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 2685)

Label	Polynomial	Discriminant	Galois group	Class group
16.12.59904939404541015625.1	x^16 - x^15 - 11x^14 + 12x^13 + 43x^12 - 57x^11 - 68x^10 + 138x^9 + 26x^8 - 183x^7 + 29x^6 + 137x^5 - 20x^4 - 54x^3 + 8x + 1	\( 5^{12}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2} \)	16T1340	Trivial (GRH)
16.12.79206727576336328125.1	x^16 - 7x^15 + 10x^14 + 33x^13 - 93x^12 - 40x^11 + 290x^10 - 53x^9 - 465x^8 + 191x^7 + 392x^6 - 181x^5 - 155x^4 + 62x^3 + 20x^2 - 5x - 1	\( 5^{8}\cdot 181\cdot 439^{2}\cdot 2411^{2} \)	16T1905	Trivial
16.12.80608086462750390625.1	x^16 - 2x^15 - 14x^14 + 38x^13 + 34x^12 - 176x^11 + 82x^10 + 230x^9 - 268x^8 - 12x^7 + 127x^6 - 11x^5 - 16x^4 - 23x^3 + 5x^2 + 7x - 1	\( 5^{8}\cdot 19^{2}\cdot 29^{6}\cdot 31^{2} \)	16T1340	Trivial (GRH)
16.12.135039180647105281341.1	x^16 - 4x^15 + 17x^13 - 22x^12 - 6x^11 + 49x^10 - 21x^9 - 39x^8 - 6x^7 + x^6 + 36x^5 + 19x^4 - 19x^3 - 10x^2 + 2x + 1	\( 3^{6}\cdot 19^{4}\cdot 73\cdot 103^{4}\cdot 173 \)	16T1879	Trivial
16.12.137084215713134765625.1	x^16 - 3x^15 - 10x^14 + 34x^13 + 35x^12 - 142x^11 - 56x^10 + 268x^9 + 66x^8 - 218x^7 - 88x^6 + 32x^5 + 68x^4 + 33x^3 - 16x^2 - 4x + 1	\( 3^{8}\cdot 5^{12}\cdot 11^{2}\cdot 29^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T547)	Trivial (GRH)
16.12.157633109816006250000.1	x^16 - 11x^14 + 41x^12 - 49x^10 - 37x^8 + 103x^6 - 16x^4 - 37x^2 + 1	\( 2^{4}\cdot 3^{12}\cdot 5^{8}\cdot 83^{4} \)	16T1046	Trivial (GRH)
16.12.178657056758056640625.1	x^16 - 2x^15 - 8x^14 + 29x^13 - 18x^12 - 106x^11 + 223x^10 + 67x^9 - 495x^8 + 211x^7 + 419x^6 - 336x^5 - 112x^4 + 149x^3 - 10x^2 - 12x + 1	\( 3^{8}\cdot 5^{12}\cdot 59^{2}\cdot 179^{2} \)	16T1224	Trivial
16.12.228295483029373059072.1	x^16 - 14x^14 + 71x^12 - 4x^11 - 168x^10 + 20x^9 + 200x^8 - 36x^7 - 128x^6 + 36x^5 + 48x^4 - 20x^3 - 10x^2 + 4x + 1	\( 2^{32}\cdot 3^{8}\cdot 17^{4}\cdot 97 \)	16T1590	Trivial
16.12.230208256960351953125.1	x^16 - 7x^15 + 12x^14 + 11x^13 - 39x^12 + 14x^11 + 12x^10 - 6x^9 + 36x^8 - 57x^7 - 26x^6 + 73x^5 + 8x^4 - 33x^3 - 4x^2 + 5x + 1	\( 5^{8}\cdot 29^{4}\cdot 941^{3} \)	16T1432	Trivial
16.12.239375724952041015625.1	x^16 - 2x^15 - 11x^14 + 25x^13 + 30x^12 - 93x^11 - 3x^10 + 138x^9 - 76x^8 - 67x^7 + 72x^6 - 25x^5 - 6x^4 + 27x^3 - 9x^2 - 3x + 1	\( 5^{10}\cdot 7^{2}\cdot 29^{8} \)	$C_2.C_2\wr C_2^2$ (as 16T400)	Trivial (GRH)
16.12.240533111170777145581.1	x^16 - 3x^15 - 7x^14 + 20x^13 + 27x^12 - 51x^11 - 79x^10 + 63x^9 + 152x^8 - 42x^7 - 160x^6 + 20x^5 + 80x^4 - 8x^3 - 16x^2 + x + 1	\( 7^{2}\cdot 19^{4}\cdot 43^{2}\cdot 103^{4}\cdot 181 \)	16T1879	Trivial
