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 38 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.22788341917286400.1	x^16 - 2x^15 + 6x^14 - 8x^13 + 9x^12 - 6x^11 - 4x^10 + 12x^9 - 19x^8 + 24x^7 - 16x^6 + 2x^5 + 9x^4 - 16x^3 + 14x^2 - 6x + 1	\( 2^{24}\cdot 3^{8}\cdot 5^{2}\cdot 7^{2}\cdot 13^{2} \)	16T1697	Trivial
16.0.3851229784021401600.1	x^16 + 8x^14 - 8x^13 + 25x^12 - 20x^11 + 10x^10 + 8x^9 - 20x^8 + 32x^7 + 2x^6 + 20x^5 + 21x^4 - 48x^3 + 28x^2 - 8x + 1	\( 2^{24}\cdot 3^{8}\cdot 5^{2}\cdot 7^{2}\cdot 13^{4} \)	16T1697	$[2]$
16.0.288597580185600000000.1	x^16 - 6x^15 + 21x^14 - 48x^13 + 89x^12 - 140x^11 + 201x^10 - 246x^9 + 260x^8 - 246x^7 + 201x^6 - 140x^5 + 89x^4 - 48x^3 + 21x^2 - 6x + 1	\( 2^{28}\cdot 3^{2}\cdot 5^{8}\cdot 7^{2}\cdot 79^{2} \)	16T1697	Trivial
16.4.288597580185600000000.1	x^16 - 6x^15 + 17x^14 - 28x^13 + 20x^12 + 14x^11 - 70x^10 + 82x^9 - 81x^8 + 26x^7 + 34x^6 - 54x^5 + 40x^4 - 12x^3 - 17x^2 + 10x - 1	\( 2^{28}\cdot 3^{2}\cdot 5^{8}\cdot 7^{2}\cdot 79^{2} \)	16T1697	Trivial
16.0.288597580185600000000.2	x^16 - 6x^15 + 23x^14 - 62x^13 + 148x^12 - 310x^11 + 565x^10 - 906x^9 + 1372x^8 - 1890x^7 + 2205x^6 - 1954x^5 + 1263x^4 - 560x^3 + 170x^2 - 32x + 4	\( 2^{28}\cdot 3^{2}\cdot 5^{8}\cdot 7^{2}\cdot 79^{2} \)	16T1697	Trivial
16.4.288597580185600000000.2	x^16 - 6x^15 + 11x^14 - 2x^13 - 14x^12 + 10x^11 + 27x^10 - 74x^9 + 73x^8 - 40x^7 + 4x^6 + 16x^5 - 34x^4 + 40x^3 - 12x^2 - 8x + 4	\( 2^{28}\cdot 3^{2}\cdot 5^{8}\cdot 7^{2}\cdot 79^{2} \)	16T1697	Trivial
16.8.467721938534400000000.1	x^16 - 8x^15 + 18x^14 + 12x^13 - 95x^12 + 104x^11 + 16x^10 - 136x^9 + 185x^8 - 136x^7 + 16x^6 + 104x^5 - 95x^4 + 12x^3 + 18x^2 - 8x + 1	\( 2^{40}\cdot 3^{2}\cdot 5^{8}\cdot 11^{2} \)	16T1697	Trivial (GRH)
16.4.3468060367257600000000.1	x^16 + 6x^14 + 20x^12 - 10x^10 - 87x^8 - 70x^6 + 8x^2 + 1	\( 2^{28}\cdot 3^{8}\cdot 5^{8}\cdot 71^{2} \)	16T1697	Trivial (GRH)
16.8.3468060367257600000000.1	x^16 - 6x^14 + 20x^12 + 10x^10 - 87x^8 + 70x^6 - 8x^2 + 1	\( 2^{28}\cdot 3^{8}\cdot 5^{8}\cdot 71^{2} \)	16T1697	Trivial (GRH)
16.4.4158825961881600000000.1	x^16 + 4x^14 - 7x^12 - 62x^10 - 179x^8 - 376x^6 - 436x^4 - 160x^2 + 16	\( 2^{24}\cdot 3^{8}\cdot 5^{8}\cdot 311^{2} \)	16T1697	Trivial (GRH)
16.4.42804101047910400000000.1	x^16 - 2x^15 + 5x^14 + 22x^13 - 88x^12 + 256x^11 - 381x^10 + 376x^9 - 117x^8 - 156x^7 + 171x^6 + 40x^5 - 82x^4 - 18x^3 + x^2 + 2x + 1	\( 2^{24}\cdot 3^{2}\cdot 5^{8}\cdot 11^{2}\cdot 31^{2}\cdot 79^{2} \)	16T1697	Trivial (GRH)
16.12.71036492473958400000000.1	x^16 - 10x^14 + 29x^12 - 110x^8 + 110x^6 + 32x^4 - 60x^2 + 9	\( 2^{32}\cdot 3^{6}\cdot 5^{8}\cdot 241^{2} \)	16T1697	Trivial (GRH)
