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Results (displaying all 20 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.43337501504009177923584.1	x¹⁶ + 4x¹⁴ + 28x¹² + 35x¹⁰ + 14x⁸ + 28x⁶ + 56x⁴ + 39x² + 9	$ 2^{32}\cdot 3^{6}\cdot 7^{12} $	16T1127	Trivial
16.0.43337501504009177923584.2	x¹⁶ - 4x¹⁴ + 28x¹² - 35x¹⁰ + 14x⁸ - 28x⁶ + 56x⁴ - 39x² + 9	$ 2^{32}\cdot 3^{6}\cdot 7^{12} $	16T1127	Trivial
16.0.328957086593322477158400.1	x¹⁶ - x¹² - 30x⁸ + 86x⁴ + 25	$ 2^{32}\cdot 3^{12}\cdot 5^{2}\cdot 7^{8} $	16T1127	$[4]$
16.4.328957086593322477158400.1	x¹⁶ - 6x¹⁴ + x¹² - 78x¹⁰ + 69x⁸ - 72x⁶ + 211x⁴ + 1080x² + 625	$ 2^{32}\cdot 3^{12}\cdot 5^{2}\cdot 7^{8} $	16T1127	Trivial (GRH)
16.0.328957086593322477158400.2	x¹⁶ - 12x¹⁴ + 83x¹² - 312x¹⁰ + 765x⁸ - 1038x⁶ + 677x⁴ + 270x² + 25	$ 2^{32}\cdot 3^{12}\cdot 5^{2}\cdot 7^{8} $	16T1127	$[2]$
16.4.328957086593322477158400.2	x¹⁶ - 12x¹⁴ + 55x¹² - 120x¹⁰ + 57x⁸ + 306x⁶ - 851x⁴ + 990x² + 625	$ 2^{32}\cdot 3^{12}\cdot 5^{2}\cdot 7^{8} $	16T1127	Trivial (GRH)
16.4.489278800632769167753216.1	x¹⁶ - 10x¹² - 15x⁸ + 68x⁴ + 4	$ 2^{32}\cdot 3^{12}\cdot 11^{8} $	16T1127	Trivial
16.4.489278800632769167753216.2	x¹⁶ - 7x¹² - 3x⁸ + 8x⁴ + 4	$ 2^{32}\cdot 3^{12}\cdot 11^{8} $	16T1127	Trivial
16.4.412397103845080712794341376.1	x¹⁶ + 16x¹⁴ - 44x¹³ - 184x¹² - 704x¹¹ - 4408x¹⁰ - 5608x⁹ - 18369x⁸ - 43392x⁷ + 2516x⁶ + 66088x⁵ + 174378x⁴ + 232896x³ + 377232x² + 134388x + 265561	$ 2^{40}\cdot 41^{6}\cdot 281^{2} $	16T1127	$[2]$ (GRH)
16.4.412397103845080712794341376.2	x¹⁶ - 32x¹⁴ - 52x¹³ + 288x¹² + 1048x¹¹ - 552x¹⁰ - 8720x⁹ - 12086x⁸ + 31472x⁷ + 107288x⁶ + 16560x⁵ - 388460x⁴ - 381712x³ + 556960x² + 1676384x + 332612	$ 2^{40}\cdot 41^{6}\cdot 281^{2} $	16T1127	$[2]$ (GRH)
16.8.8517153582795178291400802304000000.1	x¹⁶ - 2x¹⁵ - 85x¹⁴ + 582x¹³ - 7876x¹² + 12454x¹¹ + 65721x¹⁰ - 124402x⁹ + 1310177x⁸ - 1272146x⁷ + 2227616x⁶ - 23486622x⁵ + 43234682x⁴ - 101529080x³ + 168658082x² - 24597176x - 62213719	$ 2^{24}\cdot 5^{6}\cdot 409^{2}\cdot 761^{6} $	16T1127	$[2, 2]$ (GRH)
