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 matches 1-50 of )

Label	Polynomial	Discriminant	Galois group	Class group
16.0.1308342779541015625.1	x^16 - 5x^15 + 8x^14 - 10x^13 + 28x^12 - 25x^11 + 36x^10 - 50x^9 + 35x^8 - 50x^7 + 36x^6 - 25x^5 + 28x^4 - 10x^3 + 8x^2 - 5x + 1	\( 5^{14}\cdot 11^{8} \)	$C_2^3.C_4$ (as 16T36)	$[2]$
16.0.1846757322198614016.9	x^16 - 8x^15 + 32x^14 - 80x^13 + 148x^12 - 232x^11 + 316x^10 - 328x^9 + 190x^8 + 56x^7 - 264x^6 + 312x^5 - 184x^4 - 16x^3 + 128x^2 - 104x + 34	\( 2^{48}\cdot 3^{8} \)	$C_2^2:D_4$ (as 16T43)	$[2]$
16.0.2090628617375390625.1	x^16 - x^15 + 5x^14 + 14x^13 + 6x^12 + 35x^11 + 42x^10 + 20x^9 + 31x^8 - 20x^7 + 42x^6 - 35x^5 + 6x^4 - 14x^3 + 5x^2 + x + 1	\( 3^{8}\cdot 5^{8}\cdot 13^{8} \)	$D_4\times C_2$ (as 16T9)	$[2]$
16.0.2174327193600000000.1	x^16 - 2x^14 + 2x^12 - 12x^11 + 18x^10 + 24x^9 - 37x^8 - 48x^7 + 90x^6 - 48x^5 + 56x^4 - 84x^3 + 52x^2 - 12x + 1	\( 2^{36}\cdot 3^{4}\cdot 5^{8} \)	$Q_8 : C_2^2$ (as 16T23)	$[2]$
16.0.2467585431025000000.1	x^16 + x^14 - x^12 - 3x^10 + 8x^8 + 26x^6 + 21x^4 + 2x^2 + 1	\( 2^{6}\cdot 5^{8}\cdot 11^{2}\cdot 13^{8} \)	16T1656	$[2]$
16.0.2528149687744140625.1	x^16 - 6x^15 + 18x^14 - 34x^13 + 45x^12 - 35x^11 + 9x^10 + 12x^9 + x^8 - 33x^7 + 99x^6 - 92x^5 + 108x^4 - 46x^3 + 24x^2 + 9x + 1	\( 5^{12}\cdot 11^{4}\cdot 29^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T542)	$[2]$
16.0.2565942505126953125.1	x^16 - 7x^15 + 22x^14 - 52x^13 + 113x^12 - 197x^11 + 280x^10 - 375x^9 + 431x^8 - 375x^7 + 280x^6 - 197x^5 + 113x^4 - 52x^3 + 22x^2 - 7x + 1	\( 5^{12}\cdot 101^{5} \)	16T1281	$[2]$
16.0.2690420062500000000.1	x^16 - 5x^15 + 22x^14 - 55x^13 + 125x^12 - 195x^11 + 297x^10 - 330x^9 + 384x^8 - 320x^7 + 283x^6 - 170x^5 + 115x^4 - 50x^3 + 23x^2 - 5x + 1	\( 2^{8}\cdot 3^{16}\cdot 5^{12} \)	$A_4:C_4$ (as 16T62)	$[2]$
16.0.3061100160000000000.1	x^16 - 6x^15 + 14x^14 - 83x^12 + 216x^11 - 199x^10 - 210x^9 + 862x^8 - 1110x^7 + 578x^6 + 138x^5 - 164x^4 - 390x^3 + 683x^2 - 438x + 109	\( 2^{16}\cdot 3^{14}\cdot 5^{10} \)	$(C_4\times C_8):C_2$ (as 16T114)	$[2]$
