¹⁴ + 16x¹² - 100x¹⁰ + 385x⁸ - 864x⁶ + 1170x⁴ - 864x² + 324	\( 2^{38}\cdot 3^{4}\cdot 7^{8} \)	$C_2^4.C_2^3$ (as 16T329)	Trivial
16.0.194301296640000000000.1	x¹⁶ - 2x¹⁵ + 2x¹⁴ - 4x¹³ + 5x¹² + 36x¹¹ + 54x¹⁰ - 216x⁹ - 93x⁸ + 500x⁷ + 776x⁶ - 470x⁵ - 1299x⁴ - 672x³ + 610x² + 772x + 349	\( 2^{24}\cdot 3^{4}\cdot 5^{10}\cdot 11^{4} \)	$C_2^4.C_2^3$ (as 16T329)	Trivial (GRH)
16.8.231260683111582301945856.1	x¹⁶ - 15x¹⁴ - 16x¹³ + 83x¹² + 150x¹¹ - 231x¹⁰ - 480x⁹ + 456x⁸ + 812x⁷ - 657x⁶ - 888x⁵ + 915x⁴ + 406x³ - 921x² + 472x - 83	\( 2^{24}\cdot 3^{12}\cdot 11^{10} \)	$C_2^4.C_2^3$ (as 16T329)	Trivial (GRH)
16.0.231260683111582301945856.2	x¹⁶ - 2x¹⁵ - 4x¹⁴ + 20x¹³ - 49x¹² + 38x¹¹ + 225x¹⁰ - 426x⁹ + 1078x⁸ - 624x⁷ + 555x⁶ - 130x⁵ - 160x⁴ - 616x³ - 550x² + 484x + 484	\( 2^{24}\cdot 3^{12}\cdot 11^{10} \)	$C_2^4.C_2^3$ (as 16T329)	$[4]$ (GRH)
16.0.287742083309962730143744.6	x¹⁶ - 2x¹⁵ + 5x¹⁴ - 20x¹³ + 40x¹² - 48x¹¹ + 274x¹⁰ + 44x⁹ + 703x⁸ + 142x⁷ + 591x⁶ - 120x⁵ + 412x⁴ - 20x³ + 706x² - 56x + 196	\( 2^{34}\cdot 7^{4}\cdot 17^{8} \)	$C_2^4.C_2^3$ (as 16T329)	$[2]$ (GRH)
16.8.547527072574775633117184.1	x¹⁶ - 4x¹⁵ - 4x¹⁴ + 44x¹³ - 74x¹² - 44x¹¹ + 332x¹⁰ - 404x⁹ - 164x⁸ + 756x⁷ - 144x⁶ - 612x⁵ - 198x⁴ + 756x³ - 324x + 81	\( 2^{46}\cdot 3^{12}\cdot 11^{4} \)	$C_2^4.C_2^3$ (as 16T329)	Trivial (GRH)
16.8.732410773216200100000000.1	x¹⁶ - x¹⁴ - 88x¹² + 15x¹⁰ + 1721x⁸ + 165x⁶ - 10648x⁴ - 1331x² + 14641	\( 2^{8}\cdot 5^{8}\cdot 11^{4}\cdot 29^{8} \)	$C_2^4.C_2^3$ (as 16T329)	Trivial (GRH)
16.8.8470319941522177744961536.1	x¹⁶ - 8x¹⁵ + 16x¹⁴ - 12x¹³ + 86x¹² - 28x¹¹ - 952x¹⁰ + 2264x⁹ - 2803x⁸ + 3860x⁷ - 4812x⁶ + 3992x⁵ - 3060x⁴ + 2068x³ - 864x² + 428x - 167	\( 2^{44}\cdot 7^{8}\cdot 17^{4} \)	$C_2^4.C_2^3$ (as 16T329)	Trivial (GRH)
16.8.8570160209533064970240000.3	x¹⁶ - 2x¹⁵ - 8x¹⁴ + 12x¹³ + 26x¹² + 64x¹¹ - 240x¹⁰ - 296x⁹ + 1136x⁸ - 872x⁷ - 816x⁶ + 3088x⁵ - 2680x⁴ - 96x³ + 832x² - 224x + 16	\( 2^{24}\cdot 3^{10}\cdot 5^{4}\cdot 7^{12} \)	$C_2^4.C_2^3$ (as 16T329)	Trivial (GRH)
