Global number field search results

Further refine search

Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying all 16 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.2958032106585007347029.1	x^16 - 3x^15 + 11x^14 - 17x^13 - 15x^12 + 77x^11 - 260x^10 + 449x^9 - 103x^8 + 899x^7 - 1043x^6 + 452x^5 + 1270x^4 - 19641x^3 + 44557x^2 - 38536x + 55763	\( 29^{5}\cdot 229^{6} \)	16T1540	$[2]$
16.0.2487705001637991178851389.1	x^16 - 2x^15 + 18x^14 - 22x^13 + 185x^12 + 160x^11 + 1018x^10 + 1793x^9 + 1186x^8 + 1389x^7 + 356x^6 + 1348x^5 + 3918x^4 + 4422x^3 + 4436x^2 + 2396x + 627	\( 29^{7}\cdot 229^{6} \)	16T1540	$[2]$ (GRH)
16.2.120225114802785897280700416.1	x^16 - 6x^15 + 16x^14 + 36x^13 + 140x^12 - 292x^11 + 1777x^10 + 11270x^9 + 22925x^8 + 23814x^7 + 45858x^6 + 109772x^5 - 335441x^4 - 243898x^3 + 67953x^2 - 366316x - 644531	\( -\,2^{18}\cdot 2777^{6} \)	16T1540	Trivial (GRH)
16.2.120225114802785897280700416.2	x^16 - 40x^14 + 913x^12 - 11905x^10 + 86554x^8 - 280033x^6 - 234561x^4 + 3932232x^2 - 7711729	\( -\,2^{18}\cdot 2777^{6} \)	16T1540	$[2]$ (GRH)
16.6.1923601836844574356491206656.1	x^16 - 4x^15 - 3x^14 - 62x^13 - 81x^12 + 406x^11 - 126x^10 - 4020x^9 + 1636x^8 + 14044x^7 - 9588x^6 + 31032x^5 + 72748x^4 - 68136x^3 + 23056x^2 + 52144x - 135176	\( -\,2^{22}\cdot 2777^{6} \)	16T1540	$[2]$ (GRH)
16.6.1923601836844574356491206656.2	x^16 - 8x^15 + 23x^14 + 48x^13 - 278x^12 - 146x^11 + 2075x^10 + 1380x^9 - 26931x^8 + 55838x^7 - 62366x^6 - 20046x^5 + 361957x^4 - 755594x^3 + 106561x^2 + 666172x - 228737	\( -\,2^{22}\cdot 2777^{6} \)	16T1540	$[2]$ (GRH)
16.2.24069030761845230082571042816.1	x^16 + 96x^14 + 4027x^12 + 102629x^10 + 1484794x^8 + 7802516x^6 - 127502953x^4 - 2709088250x^2 - 16448598731	\( -\,2^{16}\cdot 59^{5}\cdot 283^{6} \)	16T1540	$[2]$ (GRH)
16.2.24069030761845230082571042816.2	x^16 + 29x^14 + 351x^12 - 16718x^10 - 723765x^8 - 16329383x^6 - 257317467x^4 - 2787898090x^2 - 16448598731	\( -\,2^{16}\cdot 59^{5}\cdot 283^{6} \)	16T1540	$[2]$ (GRH)
16.4.6329643282720100095594349789184.1	x^16 - 116x^14 + 5797x^12 - 191949x^10 + 2461885x^8 + 18869088x^6 - 1330254716x^4 + 21678166450x^2 + 362422200389	\( 2^{16}\cdot 149^{5}\cdot 331^{6} \)	16T1540	$[2, 2]$ (GRH)
16.4.6329643282720100095594349789184.2	x^16 - 26x^14 - 1462x^12 + 66907x^10 - 1701276x^8 + 18738707x^6 + 630660678x^4 - 23155221181x^2 + 362422200389	\( 2^{16}\cdot 149^{5}\cdot 331^{6} \)	16T1540	Trivial (GRH)
16.0.63032584989723012513503859703808.1	x^16 + 150x^14 + 9022x^12 + 280004x^10 + 4809504x^8 + 45653880x^6 + 226136664x^4 + 493550656x^2 + 246775328	\( 2^{37}\cdot 2777^{6} \)	16T1540	$[2, 4, 13224]$ (GRH)
16.16.63032584989723012513503859703808.1	x^16 - 166x^14 + 7455x^12 - 156124x^10 + 1784928x^8 - 11686200x^6 + 43151292x^4 - 82221416x^2 + 61693832	\( 2^{37}\cdot 2777^{6} \)	16T1540	$[2]$ (GRH)
16.0.63032584989723012513503859703808.2	x^16 + 138x^14 + 7449x^12 + 200900x^10 + 2870766x^8 + 21354056x^6 + 77612932x^4 + 118011392x^2 + 61693832	\( 2^{37}\cdot 2777^{6} \)	16T1540	$[2, 57110]$ (GRH)
16.16.63032584989723012513503859703808.2	x^16 - 138x^14 + 7449x^12 - 200900x^10 + 2870766x^8 - 21354056x^6 + 77612932x^4 - 118011392x^2 + 61693832	\( 2^{37}\cdot 2777^{6} \)	16T1540	$[2]$ (GRH)
16.8.17674106936653806821593702105612288.1	x^16 - 8x^15 + 44x^14 - 48x^13 - 15144x^12 + 116112x^11 - 623602x^10 + 3417148x^9 + 28558154x^8 - 135009802x^7 - 275572557x^6 - 275460052x^5 - 6335264560x^4 - 9237377352x^3 - 24258026543x^2 - 55655339026x + 107356128521	\( 2^{18}\cdot 43^{5}\cdot 2777^{6} \)	16T1540	$[2, 2]$ (GRH)
16.8.17674106936653806821593702105612288.2	x^16 - 8x^15 + 109x^14 - 396x^13 - 7806x^12 + 103132x^11 - 1473708x^10 + 10191282x^9 - 58674377x^8 + 277896694x^7 - 386542951x^6 + 544899228x^5 + 8527873477x^4 - 40290083306x^3 - 98131356986x^2 - 5263574216x + 33687444374	\( 2^{18}\cdot 43^{5}\cdot 2777^{6} \)	16T1540	$[2, 2]$ (GRH)