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 62)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.8336000000000000.1	x^16 - 4x^15 + 7x^14 - 8x^13 + 7x^12 - 2x^10 - 6x^9 + 5x^8 + 6x^7 - 2x^6 + 7x^4 + 8x^3 + 7x^2 + 4x + 1	\( 2^{16}\cdot 5^{12}\cdot 521 \)	16T1616	Trivial
16.0.10065687500000000.1	x^16 - 3x^15 + 4x^14 - 3x^13 + 10x^12 - 25x^11 + 35x^10 - 39x^9 + 52x^8 - 66x^7 + 72x^6 - 80x^5 + 82x^4 - 61x^3 + 29x^2 - 8x + 1	\( 2^{8}\cdot 5^{12}\cdot 11^{5} \)	16T1616	Trivial
16.0.162488139892578125.1	x^16 - 8x^15 + 27x^14 - 49x^13 + 49x^12 - 21x^11 - 6x^10 + 8x^9 + 13x^8 - 45x^7 + 70x^6 - 70x^5 + 52x^4 - 31x^3 + 9x^2 + x + 1	\( 5^{12}\cdot 29^{4}\cdot 941 \)	16T1616	Trivial
16.0.24026314848876953125.1	x^16 - 8x^15 + 31x^14 - 77x^13 + 138x^12 - 191x^11 + 211x^10 - 186x^9 + 131x^8 - 79x^7 + 41x^6 - 10x^5 - 7x^3 + 2x^2 + 3x + 1	\( 5^{12}\cdot 29^{4}\cdot 61\cdot 2281 \)	16T1616	Trivial
16.4.24283409190781714432.1	x^16 - 8x^15 + 24x^14 - 24x^13 - 36x^12 + 120x^11 - 88x^10 - 80x^9 + 166x^8 - 56x^7 - 56x^6 + 40x^5 - 12x^4 + 8x^3 - 1	\( 2^{56}\cdot 337 \)	16T1616	Trivial
16.4.24283409190781714432.2	x^16 - 8x^15 + 32x^14 - 80x^13 + 132x^12 - 136x^11 + 56x^10 + 72x^9 - 166x^8 + 184x^7 - 160x^6 + 128x^5 - 100x^4 + 72x^3 - 32x^2 + 8x - 1	\( 2^{56}\cdot 337 \)	16T1616	Trivial
16.2.29288304000000000000.1	x^16 - 4x^15 + 5x^14 - 2x^13 + 4x^12 - 18x^11 + 20x^10 + 40x^9 - 104x^8 + 20x^7 + 215x^6 - 366x^5 + 241x^4 - 58x^3 + 2x^2 - 2x + 1	\( -\,2^{16}\cdot 3^{10}\cdot 5^{12}\cdot 31 \)	16T1616	Trivial
16.2.30018625312500000000.1	x^16 - 4x^15 + x^14 + 24x^13 - 48x^12 + 4x^11 + 91x^10 - 93x^9 - 16x^8 + 77x^7 - 47x^6 + 15x^5 + 21x^4 - 35x^3 + 15x - 5	\( -\,2^{8}\cdot 3^{8}\cdot 5^{13}\cdot 11^{4} \)	16T1616	Trivial
16.6.30018625312500000000.1	x^16 - 3x^14 - 16x^12 - 2x^10 + 66x^8 - 5x^6 - 30x^4 + 10x^2 - 5	\( -\,2^{8}\cdot 3^{8}\cdot 5^{13}\cdot 11^{4} \)	16T1616	Trivial
16.6.30018625312500000000.2	x^16 - 2x^14 - x^12 + 7x^10 - 24x^8 + 45x^6 - 45x^4 + 25x^2 - 5	\( -\,2^{8}\cdot 3^{8}\cdot 5^{13}\cdot 11^{4} \)	16T1616	Trivial
16.8.69108571557861328125.1	x^16 - 3x^15 - 6x^14 + 15x^13 + 3x^12 - 15x^11 + 6x^10 - 12x^9 + 23x^8 - 12x^7 + 6x^6 - 15x^5 + 3x^4 + 15x^3 - 6x^2 - 3x + 1	\( 3^{8}\cdot 5^{12}\cdot 29^{4}\cdot 61 \)	16T1616	Trivial (GRH)