16.0.3082688233381822464.1	x^16 - 6x^15 + 16x^14 - 18x^13 - 14x^12 + 66x^11 - 56x^10 - 42x^9 + 118x^8 - 42x^7 - 56x^6 + 66x^5 - 14x^4 - 18x^3 + 16x^2 - 6x + 1	\( 2^{28}\cdot 3^{14}\cdot 7^{4} \)	$D_4^2.C_2$ (as 16T376)	$[2]$
16.0.3482851737600000000.1	x^16 - 8x^15 + 26x^14 - 42x^13 + 30x^12 + 2x^11 - 50x^10 + 184x^9 - 140x^8 - 522x^7 + 1272x^6 - 1220x^5 + 621x^4 - 186x^3 + 40x^2 - 8x + 1	\( 2^{24}\cdot 3^{12}\cdot 5^{8} \)	$C_2^2:D_4$ (as 16T43)	$[2]$
16.0.3482851737600000000.2	x^16 - 2x^15 + 2x^14 - 4x^13 - 22x^12 + 2x^11 + 48x^10 + 114x^9 + 163x^8 + 114x^7 + 48x^6 + 2x^5 - 22x^4 - 4x^3 + 2x^2 - 2x + 1	\( 2^{24}\cdot 3^{12}\cdot 5^{8} \)	$D_4\times C_2$ (as 16T9)	$[2]$
16.0.3482851737600000000.4	x^16 - 8x^14 + 29x^12 - 59x^10 + 76x^8 - 61x^6 + 29x^4 - 7x^2 + 1	\( 2^{24}\cdot 3^{12}\cdot 5^{8} \)	$C_4^2:C_2^2$ (as 16T117)	$[2]$
16.0.3482851737600000000.5	x^16 - 5x^14 + 13x^12 - 50x^10 + 118x^8 - 50x^6 + 13x^4 - 5x^2 + 1	\( 2^{24}\cdot 3^{12}\cdot 5^{8} \)	$C_2^2 \times D_4$ (as 16T25)	$[2]$
16.0.3790869843994140625.1	x^16 - 5x^15 + 5x^14 + 10x^13 - 12x^12 - 15x^11 - 10x^10 + 50x^9 + 79x^8 - 240x^7 + 160x^6 + 15x^5 - 58x^4 + 20x^3 + 5x^2 - 5x + 1	\( 5^{12}\cdot 353^{4} \)	$C_2^4.(C_4\times S_3)$ (as 16T725)	$[2]$
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	$[2]$
16.0.4055251992431640625.1	x^16 - 2x^15 + 6x^14 - 8x^13 + 20x^12 - 22x^11 + 43x^10 - 39x^9 + 63x^8 - 21x^7 + 33x^6 + 4x^5 + 29x^4 + 26x^3 + 17x^2 + 4x + 1	\( 5^{12}\cdot 359^{4} \)	16T1031	$[2]$
16.0.4074443918442233856.1	x^16 - 2x^15 + 4x^14 + 4x^13 - 28x^12 - 2x^11 + 64x^10 + 2x^9 - 77x^8 - 18x^7 + 40x^6 + 18x^5 + 4x^4 + 16x^3 + 16x^2 + 6x + 1	\( 2^{28}\cdot 3^{12}\cdot 13^{4} \)	$C_2^4.C_2^3$ (as 16T373)	$[2]$
16.0.4146377695556640625.1	x^16 - x^15 - 2x^14 + 6x^13 - 2x^12 + 19x^11 - 5x^10 - 60x^9 + 96x^8 + 60x^7 - 5x^6 - 19x^5 - 2x^4 - 6x^3 - 2x^2 + x + 1	\( 5^{12}\cdot 19^{8} \)	$C_2^2 : C_4$ (as 16T10)	$[2]$
16.0.4146377695556640625.2	x^16 - x^15 + x^14 - 7x^13 + 29x^12 - 45x^11 + 23x^10 + 21x^9 + 23x^8 - 21x^7 + 23x^6 + 45x^5 + 29x^4 + 7x^3 + x^2 + x + 1	\( 5^{12}\cdot 19^{8} \)	$QD_{16}$ (as 16T12)	$[2]$
