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 all 50 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.2.26611481600000000.1	x^16 - 2x^15 + 4x^13 - 2x^12 + 7x^10 - 20x^9 - 11x^8 + 28x^7 + x^6 - 4x^5 + 11x^4 - 10x^3 - 5x^2 + 4x - 1	\( -\,2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 71 \)	16T1719	Trivial
16.0.34870903681646592.1	x^16 - 6x^15 + 20x^14 - 46x^13 + 77x^12 - 84x^11 + 35x^10 + 54x^9 - 107x^8 + 78x^7 - 8x^6 - 32x^5 + 27x^4 - 8x^3 + x^2 - 2x + 1	\( 2^{16}\cdot 3^{13}\cdot 7^{4}\cdot 139 \)	16T1719	Trivial
16.0.65306834161051392.1	x^16 - 2x^13 + 2x^12 - 3x^10 - 3x^9 + 3x^8 + 4x^7 - 15x^6 - 3x^5 + 18x^4 + 8x^3 - 3x^2 - x + 1	\( 2^{8}\cdot 3^{12}\cdot 7^{5}\cdot 13^{4} \)	16T1719	Trivial
16.2.190802976100000000.1	x^16 - x^15 - x^14 - 3x^12 - 6x^11 + 5x^10 - x^9 - 4x^8 - x^7 + 5x^6 - 6x^5 - 3x^4 - x^2 - x + 1	\( -\,2^{8}\cdot 5^{8}\cdot 11^{4}\cdot 19^{4} \)	16T1719	Trivial
16.4.2782586470400000000.1	x^16 - 4x^15 + 8x^14 - 10x^13 + 16x^11 - 30x^10 + 40x^9 - 42x^8 + 26x^7 + 32x^6 - 134x^5 + 161x^4 - 20x^3 - 120x^2 + 100x - 25	\( 2^{24}\cdot 5^{8}\cdot 11^{4}\cdot 29 \)	16T1719	Trivial
16.4.2782586470400000000.2	x^16 - 4x^15 + 26x^13 - 49x^12 - 10x^11 + 152x^10 - 194x^9 + 8x^8 + 230x^7 - 312x^6 + 250x^5 - 162x^4 + 96x^3 - 42x^2 + 10x - 1	\( 2^{24}\cdot 5^{8}\cdot 11^{4}\cdot 29 \)	16T1719	Trivial
16.4.2782586470400000000.3	x^16 - 4x^15 + 2x^14 + 6x^13 + 5x^12 - 12x^11 - 60x^10 + 142x^9 - 116x^8 + 56x^7 + 16x^6 - 154x^5 + 226x^4 - 158x^3 + 60x^2 - 12x + 1	\( 2^{24}\cdot 5^{8}\cdot 11^{4}\cdot 29 \)	16T1719	Trivial
16.4.2782586470400000000.4	x^16 - 4x^15 + 10x^14 - 30x^13 + 74x^12 - 122x^11 + 164x^10 - 216x^9 + 231x^8 - 134x^7 - 32x^6 + 132x^5 - 110x^4 + 46x^3 - 10x^2 - 2x + 1	\( 2^{24}\cdot 5^{8}\cdot 11^{4}\cdot 29 \)	16T1719	Trivial
16.0.3625256545900000000.1	x^16 + 2x^14 + 2x^12 + 7x^8 + 6x^6 + 21x^4 + 13x^2 + 19	\( 2^{8}\cdot 5^{8}\cdot 11^{4}\cdot 19^{5} \)	16T1719	Trivial
16.0.3625256545900000000.2	x^16 - 7x^15 + 25x^14 - 64x^13 + 134x^12 - 237x^11 + 360x^10 - 476x^9 + 547x^8 - 540x^7 + 460x^6 - 333x^5 + 200x^4 - 98x^3 + 37x^2 - 9x + 1	\( 2^{8}\cdot 5^{8}\cdot 11^{4}\cdot 19^{5} \)	16T1719	Trivial
16.6.4770074402500000000.1	x^16 - x^15 - 5x^14 + 7x^13 + 3x^12 - 10x^11 + 14x^10 - 29x^9 + 19x^8 + 42x^7 - 84x^6 + 71x^5 - 44x^4 + 24x^3 - 4x^2 - 4x + 1	\( -\,2^{8}\cdot 5^{10}\cdot 11^{4}\cdot 19^{4} \)	16T1719	Trivial (GRH)
16.6.5661124198400000000.1	x^16 - 2x^15 - 4x^14 + 6x^13 + 6x^12 + 20x^11 - 70x^10 + 50x^9 - 13x^8 - 16x^7 + 90x^6 - 114x^5 + 90x^4 - 70x^3 + 14x^2 + 12x + 1	\( -\,2^{24}\cdot 5^{8}\cdot 11^{4}\cdot 59 \)	16T1719	Trivial (GRH)
16.8.8795570003734765625.1	x^16 - 5x^15 + 2x^14 + 32x^13 - 58x^12 - 51x^11 + 221x^10 - 70x^9 - 337x^8 + 302x^7 + 183x^6 - 327x^5 + 40x^4 + 117x^3 - 53x^2 + 3x + 1	\( 5^{8}\cdot 11^{4}\cdot 19^{4}\cdot 11801 \)	16T1719	Trivial (GRH)