16.8.69108571557861328125.2	x^16 - x^15 - 8x^14 + 16x^13 + x^12 - 35x^11 + 38x^10 + 5x^9 - 33x^8 + 5x^7 + 38x^6 - 35x^5 + x^4 + 16x^3 - 8x^2 - x + 1	\( 3^{8}\cdot 5^{12}\cdot 29^{4}\cdot 61 \)	16T1616	Trivial (GRH)
16.4.130280130020573708288.1	x^16 - 8x^14 - 8x^13 + 16x^12 + 32x^11 + 16x^10 + 8x^9 - 30x^8 - 128x^7 - 48x^6 + 232x^5 + 336x^4 + 208x^3 + 72x^2 + 8x - 1	\( 2^{60}\cdot 113 \)	16T1616	Trivial
16.4.130280130020573708288.2	x^16 + 8x^14 - 8x^13 + 16x^12 - 48x^11 + 48x^10 - 72x^9 + 98x^8 - 128x^7 + 32x^6 - 72x^5 + 48x^4 + 32x^3 - 24x^2 + 8x - 1	\( 2^{60}\cdot 113 \)	16T1616	Trivial
16.10.202794005063232421875.1	x^16 - 10x^14 - 10x^13 + 29x^12 + 70x^11 + 25x^10 - 105x^9 - 179x^8 - 105x^7 + 25x^6 + 70x^5 + 29x^4 - 10x^3 - 10x^2 + 1	\( -\,3^{8}\cdot 5^{12}\cdot 29^{4}\cdot 179 \)	16T1616	Trivial (GRH)
16.6.202794005063232421875.1	x^16 - 2x^15 - 7x^14 + 12x^13 + 33x^12 - 42x^11 - 96x^10 + 71x^9 + 183x^8 - 22x^7 - 249x^6 - 40x^5 + 153x^4 + 86x^3 - 48x^2 - 48x + 16	\( -\,3^{8}\cdot 5^{12}\cdot 29^{4}\cdot 179 \)	16T1616	Trivial (GRH)
16.10.202794005063232421875.2	x^16 - 8x^15 + 29x^14 - 63x^13 + 76x^12 - x^11 - 163x^10 + 276x^9 - 183x^8 - 77x^7 + 243x^6 - 172x^5 + 26x^4 + 31x^3 - 14x^2 - x + 1	\( -\,3^{8}\cdot 5^{12}\cdot 29^{4}\cdot 179 \)	16T1616	Trivial (GRH)
16.6.202794005063232421875.2	x^16 - 2x^15 - 3x^14 + 9x^13 - 2x^12 - 20x^11 - 4x^10 + 77x^9 + 8x^8 - 161x^7 + 74x^6 + 67x^5 - 42x^4 - 2x^3 - 2x^2 + 2x + 1	\( -\,3^{8}\cdot 5^{12}\cdot 29^{4}\cdot 179 \)	16T1616	Trivial (GRH)
16.0.259035136000000000000.1	x^16 - 2x^15 + 14x^14 - 28x^13 + 97x^12 - 174x^11 + 402x^10 - 572x^9 + 971x^8 - 986x^7 + 1284x^6 - 760x^5 + 806x^4 - 88x^3 + 240x^2 + 80x + 76	\( 2^{24}\cdot 5^{12}\cdot 63241 \)	16T1616	$[2]$ (GRH)
16.8.259035136000000000000.1	x^16 - 8x^15 + 18x^14 + 14x^13 - 102x^12 + 66x^11 + 178x^10 - 208x^9 - 140x^8 + 246x^7 + 32x^6 - 136x^5 + 21x^4 + 26x^3 - 8x^2 + 1	\( 2^{24}\cdot 5^{12}\cdot 63241 \)	16T1616	Trivial (GRH)
16.0.388534547052507430912.1	x^16 - 8x^15 + 40x^14 - 136x^13 + 340x^12 - 672x^11 + 1112x^10 - 1600x^9 + 2024x^8 - 2192x^7 + 2024x^6 - 1664x^5 + 1144x^4 - 560x^3 + 208x^2 - 32x + 2	\( 2^{60}\cdot 337 \)	16T1616	Trivial
