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 171)

Label	Polynomial	Discriminant	Galois group	Class group
16.2.13972911310408283.1	x^16 - 2x^15 + 2x^14 - 7x^13 + 10x^12 - 10x^11 + 19x^10 - 18x^9 + 18x^8 - 22x^7 + 13x^6 - 14x^5 + 8x^4 - 3x^3 + 4x^2 + x + 1	\( -\,4271\cdot 22247\cdot 147057059 \)	$S_{16}$ (as 16T1954)	Trivial
16.2.15968672198702159.1	x^16 - x^14 + x^12 - 3x^11 - 4x^10 + 5x^9 + 3x^8 - x^7 - 2x^6 + 2x^5 - 5x^3 + 3x^2 + x - 1	\( -\,15968672198702159 \)	$S_{16}$ (as 16T1954)	Trivial
16.4.166581322179183497.1	x^16 - 4x^15 + 7x^14 - 5x^13 - 6x^12 + 20x^11 - 28x^10 + 26x^9 - 19x^8 + 10x^7 + 3x^6 - 16x^5 + 21x^4 - 14x^3 + 3x^2 + x - 1	\( 1609\cdot 15809\cdot 31393\cdot 208609 \)	$S_{16}$ (as 16T1954)	Trivial
16.4.286362324116320597.1	x^16 - 2x^15 + 6x^13 - 6x^12 + 2x^11 - 8x^10 + 6x^9 + x^8 + 3x^7 - 7x^6 + 8x^5 - 12x^4 + 13x^3 - 5x^2 + 1	\( 5120891\cdot 55920409967 \)	$S_{16}$ (as 16T1954)	Trivial
16.4.318801818760934469.1	x^16 - 3x^15 + 5x^14 - 4x^13 - 4x^12 + 11x^11 - 6x^10 - 14x^9 + 41x^8 - 49x^7 + 36x^6 - 12x^5 - 7x^4 + 12x^3 - 10x^2 + 5x - 1	\( 31\cdot 59\cdot 11549\cdot 15092552789 \)	$S_{16}$ (as 16T1954)	Trivial
16.6.378431998703576723.1	x^16 - 3x^14 - 4x^13 + x^12 + 4x^11 + 6x^9 + 7x^8 - 5x^7 - 14x^6 - x^5 + 12x^4 - 6x^2 + 1	\( -\,79\cdot 4501009\cdot 1064267693 \)	$S_{16}$ (as 16T1954)	Trivial
16.0.1049713133796375193.1	x^16 + x^14 + 2x^12 + 3x^10 + 3x^8 + 3x^6 - x^5 + 3x^4 + 2x^2 + 1	\( 1948109\cdot 538836961277 \)	$S_{16}$ (as 16T1954)	Trivial
16.6.2255320901676777119.1	x^16 - 3x^15 + 4x^14 - 7x^13 + 12x^12 - 21x^11 + 28x^10 - 30x^9 + 34x^8 - 38x^7 + 51x^6 - 51x^5 + 27x^4 + 3x^3 - 17x^2 + 9x - 1	\( -\,167\cdot 13504915578902857 \)	$S_{16}$ (as 16T1954)	Trivial
16.0.18008850183328692241.1	x^16 - x + 1	\( 109\cdot 165218809021364149 \)	$S_{16}$ (as 16T1954)	Trivial
16.2.18884637964090410991.1	x^16 - x - 1	\( -\,227\cdot 246027323\cdot 338142271 \)	$S_{16}$ (as 16T1954)	Trivial
16.2.37996459452980338388.1	x^16 - 3x^15 + 2x^14 + 3x^13 - 7x^12 + 3x^11 + 9x^10 - 9x^9 - 6x^8 + 8x^7 - 6x^5 + 3x^4 + 5x^3 - x^2 - 3x - 1	\( -\,2^{2}\cdot 13\cdot 491\cdot 1861\cdot 17729\cdot 45105311 \)	$S_{16}$ (as 16T1954)	Trivial