16.8.11769324018218625600000000.1	x¹⁶ - 5x¹⁴ - 52x¹² + 55x¹⁰ + 484x⁸ - 145x⁶ - 733x⁴ - 100x² + 16	\( 2^{12}\cdot 3^{12}\cdot 5^{8}\cdot 7^{12} \)	$C_2^4.C_2^3$ (as 16T329)	$[2]$ (GRH)
16.0.35103376218247434118103040000.1	x¹⁶ + 52x¹⁴ + 890x¹² + 7088x¹⁰ + 30091x⁸ + 70800x⁶ + 88650x⁴ + 49500x² + 5625	\( 2^{36}\cdot 3^{10}\cdot 5^{4}\cdot 7^{12} \)	$C_2^4.C_2^3$ (as 16T329)	$[2, 2, 2, 96]$ (GRH)
16.16.35103376218247434118103040000.1	x¹⁶ - 52x¹⁴ + 890x¹² - 7088x¹⁰ + 30091x⁸ - 70800x⁶ + 88650x⁴ - 49500x² + 5625	\( 2^{36}\cdot 3^{10}\cdot 5^{4}\cdot 7^{12} \)	$C_2^4.C_2^3$ (as 16T329)	Trivial (GRH)
16.0.35103376218247434118103040000.2	x¹⁶ - 12x¹⁴ + 22x¹² - 408x¹⁰ + 5971x⁸ + 10320x⁶ + 116250x⁴ - 148500x² + 50625	\( 2^{36}\cdot 3^{10}\cdot 5^{4}\cdot 7^{12} \)	$C_2^4.C_2^3$ (as 16T329)	$[2, 4, 4]$ (GRH)
16.0.35103376218247434118103040000.3	x¹⁶ + 12x¹⁴ + 22x¹² + 408x¹⁰ + 5971x⁸ - 10320x⁶ + 116250x⁴ + 148500x² + 50625	\( 2^{36}\cdot 3^{10}\cdot 5^{4}\cdot 7^{12} \)	$C_2^4.C_2^3$ (as 16T329)	$[2, 4, 4]$ (GRH)
16.16.56543072165403532840000000000.1	x¹⁶ - 90x¹⁴ - 52x¹³ + 3017x¹² + 2658x¹¹ - 49046x¹⁰ - 49347x⁹ + 421718x⁸ + 421830x⁷ - 1949561x⁶ - 1743798x⁵ + 4584026x⁴ + 3252475x³ - 4442610x² - 1991175x + 483025	\( 2^{12}\cdot 5^{10}\cdot 29^{8}\cdot 41^{4} \)	$C_2^4.C_2^3$ (as 16T329)	Trivial (GRH)
16.8.74998863177338890240000000000.1	x¹⁶ + 9x¹⁴ - 843x¹² - 14469x¹⁰ - 2679x⁸ + 853160x⁶ + 1398760x⁴ - 11446600x² + 5856400	\( 2^{20}\cdot 5^{10}\cdot 11^{4}\cdot 29^{8} \)	$C_2^4.C_2^3$ (as 16T329)	$[2]$ (GRH)
16.8.74998863177338890240000000000.2	x¹⁶ + 6x¹⁴ - 938x¹² + 2544x¹⁰ + 199521x⁸ - 1425270x⁶ - 934120x⁴ + 11180400x² + 5856400	\( 2^{20}\cdot 5^{10}\cdot 11^{4}\cdot 29^{8} \)	$C_2^4.C_2^3$ (as 16T329)	$[2]$ (GRH)
16.0.379681744835278131840000000000.1	x¹⁶ + 101x¹⁴ + 3757x¹² + 70889x¹⁰ + 762106x⁸ + 4851165x⁶ + 18017505x⁴ + 35937000x² + 29648025	\( 2^{16}\cdot 3^{4}\cdot 5^{10}\cdot 11^{4}\cdot 29^{8} \)	$C_2^4.C_2^3$ (as 16T329)	$[2, 2, 2, 2, 1640]$ (GRH)