16.0.4146377695556640625.3	x^16 - 3x^15 + 4x^14 - 5x^12 + 8x^11 - 5x^9 + x^8 + 5x^7 - 8x^5 - 5x^4 + 4x^2 + 3x + 1	\( 5^{12}\cdot 19^{8} \)	$C_2^4.D_4$ (as 16T330)	$[2]$
16.0.4146377695556640625.4	x^16 - 6x^15 + 21x^14 - 49x^13 + 82x^12 - 109x^11 + 111x^10 - 92x^9 + 89x^8 + 3x^7 + 108x^6 + 70x^5 + 171x^4 + 60x^3 + 115x^2 + 25x + 25	\( 5^{12}\cdot 19^{8} \)	$C_2\wr C_4$ (as 16T172)	$[2]$
16.0.4415251562500000000.1	x^16 - 3x^15 + 2x^14 - 4x^13 + x^12 + 67x^11 - 160x^10 + 48x^9 + 334x^8 - 631x^7 + 535x^6 - 261x^5 + 126x^4 - 92x^3 + 48x^2 - 11x + 1	\( 2^{8}\cdot 5^{14}\cdot 41^{4} \)	$C_4.C_2^2:D_4$ (as 16T209)	$[2]$
16.0.4508684868648960000.1	x^16 - 8x^14 + 44x^12 - 24x^11 - 168x^10 + 252x^9 + 335x^8 - 1536x^7 + 2352x^6 - 2028x^5 + 1052x^4 - 336x^3 + 76x^2 - 12x + 1	\( 2^{40}\cdot 3^{8}\cdot 5^{4} \)	$Q_8 : C_2^2$ (as 16T23)	$[2]$
16.0.5258930030792146944.3	x^16 + 4x^14 + 4x^12 + 16x^10 - 20x^8 - 8x^6 + 16x^4 + 16x^2 + 4	\( 2^{40}\cdot 3^{14} \)	$C_2\times SD_{16}$ (as 16T48)	$[2]$
16.0.5308416000000000000.1	x^16 + 4x^14 - 4x^10 + 34x^8 - 4x^6 + 4x^2 + 1	\( 2^{28}\cdot 3^{4}\cdot 5^{12} \)	$C_2^2.D_4$ (as 16T33)	$[2]$
16.0.5308416000000000000.2	x^16 - 4x^15 + 8x^14 - 16x^13 + 8x^12 + 16x^11 + 20x^9 - 14x^8 - 20x^7 - 16x^5 + 8x^4 + 16x^3 + 8x^2 + 4x + 1	\( 2^{28}\cdot 3^{4}\cdot 5^{12} \)	$C_2^2.D_4$ (as 16T33)	$[2]$
16.0.6003725062500000000.2	x^16 - 6x^14 + 14x^12 - 2x^10 - 6x^8 - 14x^6 + 81x^4 - 68x^2 + 16	\( 2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 11^{4} \)	$C_2^4.C_2^4$ (as 16T459)	$[2]$
16.0.6052387225600000000.5	x^16 - 2x^14 + 2x^12 + 23x^10 - 22x^8 - 16x^6 + 18x^4 + 11x^2 + 1	\( 2^{24}\cdot 5^{8}\cdot 31^{4} \)	$C_2\times D_4^2.C_2$ (as 16T602)	$[2]$
16.0.6338465731314712576.1	x^16 - 6x^14 + 19x^12 - 26x^10 + 22x^8 - 14x^6 + 35x^4 - 10x^2 + 1	\( 2^{40}\cdot 7^{8} \)	$C_2\times C_4\wr C_2$ (as 16T111)	$[2]$
16.0.6338465731314712576.2	x^16 - 6x^14 - 12x^13 - 6x^12 + 52x^11 + 166x^10 + 280x^9 + 346x^8 + 280x^7 + 166x^6 + 52x^5 - 6x^4 - 12x^3 - 6x^2 + 1	\( 2^{40}\cdot 7^{8} \)	$C_2\wr C_2^2$ (as 16T127)	$[2]$