16.2.435088857471835120220.1	x^16 - 2x^15 - 3x^14 + 8x^13 + x^12 - 10x^11 + 4x^10 + 3x^9 - 5x^8 + 2x^7 + 2x^6 + 3x^4 - 3x^3 - 4x^2 + 1	\( -\,2^{2}\cdot 5\cdot 29\cdot 864859789\cdot 867369731 \)	$S_{16}$ (as 16T1954)	Trivial
16.0.7457144311678317217216.1	x^16 - 3x^15 + 4x^14 - 2x^13 - 4x^12 + 8x^11 - 5x^10 - x^9 + 7x^8 - 5x^7 - x^6 + 4x^5 - 2x^4 - 4x^3 + x^2 + 3x + 1	\( 2^{6}\cdot 1555117\cdot 74925474977107 \)	$S_{16}$ (as 16T1954)	Trivial
16.2.28697814281474976710656.1	x^16 - 4x - 1	\( -\,2^{16}\cdot 197\cdot 2222811648100643 \)	$S_{16}$ (as 16T1954)	Trivial (GRH)
16.2.28716260744073709551616.1	x^16 - 2x - 1	\( -\,2^{16}\cdot 19\cdot 824911\cdot 27956787259 \)	$S_{16}$ (as 16T1954)	Trivial (GRH)
16.4.54592316476665023114704.1	x^16 - 3x^15 + 5x^14 - 4x^13 - 2x^12 + 13x^11 - 23x^10 + 24x^9 - 14x^8 - 2x^7 + 14x^6 - 17x^5 + 10x^4 - 2x^3 - 2x^2 + x - 1	\( 2^{4}\cdot 113\cdot 5601191\cdot 5390793727243 \)	$S_{16}$ (as 16T1954)	Trivial (GRH)
16.4.101399053047272716481537.1	x^16 - 3x^15 + 5x^14 - 4x^13 - 2x^12 + 13x^11 - 23x^10 + 24x^9 - 14x^8 - 2x^7 + 14x^6 - 17x^5 + 9x^4 - 2x^3 - 2x^2 + 2x - 1	\( 11\cdot 38371\cdot 8394161\cdot 28619418257 \)	$S_{16}$ (as 16T1954)	Trivial (GRH)
16.8.151540380182821271395392.1	x^16 - x^15 - 12x^14 + 8x^13 + 58x^12 - 19x^11 - 145x^10 + 2x^9 + 201x^8 + 46x^7 - 155x^6 - 51x^5 + 64x^4 + 19x^3 - 13x^2 - 2x + 1	\( 2^{6}\cdot 3^{3}\cdot 370147\cdot 236924733342337 \)	$S_{16}$ (as 16T1954)	Trivial (GRH)
16.0.273533640903657293676544.1	x^16 - 4x + 4	\( 2^{16}\cdot 20693\cdot 201700677912653 \)	$S_{16}$ (as 16T1954)	Trivial (GRH)
16.2.314733193346436850809207.1	x^16 - x - 3	\( -\,3^{16}\cdot 1042081\cdot 7016184407 \)	$S_{16}$ (as 16T1954)	Trivial
16.2.330929268903657293676544.1	x^16 - 4x - 4	\( -\,2^{16}\cdot 295081\cdot 17112521337559 \)	$S_{16}$ (as 16T1954)	Trivial (GRH)
16.0.489671653807314587353088.1	x^16 - 8x + 8	\( 2^{18}\cdot 136813\cdot 13653301359029 \)	$S_{16}$ (as 16T1954)	Trivial
16.0.575765095807314587353088.1	x^16 - 2x + 2	\( 2^{16}\cdot 7\cdot 13\cdot 223\cdot 857\cdot 444517\cdot 1136449 \)	$S_{16}$ (as 16T1954)	Trivial (GRH)
16.0.604462471913424206493713.1	x^16 - x + 2	\( 604462471913424206493713 \)	$S_{16}$ (as 16T1954)	Trivial
16.2.633160723807314587353088.1	x^16 - 2x - 2	\( -\,2^{16}\cdot 17\cdot 113\cdot 1487\cdot 75169\cdot 44994241 \)	$S_{16}$ (as 16T1954)	Trivial