16.8.8517153582795178291400802304000000.2	x¹⁶ - 4x¹⁵ - 18x¹⁴ + 400x¹³ - 1843x¹² + 1206x¹¹ + 13958x¹⁰ - 205180x⁹ + 755165x⁸ - 1516280x⁷ - 13742081x⁶ + 61595184x⁵ + 162479515x⁴ - 291554556x³ - 960643601x² - 369718978x + 315886199	$ 2^{24}\cdot 5^{6}\cdot 409^{2}\cdot 761^{6} $	16T1127	$[2, 2]$ (GRH)
16.0.8926609275800253364594278400000000.1	x¹⁶ + 244x¹⁴ + 20637x¹² + 815784x¹⁰ + 16689063x⁸ + 188396254x⁶ + 1187687160x⁴ + 3924173404x² + 5300131204	$ 2^{38}\cdot 5^{8}\cdot 89^{6}\cdot 409^{2} $	16T1127	$[2, 2, 2, 136716]$ (GRH)
16.16.8926609275800253364594278400000000.1	x¹⁶ - 244x¹⁴ + 20637x¹² - 815784x¹⁰ + 16689063x⁸ - 188396254x⁶ + 1187687160x⁴ - 3924173404x² + 5300131204	$ 2^{38}\cdot 5^{8}\cdot 89^{6}\cdot 409^{2} $	16T1127	Trivial (GRH)
16.0.8926609275800253364594278400000000.2	x¹⁶ + 192x¹⁴ + 15178x¹² + 640620x¹⁰ + 15610103x⁸ + 220323372x⁶ + 1690250170x⁴ + 5883712036x² + 5300131204	$ 2^{38}\cdot 5^{8}\cdot 89^{6}\cdot 409^{2} $	16T1127	$[2, 2, 2, 137196]$ (GRH)
16.16.8926609275800253364594278400000000.2	x¹⁶ - 192x¹⁴ + 15178x¹² - 640620x¹⁰ + 15610103x⁸ - 220323372x⁶ + 1690250170x⁴ - 5883712036x² + 5300131204	$ 2^{38}\cdot 5^{8}\cdot 89^{6}\cdot 409^{2} $	16T1127	Trivial (GRH)
16.12.969363393189495136925157683101696000000.1	x¹⁶ - 680x¹⁴ + 157048x¹² - 13850960x¹⁰ + 284605746x⁸ + 8558318760x⁶ - 123855275832x⁴ - 563817515520x² + 7617130807225	$ 2^{56}\cdot 5^{6}\cdot 41^{6}\cdot 13463^{2} $	16T1127	$[2]$ (GRH)
16.12.969363393189495136925157683101696000000.2	x¹⁶ - 488x¹⁴ + 89720x¹² - 7274880x¹⁰ + 175440370x⁸ + 8802042632x⁶ - 496964895416x⁴ + 4478436792880x² + 7617130807225	$ 2^{56}\cdot 5^{6}\cdot 41^{6}\cdot 13463^{2} $	16T1127	$[2, 2]$ (GRH)
16.8.35717732754345647446813752640158274945024000000.1	x¹⁶ + 6016x¹⁴ + 8466180x¹² - 3440773616x¹⁰ - 7383828560092x⁸ + 2977885992852704x⁶ + 521183847139500304x⁴ - 244559727285312582720x² + 4490644386843206976400	$ 2^{56}\cdot 5^{6}\cdot 17^{2}\cdot 41^{6}\cdot 137^{2}\cdot 35089^{2} $	16T1127	$[2, 2, 2, 2]$ (GRH)
16.8.35717732754345647446813752640158274945024000000.2	x¹⁶ - 256x¹⁴ - 3250812x¹² + 560738536x¹⁰ + 1565106740490x⁸ + 40185108913616x⁶ - 118702711888152884x⁴ - 1229247489897179560x² + 280665274177700436025	$ 2^{56}\cdot 5^{6}\cdot 17^{2}\cdot 41^{6}\cdot 137^{2}\cdot 35089^{2} $	16T1127	$[2, 2, 2, 2]$ (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