16.4.71036492473958400000000.1	x^16 - 48x^12 - 66x^10 + 550x^8 + 1584x^6 + 1353x^4 + 378x^2 + 9	\( 2^{32}\cdot 3^{6}\cdot 5^{8}\cdot 241^{2} \)	16T1697	Trivial (GRH)
16.8.71036492473958400000000.1	x^16 - 10x^14 - 7x^12 + 128x^10 - 50x^8 - 318x^6 + 72x^4 + 216x^2 + 9	\( 2^{32}\cdot 3^{6}\cdot 5^{8}\cdot 241^{2} \)	16T1697	Trivial (GRH)
16.12.71036492473958400000000.2	x^16 - 14x^14 + 71x^12 - 144x^10 + 25x^8 + 292x^6 - 301x^4 + 30x^2 + 9	\( 2^{32}\cdot 3^{6}\cdot 5^{8}\cdot 241^{2} \)	16T1697	Trivial (GRH)
16.4.71036492473958400000000.2	x^16 + 2x^14 - 59x^12 - 296x^10 - 550x^8 - 454x^6 - 136x^4 + 12x^2 + 9	\( 2^{32}\cdot 3^{6}\cdot 5^{8}\cdot 241^{2} \)	16T1697	Trivial (GRH)
16.8.71036492473958400000000.2	x^16 + 10x^14 - 7x^12 - 128x^10 - 50x^8 + 318x^6 + 72x^4 - 216x^2 + 9	\( 2^{32}\cdot 3^{6}\cdot 5^{8}\cdot 241^{2} \)	16T1697	Trivial (GRH)
16.0.775815404558745600000000.1	x^16 + 28x^14 + 298x^12 + 1544x^10 + 4083x^8 + 5288x^6 + 3322x^4 + 1764x^2 + 441	\( 2^{52}\cdot 3^{2}\cdot 5^{8}\cdot 7^{2} \)	16T1697	$[2]$ (GRH)
16.12.775815404558745600000000.1	x^16 - 28x^14 + 298x^12 - 1544x^10 + 4083x^8 - 5288x^6 + 3322x^4 - 1764x^2 + 441	\( 2^{52}\cdot 3^{2}\cdot 5^{8}\cdot 7^{2} \)	16T1697	Trivial (GRH)
16.4.775815404558745600000000.1	x^16 + 4x^14 + 10x^12 - 16x^10 - 465x^8 - 1000x^6 + 1342x^4 + 3612x^2 + 441	\( 2^{52}\cdot 3^{2}\cdot 5^{8}\cdot 7^{2} \)	16T1697	Trivial (GRH)
16.8.775815404558745600000000.1	x^16 + 4x^14 - 78x^12 - 112x^10 + 1363x^8 - 1696x^6 + 1298x^4 - 1932x^2 + 441	\( 2^{52}\cdot 3^{2}\cdot 5^{8}\cdot 7^{2} \)	16T1697	Trivial (GRH)
16.0.775815404558745600000000.2	x^16 + 24x^14 + 232x^12 + 1216x^10 + 3878x^8 + 7624x^6 + 8168x^4 + 3360x^2 + 441	\( 2^{52}\cdot 3^{2}\cdot 5^{8}\cdot 7^{2} \)	16T1697	$[4]$ (GRH)
16.12.775815404558745600000000.2	x^16 - 24x^14 + 232x^12 - 1216x^10 + 3878x^8 - 7624x^6 + 8168x^4 - 3360x^2 + 441	\( 2^{52}\cdot 3^{2}\cdot 5^{8}\cdot 7^{2} \)	16T1697	Trivial (GRH)
16.4.775815404558745600000000.2	x^16 + 8x^14 - 128x^10 - 650x^8 - 2120x^6 - 3232x^4 - 1344x^2 + 441	\( 2^{52}\cdot 3^{2}\cdot 5^{8}\cdot 7^{2} \)	16T1697	Trivial (GRH)
16.8.775815404558745600000000.2	x^16 - 4x^14 + 10x^12 + 16x^10 - 465x^8 + 1000x^6 + 1342x^4 - 3612x^2 + 441	\( 2^{52}\cdot 3^{2}\cdot 5^{8}\cdot 7^{2} \)	16T1697	Trivial (GRH)
16.4.1539952952111941445222400.1	x^16 - 4x^14 - 14x^12 + 40x^10 + 21x^8 - 76x^6 + 184x^4 + 520x^2 + 100	\( 2^{34}\cdot 3^{8}\cdot 5^{2}\cdot 97^{2}\cdot 241^{2} \)	16T1697	Trivial (GRH)
16.8.44742396572315465180774400.1	x^16 - 4x^15 - 6x^14 + 32x^13 - 21x^12 - 84x^11 + 92x^10 + 156x^9 - 112x^8 - 324x^7 + 92x^6 + 376x^5 + 42x^4 - 200x^3 - 52x^2 + 24x + 4	\( 2^{34}\cdot 3^{8}\cdot 5^{2}\cdot 7^{2}\cdot 47^{2}\cdot 383^{2} \)	16T1697	$[2]$ (GRH)