16.12.246882693868258203125.1	x^16 - 8x^15 + 17x^14 + 21x^13 - 115x^12 + 53x^11 + 240x^10 - 232x^9 - 218x^8 + 273x^7 + 114x^6 - 134x^5 - 55x^4 + 31x^3 + 16x^2 - 4x - 1	\( 5^{8}\cdot 29^{4}\cdot 379^{2}\cdot 6221 \)	16T1823	Trivial (GRH)
16.12.261795706633387279997.1	x^16 - 3x^15 - 8x^14 + 35x^13 + 8x^12 - 150x^11 + 86x^10 + 289x^9 - 295x^8 - 248x^7 + 358x^6 + 93x^5 - 184x^4 - 19x^3 + 36x^2 + 3x - 1	\( 7^{2}\cdot 19^{4}\cdot 43^{2}\cdot 103^{4}\cdot 197 \)	16T1879	Trivial
16.12.277795632642462908416.1	x^16 - 7x^14 + 14x^12 + 2x^10 - 27x^8 + x^6 + 35x^4 - 19x^2 + 1	\( 2^{16}\cdot 89^{2}\cdot 731531^{2} \)	16T1945	Trivial (GRH)
16.12.284052722662986805169.1	x^16 - 8x^15 + 18x^14 + 14x^13 - 98x^12 + 42x^11 + 213x^10 - 163x^9 - 270x^8 + 232x^7 + 208x^6 - 162x^5 - 88x^4 + 49x^3 + 16x^2 - 4x - 1	\( 43^{2}\cdot 521^{2}\cdot 4337^{2}\cdot 30089 \)	16T1948	Trivial (GRH)
16.12.290029415062500000000.1	x^16 - 28x^12 + 119x^8 - 150x^6 + 73x^4 - 15x^2 + 1	\( 2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 29^{4} \)	$C_2^2.C_2^5.C_2$ (as 16T610)	Trivial (GRH)
16.12.290029415062500000000.2	x^16 - 13x^14 + 56x^12 - 64x^10 - 141x^8 + 348x^6 - 156x^4 - x^2 + 1	\( 2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 29^{4} \)	$C_2^2.C_2^5.C_2$ (as 16T610)	Trivial (GRH)
16.12.302231793843017578125.1	x^16 - x^15 - 10x^14 - 4x^13 + 28x^12 + 43x^11 + 14x^10 - 28x^9 - 114x^8 - 156x^7 + 37x^6 + 162x^5 + 25x^4 - 51x^3 - 11x^2 + 5x + 1	\( 3^{8}\cdot 5^{12}\cdot 181\cdot 1021^{2} \)	16T1771	Trivial (GRH)
16.12.307463056776831238144.1	x^16 - 5x^14 + 23x^10 - 11x^8 - 28x^6 + 30x^4 - 10x^2 + 1	\( 2^{16}\cdot 811^{2}\cdot 84457^{2} \)	16T1945	Trivial (GRH)
16.12.311946891241987732329.1	x^16 - 8x^15 + 22x^14 - 14x^13 - 59x^12 + 172x^11 - 165x^10 - 132x^9 + 425x^8 - 160x^7 - 285x^6 + 188x^5 + 74x^4 - 56x^3 - 9x^2 + 6x + 1	\( 3^{2}\cdot 277^{8} \)	$C_2^3.Q_8.C_6$ (as 16T732)	Trivial (GRH)
16.12.332590791101555078125.1	x^16 - 8x^15 + 19x^14 + 7x^13 - 86x^12 + 61x^11 + 140x^10 - 139x^9 - 157x^8 + 131x^7 + 161x^6 - 76x^5 - 104x^4 + 28x^3 + 27x^2 - 5x - 1	\( 5^{8}\cdot 11\cdot 29\cdot 139\cdot 138571^{2} \)	16T1905	Trivial
16.12.365421456000000000000.1	x^16 - 2x^15 - 10x^14 + 32x^13 + 4x^12 - 146x^11 + 189x^10 + 144x^9 - 439x^8 + 152x^7 + 251x^6 - 202x^5 - 16x^4 + 56x^3 - 10x^2 - 4x + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 59^{2} \)	16T1102	Trivial (GRH)
16.12.365421456000000000000.2	x^16 - 2x^14 - 5x^12 - 7x^10 + 69x^8 - 98x^6 + 55x^4 - 13x^2 + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 59^{2} \)	$C_2\times C_2\wr C_4$ (as 16T261)	Trivial (GRH)