16.0.43337501504009177923584.1	x¹⁶ + 4x¹⁴ + 28x¹² + 35x¹⁰ + 14x⁸ + 28x⁶ + 56x⁴ + 39x² + 9	\( 2^{32}\cdot 3^{6}\cdot 7^{12} \)	16T1127	Trivial
16.0.43337501504009177923584.2	x¹⁶ - 4x¹⁴ + 28x¹² - 35x¹⁰ + 14x⁸ - 28x⁶ + 56x⁴ - 39x² + 9	\( 2^{32}\cdot 3^{6}\cdot 7^{12} \)	16T1127	Trivial
16.0.328957086593322477158400.1	x¹⁶ - x¹² - 30x⁸ + 86x⁴ + 25	\( 2^{32}\cdot 3^{12}\cdot 5^{2}\cdot 7^{8} \)	16T1127	$[4]$
16.4.328957086593322477158400.1	x¹⁶ - 6x¹⁴ + x¹² - 78x¹⁰ + 69x⁸ - 72x⁶ + 211x⁴ + 1080x² + 625	\( 2^{32}\cdot 3^{12}\cdot 5^{2}\cdot 7^{8} \)	16T1127	Trivial (GRH)
16.0.328957086593322477158400.2	x¹⁶ - 12x¹⁴ + 83x¹² - 312x¹⁰ + 765x⁸ - 1038x⁶ + 677x⁴ + 270x² + 25	\( 2^{32}\cdot 3^{12}\cdot 5^{2}\cdot 7^{8} \)	16T1127	$[2]$
16.4.328957086593322477158400.2	x¹⁶ - 12x¹⁴ + 55x¹² - 120x¹⁰ + 57x⁸ + 306x⁶ - 851x⁴ + 990x² + 625	\( 2^{32}\cdot 3^{12}\cdot 5^{2}\cdot 7^{8} \)	16T1127	Trivial (GRH)
16.4.489278800632769167753216.1	x¹⁶ - 10x¹² - 15x⁸ + 68x⁴ + 4	\( 2^{32}\cdot 3^{12}\cdot 11^{8} \)	16T1127	Trivial
16.4.489278800632769167753216.2	x¹⁶ - 7x¹² - 3x⁸ + 8x⁴ + 4	\( 2^{32}\cdot 3^{12}\cdot 11^{8} \)	16T1127	Trivial
16.4.412397103845080712794341376.1	x¹⁶ + 16x¹⁴ - 44x¹³ - 184x¹² - 704x¹¹ - 4408x¹⁰ - 5608x⁹ - 18369x⁸ - 43392x⁷ + 2516x⁶ + 66088x⁵ + 174378x⁴ + 232896x³ + 377232x² + 134388x + 265561	\( 2^{40}\cdot 41^{6}\cdot 281^{2} \)	16T1127	$[2]$ (GRH)
16.4.412397103845080712794341376.2	x¹⁶ - 32x¹⁴ - 52x¹³ + 288x¹² + 1048x¹¹ - 552x¹⁰ - 8720x⁹ - 12086x⁸ + 31472x⁷ + 107288x⁶ + 16560x⁵ - 388460x⁴ - 381712x³ + 556960x² + 1676384x + 332612	\( 2^{40}\cdot 41^{6}\cdot 281^{2} \)	16T1127	$[2]$ (GRH)
16.8.8517153582795178291400802304000000.1	x¹⁶ - 2x¹⁵ - 85x¹⁴ + 582x¹³ - 7876x¹² + 12454x¹¹ + 65721x¹⁰ - 124402x⁹ + 1310177x⁸ - 1272146x⁷ + 2227616x⁶ - 23486622x⁵ + 43234682x⁴ - 101529080x³ + 168658082x² - 24597176x - 62213719	\( 2^{24}\cdot 5^{6}\cdot 409^{2}\cdot 761^{6} \)	16T1127	$[2, 2]$ (GRH)
16.8.8517153582795178291400802304000000.2	x¹⁶ - 4x¹⁵ - 18x¹⁴ + 400x¹³ - 1843x¹² + 1206x¹¹ + 13958x¹⁰ - 205180x⁹ + 755165x⁸ - 1516280x⁷ - 13742081x⁶ + 61595184x⁵ + 162479515x⁴ - 291554556x³ - 960643601x² - 369718978x + 315886199	\( 2^{24}\cdot 5^{6}\cdot 409^{2}\cdot 761^{6} \)	16T1127	$[2, 2]$ (GRH)
