Global number field search results

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Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying all 20 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.491850248000000000.1	x^16 + 4x^12 - 3x^10 + 4x^8 - 6x^6 + x^4 - 5x^2 + 5	\( 2^{12}\cdot 5^{9}\cdot 7841^{2} \)	16T1885	Trivial
16.0.491850248000000000.2	x^16 + 3x^14 + x^12 - 4x^10 + 4x^8 + 25x^6 + 34x^4 + 20x^2 + 5	\( 2^{12}\cdot 5^{9}\cdot 7841^{2} \)	16T1885	Trivial
16.4.7484982881408000000000.1	x^16 + 10x^14 + 37x^12 + 58x^10 + 21x^8 - 37x^6 - 29x^4 + 5x^2 + 5	\( 2^{16}\cdot 5^{9}\cdot 79^{2}\cdot 3061^{2} \)	16T1885	Trivial
16.8.7484982881408000000000.1	x^16 - 10x^14 + 37x^12 - 58x^10 + 21x^8 + 37x^6 - 29x^4 - 5x^2 + 5	\( 2^{16}\cdot 5^{9}\cdot 79^{2}\cdot 3061^{2} \)	16T1885	Trivial
16.4.187124572035200000000000.1	x^16 + 2x^14 - 29x^12 - 105x^10 + 55x^8 + 700x^6 + 1075x^4 + 625x^2 + 125	\( 2^{16}\cdot 5^{11}\cdot 79^{2}\cdot 3061^{2} \)	16T1885	Trivial
16.8.187124572035200000000000.1	x^16 - 2x^14 - 29x^12 + 105x^10 + 55x^8 - 700x^6 + 1075x^4 - 625x^2 + 125	\( 2^{16}\cdot 5^{11}\cdot 79^{2}\cdot 3061^{2} \)	16T1885	Trivial (GRH)
16.0.349384945136768000000000.1	x^16 + 19x^14 + 137x^12 + 489x^10 + 937x^8 + 962x^6 + 486x^4 + 95x^2 + 5	\( 2^{16}\cdot 5^{9}\cdot 1652141^{2} \)	16T1885	$[16]$
16.16.349384945136768000000000.1	x^16 - 17x^14 + 108x^12 - 338x^10 + 572x^8 - 531x^6 + 259x^4 - 60x^2 + 5	\( 2^{16}\cdot 5^{9}\cdot 1652141^{2} \)	16T1885	Trivial (GRH)
16.0.349384945136768000000000.2	x^16 + 17x^14 + 108x^12 + 338x^10 + 572x^8 + 531x^6 + 259x^4 + 60x^2 + 5	\( 2^{16}\cdot 5^{9}\cdot 1652141^{2} \)	16T1885	$[16]$
16.16.349384945136768000000000.2	x^16 - 19x^14 + 137x^12 - 489x^10 + 937x^8 - 962x^6 + 486x^4 - 95x^2 + 5	\( 2^{16}\cdot 5^{9}\cdot 1652141^{2} \)	16T1885	Trivial (GRH)
16.12.836752522491008000000000.1	x^16 - 9x^14 + 27x^12 - 20x^10 - 46x^8 + 89x^6 - 41x^4 - 5x^2 + 5	\( 2^{16}\cdot 5^{9}\cdot 71^{2}\cdot 36011^{2} \)	16T1885	Trivial (GRH)
16.4.836752522491008000000000.1	x^16 + 9x^14 + 27x^12 + 20x^10 - 46x^8 - 89x^6 - 41x^4 + 5x^2 + 5	\( 2^{16}\cdot 5^{9}\cdot 71^{2}\cdot 36011^{2} \)	16T1885	Trivial
16.4.5176252865742848000000000.1	x^16 - 2x^15 - 4x^14 - 2x^9 - 6x^8 - 2x^7 - 4x^2 - 2x + 1	\( 2^{20}\cdot 5^{9}\cdot 479^{2}\cdot 3319^{2} \)	16T1885	$[2]$ (GRH)
16.12.20918813062275200000000000.1	x^16 - 6x^14 - 21x^12 + 145x^10 - 85x^8 - 550x^6 + 1025x^4 - 625x^2 + 125	\( 2^{16}\cdot 5^{11}\cdot 71^{2}\cdot 36011^{2} \)	16T1885	Trivial (GRH)
16.4.75856510844928000000000000000.1	x^16 + 10x^14 - 70x^12 - 750x^10 + 2445x^8 + 27000x^6 + 18720x^4 - 63360x^2 + 11520	\( 2^{32}\cdot 3^{14}\cdot 5^{15}\cdot 11^{2} \)	16T1885	Trivial (GRH)
16.4.75856510844928000000000000000.2	x^16 - 10x^14 - 70x^12 + 750x^10 + 2445x^8 - 27000x^6 + 18720x^4 + 63360x^2 + 11520	\( 2^{32}\cdot 3^{14}\cdot 5^{15}\cdot 11^{2} \)	16T1885	Trivial (GRH)
16.0.81450308316908771868672000000000000000.1	x^16 + 40x^14 + 320x^12 + 10800x^8 + 129600x^6 + 5832000	\( 2^{62}\cdot 3^{14}\cdot 5^{15}\cdot 11^{2} \)	16T1885	$[2, 8]$ (GRH)
16.8.81450308316908771868672000000000000000.1	x^16 - 40x^14 + 320x^12 + 10800x^8 - 129600x^6 + 5832000	\( 2^{62}\cdot 3^{14}\cdot 5^{15}\cdot 11^{2} \)	16T1885	$[4]$ (GRH)
16.0.81450308316908771868672000000000000000.2	x^16 + 40x^10 + 30x^8 + 320x^4 + 480x^2 + 180	\( 2^{62}\cdot 3^{14}\cdot 5^{15}\cdot 11^{2} \)	16T1885	$[2, 8]$ (GRH)
16.8.81450308316908771868672000000000000000.2	x^16 - 40x^10 + 30x^8 + 320x^4 - 480x^2 + 180	\( 2^{62}\cdot 3^{14}\cdot 5^{15}\cdot 11^{2} \)	16T1885	$[4]$ (GRH)