16.0.6338465731314712576.9	x^16 + 3x^12 + x^8 - 8x^4 + 4	\( 2^{40}\cdot 7^{8} \)	$C_2\times C_4\wr C_2$ (as 16T111)	$[2]$
16.0.6338465731314712576.10	x^16 - 8x^14 + 14x^12 + 12x^10 + 45x^8 + 92x^6 + 56x^4 + 8x^2 + 4	\( 2^{40}\cdot 7^{8} \)	$C_8:C_2^2$ (as 16T35)	$[2]$
16.0.7122039371137548288.7	x^16 - 4x^15 + 2x^14 + 4x^13 + 31x^12 - 96x^11 + 14x^10 + 298x^9 - 518x^8 + 242x^7 + 392x^6 - 768x^5 + 598x^4 - 232x^3 + 38x^2 - 2x + 1	\( 2^{24}\cdot 3^{10}\cdot 193^{3} \)	16T1472	$[2]$
16.0.7674110773159501773.1	x^16 - 7x^15 + 25x^14 - 62x^13 + 113x^12 - 113x^11 + 24x^10 - 52x^9 + 243x^8 - 232x^7 + 78x^6 - 56x^5 + 36x^4 - 8x^3 + 11x^2 - x + 1	\( 3^{10}\cdot 37^{9} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	$[2]$
16.0.7731614709228515625.1	x^16 - 5x^15 + 11x^14 - 17x^13 + 46x^11 + 18x^10 - 257x^9 + 481x^8 - 424x^7 + 141x^6 + 26x^5 - 12x^4 - 22x^3 + 20x^2 - 7x + 1	\( 3^{8}\cdot 5^{12}\cdot 13^{6} \)	$C_2\times D_8$ (as 16T29)	$[2]$
16.0.8278812383757991936.1	x^16 + 4x^14 + 4x^12 + 8x^10 + 28x^8 + 40x^6 + 32x^4 + 16x^2 + 4	\( 2^{46}\cdot 7^{6} \)	$C_2^3.(C_2\times D_4)$ (as 16T408)	$[2]$
16.0.8294400000000000000.2	x^16 - 2x^15 + 12x^14 - 6x^13 + 26x^12 + 68x^11 - 30x^10 + 222x^9 + 199x^8 - 224x^7 + 1210x^6 - 994x^5 + 1546x^4 - 698x^3 + 778x^2 - 184x + 181	\( 2^{24}\cdot 3^{4}\cdot 5^{14} \)	$(C_8:C_2):C_2$ (as 16T16)	$[2]$
16.0.8501000274280710144.1	x^16 - 4x^15 + 2x^14 - 2x^13 + 24x^12 - 42x^11 + 100x^10 - 84x^9 - 69x^8 + 70x^7 + 52x^6 - 72x^5 + 34x^4 - 6x^3 - 6x^2 + 2x + 1	\( 2^{28}\cdot 3^{8}\cdot 13^{6} \)	$C_2\wr C_2^2$ (as 16T128)	$[2]$
16.0.8501000274280710144.2	x^16 - 6x^15 + 14x^14 - 22x^13 + 42x^12 - 64x^11 + 48x^10 - 58x^9 + 187x^8 - 336x^7 + 420x^6 - 522x^5 + 648x^4 - 702x^3 + 594x^2 - 324x + 81	\( 2^{28}\cdot 3^{8}\cdot 13^{6} \)	$C_2\wr C_2^2$ (as 16T128)	$[2]$
16.0.8503056000000000000.1	x^16 - 6x^15 + 18x^14 - 36x^13 + 37x^12 - 18x^10 + 42x^9 - 60x^8 + 42x^7 - 18x^6 + 37x^4 - 36x^3 + 18x^2 - 6x + 1	\( 2^{16}\cdot 3^{12}\cdot 5^{12} \)	$D_4\times C_2$ (as 16T9)	$[2]$