16.2.719254165807314587353088.1	x^16 - 8x - 8	\( -\,2^{18}\cdot 397\cdot 45658453\cdot 151366847 \)	$S_{16}$ (as 16T1954)	Trivial
16.12.1282292012961255316565852.1	x^16 - 3x^15 - 8x^14 + 31x^13 + 16x^12 - 124x^11 + 22x^10 + 243x^9 - 114x^8 - 244x^7 + 138x^6 + 119x^5 - 68x^4 - 26x^3 + 14x^2 + 2x - 1	\( 2^{2}\cdot 53\cdot 139\cdot 176431\cdot 3604141\cdot 68432059 \)	$S_{16}$ (as 16T1954)	Trivial (GRH)
16.14.1426559715404800186341167.1	x^16 - 4x^15 - 8x^14 + 46x^13 + 13x^12 - 207x^11 + 52x^10 + 458x^9 - 222x^8 - 508x^7 + 303x^6 + 248x^5 - 162x^4 - 32x^3 + 24x^2 - 1	\( -\,26683\cdot 327203\cdot 163394721598783 \)	$S_{16}$ (as 16T1954)	Trivial (GRH)
16.6.2491013550219327741414056.1	x^16 - x^15 - 6x^14 + 5x^13 + 13x^12 - 5x^11 - 14x^10 - 10x^9 + 10x^8 + 21x^7 - 2x^6 - 9x^5 - 9x^4 - 2x^3 + 6x^2 + x - 1	\( -\,2^{3}\cdot 149\cdot 223\cdot 373717\cdot 25075645274723 \)	$S_{16}$ (as 16T1954)	Trivial (GRH)
16.14.4744409156200506114809192.1	x^16 - 4x^15 - 9x^14 + 48x^13 + 24x^12 - 227x^11 + 6x^10 + 532x^9 - 134x^8 - 635x^7 + 234x^6 + 352x^5 - 156x^4 - 68x^3 + 33x^2 + 4x - 2	\( -\,2^{3}\cdot 1259\cdot 99923\cdot 4714123477341757 \)	$S_{16}$ (as 16T1954)	Trivial (GRH)
16.10.7265701227754780855817252.1	x^16 - x^15 - 15x^14 + 13x^13 + 88x^12 - 66x^11 - 256x^10 + 168x^9 + 390x^8 - 229x^7 - 305x^6 + 168x^5 + 113x^4 - 62x^3 - 13x^2 + 9x - 1	\( -\,2^{2}\cdot 73\cdot 151\cdot 181\cdot 910414490915627051 \)	$S_{16}$ (as 16T1954)	Trivial (GRH)
16.2.7345459792379282588696576.1	x^16 - 8x + 4	\( -\,2^{24}\cdot 137\cdot 3195792128734903 \)	$S_{16}$ (as 16T1954)	Trivial (GRH)
16.2.7346640384001099511627776.1	x^16 - 8x - 1	\( -\,2^{24}\cdot 137153\cdot 3192740154287 \)	$S_{16}$ (as 16T1954)	Trivial (GRH)
16.2.7347820975620717411303424.1	x^16 - 8x - 4	\( -\,2^{24}\cdot 109\cdot 167\cdot 3061\cdot 7860177833 \)	$S_{16}$ (as 16T1954)	Trivial (GRH)
16.8.7909134166471626697078276.1	x^16 - x^15 - 12x^14 + 8x^13 + 58x^12 - 19x^11 - 145x^10 + 2x^9 + 201x^8 + 45x^7 - 155x^6 - 51x^5 + 64x^4 + 20x^3 - 13x^2 - 2x + 1	\( 2^{2}\cdot 19\cdot 24796309\cdot 4196896998742639 \)	$S_{16}$ (as 16T1954)	Trivial (GRH)
16.6.8099259377430593116830604.1	x^16 - 2x^15 - x^14 + 5x^13 - 5x^12 + 2x^11 + 4x^10 - 10x^9 + 8x^8 + x^7 - 7x^6 + 3x^5 - 2x^4 + 2x^3 + 5x^2 - x - 1	\( -\,2^{2}\cdot 241\cdot 8401721345882358005011 \)	$S_{16}$ (as 16T1954)	Trivial (GRH)