16.12.365421456000000000000.3	x^16 - 10x^14 + 38x^12 - 70x^10 + 69x^8 - 45x^6 + 27x^4 - 10x^2 + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 59^{2} \)	16T1385	Trivial (GRH)
16.12.367725112345600000000.1	x^16 - 8x^14 + 26x^12 - 55x^10 + 103x^8 - 147x^6 + 115x^4 - 35x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 119851^{2} \)	16T1868	Trivial (GRH)
16.12.390615696000000000000.1	x^16 - 3x^14 - 4x^13 - 27x^12 + 34x^11 + 85x^10 + 10x^9 - 79x^8 - 324x^7 + 335x^6 + 268x^5 - 490x^4 + 230x^3 - 32x^2 - 4x + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 61^{2} \)	16T1102	Trivial (GRH)
16.12.411187550617600000000.1	x^16 - 15x^14 + 85x^12 - 235x^10 + 352x^8 - 285x^6 + 115x^4 - 20x^2 + 1	\( 2^{24}\cdot 5^{8}\cdot 89^{4} \)	16T1116	Trivial (GRH)
16.12.466359573529600000000.1	x^16 - 8x^14 + 21x^12 - 17x^10 - 5x^8 + 2x^6 + 11x^4 - 7x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 71^{2}\cdot 1901^{2} \)	16T1868	Trivial (GRH)
16.12.524628581602100000000.1	x^16 - 16x^14 + 107x^12 - 394x^10 + 883x^8 - 1246x^6 + 1083x^4 - 520x^2 + 101	\( 2^{8}\cdot 5^{8}\cdot 29^{4}\cdot 101\cdot 271^{2} \)	16T1823	Trivial (GRH)
16.12.671846400000000000000.1	x^16 - 2x^15 - 16x^14 + 8x^13 + 113x^12 + 108x^11 - 294x^10 - 776x^9 - 297x^8 + 1148x^7 + 1764x^6 + 894x^5 + 13x^4 - 124x^3 - 24x^2 + 4x + 1	\( 2^{24}\cdot 3^{8}\cdot 5^{14} \)	$C_2\times C_2\wr C_4$ (as 16T261)	Trivial (GRH)
16.12.673301391207980597248.1	x^16 - 4x^15 + 2x^14 - 4x^13 + 13x^12 + 76x^11 - 80x^10 - 232x^9 + 81x^8 + 320x^7 + 36x^6 - 180x^5 - 51x^4 + 44x^3 + 14x^2 - 4x - 1	\( 2^{44}\cdot 337^{3} \)	16T1251	Trivial
16.12.673301391207980597248.2	x^16 - 12x^14 - 4x^13 + 48x^12 + 32x^11 - 78x^10 - 84x^9 + 78x^8 + 84x^7 - 88x^6 + 12x^5 + 37x^4 - 36x^3 + 6x^2 + 4x - 1	\( 2^{44}\cdot 337^{3} \)	16T1251	Trivial
16.12.687865856000000000000.1	x^16 - 10x^14 - 4x^13 + 26x^12 + 40x^11 - 14x^10 - 108x^9 + 21x^8 + 136x^7 - 82x^6 - 72x^5 + 82x^4 + 4x^3 - 24x^2 + 4x + 1	\( 2^{36}\cdot 5^{12}\cdot 41 \)	16T1379	Trivial (GRH)
16.12.700762351958879698944.1	x^16 - 9x^14 + 19x^12 + 2x^10 - 27x^8 + 2x^6 + 19x^4 - 9x^2 + 1	\( 2^{16}\cdot 3^{6}\cdot 19^{4}\cdot 103^{4} \)	16T1664	Trivial (GRH)
16.12.732780301186512843008.1	x^16 - 3x^15 - 8x^14 + 24x^13 + 30x^12 - 56x^11 - 121x^10 + 23x^9 + 441x^8 - 48x^7 - 842x^6 + 384x^5 + 616x^4 - 488x^3 - 32x^2 + 96x - 16	\( 2^{8}\cdot 17^{15} \)	$(C_2\times C_8).D_4$ (as 16T306)	Trivial (GRH)
16.12.741813314062500000000.1	x^16 - 9x^14 + 27x^12 - 22x^10 - 35x^8 + 72x^6 - 38x^4 + 4x^2 + 1	\( 2^{8}\cdot 3^{8}\cdot 5^{14}\cdot 269^{2} \)	16T1720	Trivial (GRH)
16.12.781528990105600000000.1	x^16 - 8x^14 + 19x^12 - 19x^10 + 36x^8 - 81x^6 + 69x^4 - 17x^2 + 1	\( 2^{20}\cdot 5^{8}\cdot 11^{4}\cdot 19^{4} \)	16T919	Trivial (GRH)