16.8.388534547052507430912.1	x^16 - 8x^15 + 24x^14 - 16x^13 - 96x^12 + 248x^11 - 64x^10 - 384x^9 + 142x^8 + 552x^7 - 288x^6 - 256x^5 + 32x^4 + 136x^3 - 8x^2 - 16x - 1	\( 2^{60}\cdot 337 \)	16T1616	Trivial (GRH)
16.8.7337169152817626953125.1	x^16 - 5x^15 + 3x^14 + 29x^13 - 68x^12 + 14x^11 + 146x^10 - 233x^9 + 105x^8 + 132x^7 - 242x^6 + 167x^5 - 43x^4 - 21x^3 + 23x^2 - 8x + 1	\( 3^{8}\cdot 5^{12}\cdot 41^{4}\cdot 1621 \)	16T1616	Trivial (GRH)
16.8.7886307649414306640625.1	x^16 - 8x^15 + 28x^14 - 56x^13 + 57x^12 + 22x^11 - 167x^10 + 252x^9 - 150x^8 - 98x^7 + 251x^6 - 176x^5 + 27x^4 + 34x^3 - 17x^2 + 1	\( 3^{8}\cdot 5^{12}\cdot 29^{4}\cdot 6961 \)	16T1616	Trivial (GRH)
16.10.8410853036812500000000.1	x^16 - x^14 - 35x^12 + 51x^10 + 244x^8 - 299x^6 - 135x^4 + 174x^2 - 29	\( -\,2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 29^{5} \)	16T1616	Trivial (GRH)
16.14.8410853036812500000000.1	x^16 - 7x^14 - 24x^12 + 314x^10 - 951x^8 + 1292x^6 - 856x^4 + 261x^2 - 29	\( -\,2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 29^{5} \)	16T1616	Trivial (GRH)
16.2.8410853036812500000000.1	x^16 + 16x^14 + 94x^12 + 242x^10 + 204x^8 - 206x^6 - 449x^4 - 232x^2 - 29	\( -\,2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 29^{5} \)	16T1616	Trivial
16.6.8410853036812500000000.1	x^16 - 8x^15 + 25x^14 - 33x^13 - 26x^12 + 208x^11 - 445x^10 + 513x^9 - 274x^8 - 55x^7 + 75x^6 + 165x^5 - 195x^4 - 50x^3 + 200x^2 - 125x + 25	\( -\,2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 29^{5} \)	16T1616	Trivial (GRH)
16.10.8410853036812500000000.2	x^16 - x^15 - 17x^14 + 11x^13 + 102x^12 - 29x^11 - 272x^10 + 9x^9 + 359x^8 + 20x^7 - 121x^6 - 168x^5 - 17x^4 + 225x^3 - 110x^2 + 8x + 1	\( -\,2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 29^{5} \)	16T1616	Trivial (GRH)
16.6.8410853036812500000000.2	x^16 - x^14 - 68x^12 - 233x^10 - 135x^8 + 173x^6 + 142x^4 - 29x^2 - 29	\( -\,2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 29^{5} \)	16T1616	Trivial (GRH)
16.10.8410853036812500000000.3	x^16 - x^15 - 13x^14 + 15x^13 + 45x^12 - 74x^11 - 34x^10 + 65x^9 - x^8 + 260x^7 + 224x^6 - 172x^5 - 320x^4 - 280x^3 + 8x^2 + 112x + 16	\( -\,2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 29^{5} \)	16T1616	Trivial (GRH)