16.0.8926609275800253364594278400000000.1	x¹⁶ + 244x¹⁴ + 20637x¹² + 815784x¹⁰ + 16689063x⁸ + 188396254x⁶ + 1187687160x⁴ + 3924173404x² + 5300131204	\( 2^{38}\cdot 5^{8}\cdot 89^{6}\cdot 409^{2} \)	16T1127	$[2, 2, 2, 136716]$ (GRH)
16.16.8926609275800253364594278400000000.1	x¹⁶ - 244x¹⁴ + 20637x¹² - 815784x¹⁰ + 16689063x⁸ - 188396254x⁶ + 1187687160x⁴ - 3924173404x² + 5300131204	\( 2^{38}\cdot 5^{8}\cdot 89^{6}\cdot 409^{2} \)	16T1127	Trivial (GRH)
16.0.8926609275800253364594278400000000.2	x¹⁶ + 192x¹⁴ + 15178x¹² + 640620x¹⁰ + 15610103x⁸ + 220323372x⁶ + 1690250170x⁴ + 5883712036x² + 5300131204	\( 2^{38}\cdot 5^{8}\cdot 89^{6}\cdot 409^{2} \)	16T1127	$[2, 2, 2, 137196]$ (GRH)
16.16.8926609275800253364594278400000000.2	x¹⁶ - 192x¹⁴ + 15178x¹² - 640620x¹⁰ + 15610103x⁸ - 220323372x⁶ + 1690250170x⁴ - 5883712036x² + 5300131204	\( 2^{38}\cdot 5^{8}\cdot 89^{6}\cdot 409^{2} \)	16T1127	Trivial (GRH)
16.12.969363393189495136925157683101696000000.1	x¹⁶ - 680x¹⁴ + 157048x¹² - 13850960x¹⁰ + 284605746x⁸ + 8558318760x⁶ - 123855275832x⁴ - 563817515520x² + 7617130807225	\( 2^{56}\cdot 5^{6}\cdot 41^{6}\cdot 13463^{2} \)	16T1127	$[2]$ (GRH)
16.12.969363393189495136925157683101696000000.2	x¹⁶ - 488x¹⁴ + 89720x¹² - 7274880x¹⁰ + 175440370x⁸ + 8802042632x⁶ - 496964895416x⁴ + 4478436792880x² + 7617130807225	\( 2^{56}\cdot 5^{6}\cdot 41^{6}\cdot 13463^{2} \)	16T1127	$[2, 2]$ (GRH)
16.8.35717732754345647446813752640158274945024000000.1	x¹⁶ + 6016x¹⁴ + 8466180x¹² - 3440773616x¹⁰ - 7383828560092x⁸ + 2977885992852704x⁶ + 521183847139500304x⁴ - 244559727285312582720x² + 4490644386843206976400	\( 2^{56}\cdot 5^{6}\cdot 17^{2}\cdot 41^{6}\cdot 137^{2}\cdot 35089^{2} \)	16T1127	$[2, 2, 2, 2]$ (GRH)
16.8.35717732754345647446813752640158274945024000000.2	x¹⁶ - 256x¹⁴ - 3250812x¹² + 560738536x¹⁰ + 1565106740490x⁸ + 40185108913616x⁶ - 118702711888152884x⁴ - 1229247489897179560x² + 280665274177700436025	\( 2^{56}\cdot 5^{6}\cdot 17^{2}\cdot 41^{6}\cdot 137^{2}\cdot 35089^{2} \)	16T1127	$[2, 2, 2, 2]$ (GRH)