16.12.813503926129374655621.1	x^16 - 8x^15 + 17x^14 + 21x^13 - 111x^12 + 29x^11 + 272x^10 - 172x^9 - 373x^8 + 269x^7 + 315x^6 - 207x^5 - 147x^4 + 80x^3 + 26x^2 - 12x + 1	\( 53^{2}\cdot 1229^{2}\cdot 1483^{2}\cdot 87181 \)	16T1948	Trivial
16.12.823293534364242578125.1	x^16 - 8x^15 + 17x^14 + 21x^13 - 118x^12 + 71x^11 + 216x^10 - 277x^9 - 110x^8 + 309x^7 - 57x^6 - 134x^5 + 67x^4 + 18x^3 - 16x^2 + 1	\( 5^{8}\cdot 19\cdot 29^{4}\cdot 79\cdot 1409^{2} \)	16T1823	Trivial (GRH)
16.12.836463237075121995776.1	x^16 - 8x^14 - 8x^13 + 14x^12 + 80x^11 + 8x^10 - 184x^9 - 216x^8 + 208x^7 + 600x^6 - 224x^5 - 608x^4 + 192x^3 + 224x^2 - 64x - 16	\( 2^{32}\cdot 41^{7} \)	16T1606	Trivial (GRH)
16.12.845468605385858351104.1	x^16 - 8x^15 + 18x^14 + 8x^13 - 78x^12 + 88x^11 - 10x^10 - 74x^9 + 175x^8 - 168x^7 - 62x^6 + 194x^5 - 49x^4 - 74x^3 + 27x^2 + 14x - 1	\( 2^{24}\cdot 41^{6}\cdot 103^{2} \)	16T876	Trivial (GRH)
16.12.905475719089201229649.1	x^16 - 8x^15 + 24x^14 - 28x^13 - 39x^12 + 234x^11 - 381x^10 + 46x^9 + 654x^8 - 890x^7 + 425x^6 + 78x^5 - 176x^4 + 64x^3 + 2x^2 - 6x + 1	\( 3^{8}\cdot 19^{4}\cdot 97^{2}\cdot 103^{4} \)	16T1664	Trivial (GRH)
16.12.921365448100612734976.1	x^16 - 10x^14 + 35x^12 - 55x^10 + 54x^8 - 55x^6 + 35x^4 - 10x^2 + 1	\( 2^{16}\cdot 10889^{4} \)	16T1538	Trivial (GRH)
16.12.1017606619113208152064.1	x^16 - 2x^15 - 13x^14 + 20x^13 + 73x^12 - 56x^11 - 265x^10 + 26x^9 + 617x^8 + 88x^7 - 744x^6 - 200x^5 + 400x^4 + 240x^3 - 136x^2 - 64x + 16	\( 2^{24}\cdot 41^{6}\cdot 113^{2} \)	16T1429	Trivial
16.12.1158738620062500000000.1	x^16 - 5x^14 - 13x^12 + 130x^10 - 311x^8 + 320x^6 - 142x^4 + 20x^2 + 1	\( 2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 41^{4} \)	16T1392	Trivial (GRH)
16.12.1180591620717411303424.1	x^16 - 16x^14 + 76x^12 - 32x^11 - 160x^10 + 144x^9 + 130x^8 - 208x^7 + 16x^6 + 112x^5 - 60x^4 - 16x^3 + 16x^2 - 1	\( 2^{70} \)	$C_2^5.C_2.C_2$ (as 16T258)	Trivial (GRH)
16.12.1186620610969600000000.1	x^16 - 10x^14 + 31x^12 - 42x^10 + 61x^8 - 76x^6 + 47x^4 - 12x^2 + 1	\( 2^{32}\cdot 5^{8}\cdot 29^{4} \)	$C_2\times D_4^2.C_2$ (as 16T509)	Trivial (GRH)
16.12.1186620610969600000000.2	x^16 - 8x^14 + 37x^12 - 110x^10 + 190x^8 - 176x^6 + 80x^4 - 16x^2 + 1	\( 2^{32}\cdot 5^{8}\cdot 29^{4} \)	$C_2\times D_4^2.C_2$ (as 16T509)	Trivial (GRH)
16.12.1250616032402500000000.1	x^16 - 3x^14 - 20x^12 + 99x^10 - 121x^8 - 45x^6 + 190x^4 - 125x^2 + 25	\( 2^{8}\cdot 5^{10}\cdot 29^{8} \)	$C_4^2:C_2^2.C_2$ (as 16T406)	Trivial (GRH)
16.12.1250616032402500000000.2	x^16 - 3x^14 - 22x^12 + 82x^10 + 41x^8 - 430x^6 + 530x^4 - 225x^2 + 25	\( 2^{8}\cdot 5^{10}\cdot 29^{8} \)	16T984	Trivial (GRH)