16.0.8503056000000000000.2	x^16 - 6x^15 + 22x^14 - 64x^13 + 133x^12 - 234x^11 + 358x^10 - 414x^9 + 439x^8 - 290x^7 + 190x^6 - 28x^5 + 17x^4 - 10x^3 + 10x^2 - 4x + 1	\( 2^{16}\cdot 3^{12}\cdot 5^{12} \)	$C_4 \times D_4$ (as 16T19)	$[2]$
16.0.8503056000000000000.3	x^16 - 7x^14 - 4x^12 + 29x^10 + 169x^8 + 232x^6 + 104x^4 + 16x^2 + 16	\( 2^{16}\cdot 3^{12}\cdot 5^{12} \)	$C_4 \times D_4$ (as 16T19)	$[2]$
16.0.9440732714731831296.1	x^16 - 4x^15 + 2x^14 - 6x^13 + 86x^12 - 218x^11 + 226x^10 - 288x^9 + 724x^8 - 930x^7 + 340x^6 + 248x^5 - 223x^4 + 30x^3 + 20x^2 - 8x + 1	\( 2^{24}\cdot 3^{14}\cdot 7^{6} \)	$C_8:C_2^2$ (as 16T45)	$[2]$
16.0.9659566875244140625.1	x^16 - 4x^15 + 12x^14 - 27x^13 + 49x^12 - 75x^11 + 82x^10 - 66x^9 + 42x^8 + 11x^7 + 30x^6 + 57x^5 + 10x^4 - 59x^3 + 36x^2 - 5x + 1	\( 5^{12}\cdot 19^{6}\cdot 29^{2} \)	$C_2^4.C_2^3.C_2$ (as 16T707)	$[2]$
16.0.9659566875244140625.2	x^16 + 7x^14 + 12x^12 + 10x^10 + 86x^8 + 155x^6 - 12x^4 - 4x^2 + 1	\( 5^{12}\cdot 19^{6}\cdot 29^{2} \)	$C_2^4.C_2^3.C_2$ (as 16T707)	$[2]$
16.0.10044752324575775625.2	x^16 + 6x^14 - 15x^13 + 15x^12 - 54x^11 + 99x^10 - 84x^9 + 159x^8 - 234x^7 + 135x^6 - 117x^5 + 162x^4 - 63x^3 - 9x^2 - 9x + 9	\( 3^{14}\cdot 5^{4}\cdot 7^{6}\cdot 13^{4} \)	$C_2^2.C_2^5.C_2$ (as 16T511)	$[2]$
16.0.10172435817406640625.1	x^16 - 7x^15 + 27x^14 - 63x^13 + 115x^12 - 167x^11 + 216x^10 - 243x^9 + 258x^8 - 243x^7 + 216x^6 - 167x^5 + 115x^4 - 63x^3 + 27x^2 - 7x + 1	\( 3^{8}\cdot 5^{8}\cdot 251^{4} \)	$C_2\times C_2^2:S_4:C_2$ (as 16T724)	$[2]$
16.0.10460890548900000000.2	x^16 - 4x^15 + 8x^14 - 21x^13 + 46x^12 - 50x^11 + 43x^10 - 29x^9 - 40x^8 - 29x^7 + 211x^6 - 75x^5 - 108x^4 + 10x^3 + 28x^2 + 9x + 1	\( 2^{8}\cdot 3^{10}\cdot 5^{8}\cdot 11^{6} \)	16T1220	$[2]$
16.0.10462769568345489408.2	x^16 - 4x^15 + 6x^14 - 8x^13 + 26x^12 - 40x^11 - 124x^10 + 560x^9 - 655x^8 - 284x^7 + 1528x^6 - 1808x^5 + 1168x^4 - 464x^3 + 114x^2 - 16x + 1	\( 2^{32}\cdot 3^{8}\cdot 13^{5} \)	$C_2.D_4^2.C_2$ (as 16T659)	$[2]$

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