16.2.18849877680085363546307759.1	x^16 - 3x + 1	\( -\,2774287\cdot 6794494470141468257 \)	$S_{16}$ (as 16T1954)	Trivial (GRH)
16.2.18849914573573510965410991.1	x^16 - 3x - 1	\( -\,159416449\cdot 118243222025184559 \)	$S_{16}$ (as 16T1954)	Trivial (GRH)
16.2.19454359036636751843212463.1	x^16 - 3x - 2	\( -\,17\cdot 29\cdot 39461174516504567633291 \)	$S_{16}$ (as 16T1954)	Trivial (GRH)
16.0.69380308928657063127368529.1	x^16 - 9x + 9	\( 3^{14}\cdot 7\cdot 4726261\cdot 438452874883 \)	$S_{16}$ (as 16T1954)	$[2]$ (GRH)
16.2.107080101182315937639087279.1	x^16 - 9x - 9	\( -\,3^{14}\cdot 22387789087137285991 \)	$S_{16}$ (as 16T1954)	Trivial (GRH)
16.16.118534508977374409590072933.1	x^16 - 2x^15 - 14x^14 + 25x^13 + 80x^12 - 120x^11 - 238x^10 + 276x^9 + 387x^8 - 311x^7 - 330x^6 + 160x^5 + 133x^4 - 32x^3 - 21x^2 + 2x + 1	\( 3\cdot 163\cdot 1069\cdot 63409\cdot 3576080911949057 \)	$S_{16}$ (as 16T1954)	Trivial (GRH)
16.10.221366558579588537003690416.1	x^16 - x^15 - 15x^14 + 13x^13 + 88x^12 - 66x^11 - 256x^10 + 168x^9 + 390x^8 - 229x^7 - 305x^6 + 168x^5 + 112x^4 - 62x^3 - 12x^2 + 9x - 1	\( -\,2^{4}\cdot 103\cdot 541\cdot 248289035249794224337 \)	$S_{16}$ (as 16T1954)	Trivial (GRH)
16.0.245840719039630063893824337.1	x^16 - 3x + 3	\( 3^{15}\cdot 101\cdot 4079\cdot 41587222655929 \)	$S_{16}$ (as 16T1954)	$[2]$ (GRH)
16.0.264661917352459501149683712.1	x^16 - 2x + 3	\( 2^{16}\cdot 3^{15}\cdot 139\cdot 449\cdot 4509532921 \)	$S_{16}$ (as 16T1954)	Trivial (GRH)
16.0.264690614728565610768824337.1	x^16 - x + 3	\( 3^{15}\cdot 18446744043191973491 \)	$S_{16}$ (as 16T1954)	Trivial (GRH)
16.16.278700300143135527087206569.1	x^16 - x^15 - 16x^14 + 13x^13 + 101x^12 - 63x^11 - 317x^10 + 141x^9 + 513x^8 - 149x^7 - 407x^6 + 73x^5 + 145x^4 - 16x^3 - 21x^2 + x + 1	\( 452134162759\cdot 616410621224591 \)	$S_{16}$ (as 16T1954)	Trivial (GRH)
16.2.283540511293288938405543087.1	x^16 - 3x - 3	\( -\,3^{15}\cdot 23\cdot 1523\cdot 564116182159129 \)	$S_{16}$ (as 16T1954)	Trivial (GRH)
16.2.411212550854000000000000000.1	x^16 - 2x - 5	\( -\,2^{16}\cdot 5^{15}\cdot 7\cdot 43\cdot 157\cdot 463\cdot 9397 \)	$S_{16}$ (as 16T1954)	Trivial (GRH)
16.0.1336291067629612758778052608.1	x^16 - 4x + 7	\( 2^{16}\cdot 10159\cdot 2007105377208699967 \)	$S_{16}$ (as 16T1954)	Trivial (GRH)