16.6.8410853036812500000000.3	x^16 - 8x^15 + 22x^14 - 8x^13 - 80x^12 + 150x^11 - 19x^10 - 176x^9 + 76x^8 + 126x^7 + 61x^6 - 374x^5 + 218x^4 + 152x^3 - 174x^2 + 18x + 31	\( -\,2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 29^{5} \)	16T1616	Trivial (GRH)
16.10.10428647580562500000000.1	x^16 - 4x^15 - 6x^14 + 59x^13 - 98x^12 - 95x^11 + 575x^10 - 780x^9 + 13x^8 + 1368x^7 - 2016x^6 + 1304x^5 - 96x^4 - 504x^3 + 392x^2 - 128x + 16	\( -\,2^{8}\cdot 3^{10}\cdot 5^{12}\cdot 41^{4} \)	16T1616	Trivial (GRH)
16.6.10428647580562500000000.1	x^16 + 15x^14 + 62x^12 - 341x^8 - 120x^6 + 348x^4 - 45x^2 - 9	\( -\,2^{8}\cdot 3^{10}\cdot 5^{12}\cdot 41^{4} \)	16T1616	Trivial (GRH)
16.4.24578273369184542916608.1	x^16 - 8x^15 + 36x^14 - 112x^13 + 254x^12 - 432x^11 + 524x^10 - 376x^9 - 69x^8 + 640x^7 - 1020x^6 + 1008x^5 - 686x^4 + 320x^3 - 96x^2 + 16x - 1	\( 2^{52}\cdot 7^{4}\cdot 2273 \)	16T1616	$[2]$ (GRH)
16.2.103127737185562500000000.1	x^16 + 21x^14 + 174x^12 + 747x^10 + 1799x^8 + 2409x^6 + 1596x^4 + 303x^2 - 89	\( -\,2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 41^{4}\cdot 89 \)	16T1616	Trivial (GRH)
16.12.118777942016000000000000.1	x^16 - 4x^15 - 6x^14 + 66x^13 - 187x^12 + 252x^11 + 184x^10 - 1592x^9 + 3196x^8 - 3142x^7 + 1104x^6 + 830x^5 - 970x^4 + 214x^3 + 88x^2 - 34x + 1	\( 2^{24}\cdot 5^{12}\cdot 29^{4}\cdot 41 \)	16T1616	Trivial (GRH)
16.4.118777942016000000000000.1	x^16 - 4x^15 + 6x^14 - 6x^13 - 55x^12 + 60x^11 + 80x^10 + 32x^9 - 428x^8 + 762x^7 - 532x^6 - 50x^5 + 242x^4 - 298x^3 + 36x^2 - 6x - 19	\( 2^{24}\cdot 5^{12}\cdot 29^{4}\cdot 41 \)	16T1616	Trivial (GRH)
16.12.118777942016000000000000.2	x^16 - 4x^15 - 18x^14 + 108x^13 - 38x^12 - 604x^11 + 872x^10 + 1024x^9 - 2740x^8 - 24x^7 + 3384x^6 - 1312x^5 - 1688x^4 + 912x^3 + 272x^2 - 160x + 16	\( 2^{24}\cdot 5^{12}\cdot 29^{4}\cdot 41 \)	16T1616	Trivial (GRH)
16.4.118777942016000000000000.2	x^16 - 4x^15 + 18x^14 - 68x^13 + 198x^12 - 440x^11 + 644x^10 - 344x^9 - 1117x^8 + 3108x^7 - 4064x^6 + 2036x^5 + 1538x^4 - 3984x^3 + 3842x^2 - 2004x + 461	\( 2^{24}\cdot 5^{12}\cdot 29^{4}\cdot 41 \)	16T1616	$[2]$ (GRH)
16.14.210271325920312500000000.1	x^16 - x^15 - 24x^14 + 46x^13 + 173x^12 - 506x^11 - 236x^10 + 1853x^9 - 1192x^8 - 1736x^7 + 2296x^6 - 177x^5 - 847x^4 + 373x^3 - 6x^2 - 17x + 1	\( -\,2^{8}\cdot 3^{8}\cdot 5^{14}\cdot 29^{5} \)	16T1616	Trivial (GRH)