16.0.736253365564278374400000000.1	x^16 + 25x^14 + 230x^12 + 949x^10 + 1761x^8 + 1560x^6 + 654x^4 + 112x^2 + 4	\( 2^{22}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8}\cdot 109^{2} \)	16T1697	$[2, 12]$ (GRH)
16.16.736253365564278374400000000.1	x^16 - 24x^14 + 235x^12 - 1206x^10 + 3467x^8 - 5532x^6 + 4544x^4 - 1560x^2 + 100	\( 2^{22}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8}\cdot 109^{2} \)	16T1697	Trivial (GRH)
16.8.736253365564278374400000000.1	x^16 + 8x^14 + 11x^12 - 46x^10 - 93x^8 + 84x^6 + 144x^4 - 88x^2 + 4	\( 2^{22}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8}\cdot 109^{2} \)	16T1697	Trivial (GRH)
16.16.4557002229445400985600000000.1	x^16 - 4x^15 - 22x^14 + 74x^13 + 191x^12 - 448x^11 - 825x^10 + 1064x^9 + 1752x^8 - 840x^7 - 1521x^6 + 104x^5 + 425x^4 + 12x^3 - 41x^2 - 2x + 1	\( 2^{28}\cdot 3^{2}\cdot 5^{8}\cdot 7^{2}\cdot 313921^{2} \)	16T1697	Trivial (GRH)
16.8.5222828538524288160000000000.1	x^16 + 4x^14 - 7x^12 - 35x^10 + 9x^8 + 81x^6 + 3x^4 - 44x^2 + 4	\( 2^{14}\cdot 3^{8}\cdot 5^{10}\cdot 7^{8}\cdot 929^{2} \)	16T1697	Trivial (GRH)
16.0.11780053849028453990400000000.1	x^16 + 24x^14 + 235x^12 + 1206x^10 + 3467x^8 + 5532x^6 + 4544x^4 + 1560x^2 + 100	\( 2^{26}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8}\cdot 109^{2} \)	16T1697	$[2, 148]$ (GRH)
16.8.27963997857697165737984000000.1	x^16 - 4x^15 - 34x^14 + 104x^13 + 441x^12 - 1348x^11 - 3712x^10 + 9632x^9 + 23487x^8 - 35876x^7 - 105858x^6 + 29756x^5 + 245106x^4 + 160028x^3 - 94616x^2 - 139192x - 41714	\( 2^{34}\cdot 3^{8}\cdot 5^{6}\cdot 7^{2}\cdot 47^{2}\cdot 383^{2} \)	16T1697	$[2]$ (GRH)
16.0.1679882599229757692313600000000.1	x^16 + 12x^14 + 68x^12 + 284x^10 + 816x^8 + 1280x^6 + 1224x^4 + 728x^2 + 196	\( 2^{50}\cdot 3^{8}\cdot 5^{8}\cdot 7^{2}\cdot 109^{2} \)	16T1697	$[2]$ (GRH)
16.0.1679882599229757692313600000000.2	x^16 + 24x^14 + 164x^12 + 652x^10 + 1632x^8 + 2056x^6 + 1896x^4 + 1288x^2 + 196	\( 2^{50}\cdot 3^{8}\cdot 5^{8}\cdot 7^{2}\cdot 109^{2} \)	16T1697	$[2]$ (GRH)
16.8.73924058337595330806214217957376000000000000.1	x^16 - 348x^14 + 26810x^12 + 670992x^10 - 74050561x^8 - 428011752x^6 + 38690866830x^4 + 445778900028x^2 + 586846391481	\( 2^{52}\cdot 3^{6}\cdot 5^{12}\cdot 7^{6}\cdot 13^{8}\cdot 31^{2} \)	16T1697	$[2, 2, 2, 2]$ (GRH)
16.8.73924058337595330806214217957376000000000000.2	x^16 + 348x^14 + 26810x^12 - 670992x^10 - 74050561x^8 + 428011752x^6 + 38690866830x^4 - 445778900028x^2 + 586846391481	\( 2^{52}\cdot 3^{6}\cdot 5^{12}\cdot 7^{6}\cdot 13^{8}\cdot 31^{2} \)	16T1697	$[2, 2, 2, 2]$ (GRH)