16.0.457186438400000000000000.1	x^16 - 4x^15 + x^14 - 6x^13 + 83x^12 - 124x^11 + 19x^10 - 368x^9 + 928x^8 - 314x^7 + 631x^6 - 2608x^5 + 1593x^4 - 808x^3 + 2724x^2 - 1488x + 281	\( 2^{20}\cdot 5^{14}\cdot 29^{4}\cdot 101 \)	16T1616	$[4]$ (GRH)
16.0.457186438400000000000000.2	x^16 - 4x^15 + 19x^14 - 64x^13 + 186x^12 - 412x^11 + 941x^10 - 2012x^9 + 3692x^8 - 4908x^7 + 4661x^6 - 3548x^5 + 2461x^4 - 1876x^3 + 784x^2 - 96x + 236	\( 2^{20}\cdot 5^{14}\cdot 29^{4}\cdot 101 \)	16T1616	$[4]$ (GRH)
16.8.863652760792125157670912.1	x^16 - 8x^15 + 28x^14 - 56x^13 + 62x^12 - 8x^11 - 92x^10 + 152x^9 - 103x^8 - 16x^7 + 88x^6 - 64x^5 + 8x^4 + 16x^3 - 8x^2 + 1	\( 2^{48}\cdot 17^{5}\cdot 2161 \)	16T1616	Trivial (GRH)
16.8.1532918827280000000000000.1	x^16 - 8x^15 + 28x^14 - 56x^13 + 61x^12 - 2x^11 - 107x^10 + 172x^9 - 113x^8 - 30x^7 + 117x^6 - 84x^5 + 12x^4 + 18x^3 - 9x^2 + 1	\( 2^{16}\cdot 5^{13}\cdot 41^{4}\cdot 6781 \)	16T1616	Trivial (GRH)
16.12.1622263383296000000000000.1	x^16 - 2x^15 - 23x^14 + 30x^13 + 178x^12 - 148x^11 - 536x^10 + 378x^9 + 502x^8 - 696x^7 - 87x^6 + 572x^5 + 54x^4 - 174x^3 - 54x^2 + 1	\( 2^{20}\cdot 5^{12}\cdot 89^{4}\cdot 101 \)	16T1616	Trivial (GRH)
16.4.1622263383296000000000000.1	x^16 - 6x^14 - 2x^13 - 27x^12 - 176x^11 + 294x^10 + 276x^9 - 591x^8 - 1226x^7 - 482x^6 + 600x^5 + 752x^4 + 252x^3 - 36x^2 - 64x - 4	\( 2^{20}\cdot 5^{12}\cdot 89^{4}\cdot 101 \)	16T1616	Trivial (GRH)
16.0.2726098620416000000000000.1	x^16 - 8x^15 + 42x^14 - 134x^13 + 339x^12 - 546x^11 + 784x^10 - 472x^9 + 1048x^8 - 120x^7 + 3230x^6 + 4970x^5 - 1418x^4 + 14004x^3 + 7924x^2 + 4096x + 10781	\( 2^{24}\cdot 5^{12}\cdot 29^{4}\cdot 941 \)	16T1616	$[20]$ (GRH)
16.12.2726098620416000000000000.1	x^16 - 4x^15 - 12x^14 + 72x^13 - 52x^12 - 60x^11 - 416x^10 + 1176x^9 + 488x^8 - 4312x^7 + 4776x^6 - 704x^5 - 2152x^4 + 1296x^3 + 112x^2 - 224x + 16	\( 2^{24}\cdot 5^{12}\cdot 29^{4}\cdot 941 \)	16T1616	Trivial (GRH)
16.16.2726098620416000000000000.1	x^16 - 6x^15 - 16x^14 + 160x^13 - 54x^12 - 1468x^11 + 2070x^10 + 5628x^9 - 12828x^8 - 7146x^7 + 32510x^6 - 6376x^5 - 34139x^4 + 19090x^3 + 10136x^2 - 8782x + 1501	\( 2^{24}\cdot 5^{12}\cdot 29^{4}\cdot 941 \)	16T1616	Trivial (GRH)