16.0.21972837990400000000.1	x^16 - 4x^15 + 6x^14 - 10x^13 + 36x^12 - 96x^11 + 196x^10 - 358x^9 + 546x^8 - 674x^7 + 738x^6 - 762x^5 + 719x^4 - 566x^3 + 334x^2 - 134x + 29	\( 2^{24}\cdot 5^{8}\cdot 11^{4}\cdot 229 \)	16T1719	Trivial
16.8.21972837990400000000.1	x^16 - 4x^15 + 4x^14 + 6x^13 - 33x^12 + 60x^11 + 12x^10 - 184x^9 + 133x^8 + 180x^7 - 220x^6 - 48x^5 + 165x^4 - 90x^3 + 14x^2 + 4x - 1	\( 2^{24}\cdot 5^{8}\cdot 11^{4}\cdot 229 \)	16T1719	Trivial (GRH)
16.0.33486988902400000000.1	x^16 - 2x^15 + 8x^14 - 8x^13 + 44x^12 - 90x^11 + 268x^10 - 372x^9 + 562x^8 - 482x^7 + 504x^6 - 302x^5 + 215x^4 - 116x^3 + 34x^2 - 42x + 29	\( 2^{24}\cdot 5^{8}\cdot 11^{4}\cdot 349 \)	16T1719	Trivial
16.10.329356056319413671875.1	x^16 - 3x^15 - 10x^14 + 37x^13 + 3x^12 - 105x^11 + 120x^10 - 24x^9 - 57x^8 - 24x^7 + 120x^6 - 105x^5 + 3x^4 + 37x^3 - 10x^2 - 3x + 1	\( -\,5^{8}\cdot 19\cdot 29^{4}\cdot 89^{4} \)	16T1719	Trivial (GRH)
16.6.329356056319413671875.1	x^16 - 2x^15 - 2x^14 - 9x^12 + 59x^11 + 27x^10 - 123x^9 - 64x^8 - 76x^7 + 148x^6 + 262x^5 - 234x^4 - 230x^3 - 18x^2 - 21x + 1	\( -\,5^{8}\cdot 19\cdot 29^{4}\cdot 89^{4} \)	16T1719	Trivial (GRH)
16.10.2270823335675957421875.1	x^16 - 3x^15 - 12x^14 + 44x^13 + 22x^12 - 210x^11 + 172x^10 + 305x^9 - 657x^8 + 238x^7 + 487x^6 - 593x^5 + 205x^4 + 32x^3 - 39x^2 + 6x + 1	\( -\,5^{8}\cdot 29^{4}\cdot 89^{4}\cdot 131 \)	16T1719	Trivial (GRH)
16.6.2270823335675957421875.1	x^16 - 6x^14 - 3x^13 + 25x^12 + 41x^11 - 82x^10 - 215x^9 - 10x^8 + 461x^7 + 609x^6 - 166x^5 - 768x^4 - 406x^3 - 90x^2 - 15x - 1	\( -\,5^{8}\cdot 29^{4}\cdot 89^{4}\cdot 131 \)	16T1719	Trivial (GRH)
16.4.2582844862715401953125.1	x^16 - 2x^15 + 3x^14 - 3x^13 - 30x^12 + 55x^11 - 133x^10 + 274x^9 - 296x^8 + 408x^7 - 545x^6 + 403x^5 - 284x^4 + 214x^3 - 61x^2 - 4x + 19	\( 5^{8}\cdot 29^{4}\cdot 89^{4}\cdot 149 \)	16T1719	Trivial (GRH)
16.8.2582844862715401953125.1	x^16 - 6x^15 + 15x^14 - 29x^13 + 51x^12 - 73x^11 + 74x^10 - 8x^9 - 57x^8 + 83x^7 - 122x^6 - 10x^5 + 120x^4 - 17x^3 - 29x^2 + 5x + 1	\( 5^{8}\cdot 29^{4}\cdot 89^{4}\cdot 149 \)	16T1719	Trivial (GRH)
16.10.7359994447968100000000.1	x^16 - 8x^14 + 2x^12 + 130x^10 - 368x^8 + 286x^6 + 11x^4 - 12x^2 - 1	\( -\,2^{8}\cdot 5^{8}\cdot 29^{4}\cdot 101^{4} \)	16T1719	Trivial (GRH)
16.2.7359994447968100000000.1	x^16 + 11x^14 + 27x^12 - 68x^10 - 389x^8 - 610x^6 - 400x^4 - 96x^2 - 1	\( -\,2^{8}\cdot 5^{8}\cdot 29^{4}\cdot 101^{4} \)	16T1719	$[2]$
16.10.110940987391802500000000.1	x^16 - 11x^14 + 15x^12 + 112x^10 - 121x^8 - 370x^6 + 130x^4 + 300x^2 - 25	\( -\,2^{8}\cdot 5^{10}\cdot 29^{4}\cdot 89^{4} \)	16T1719	Trivial (GRH)
16.14.110940987391802500000000.1	x^16 - x^15 - 21x^14 + 30x^13 + 161x^12 - 296x^11 - 504x^10 + 1221x^9 + 409x^8 - 2037x^7 + 487x^6 + 1223x^5 - 639x^4 - 177x^3 + 167x^2 - 24x - 1	\( -\,2^{8}\cdot 5^{10}\cdot 29^{4}\cdot 89^{4} \)	16T1719	Trivial (GRH)
16.2.110940987391802500000000.1	x^16 - 2x^15 + 9x^14 - 15x^13 + 40x^12 - 48x^11 + 77x^10 - 87x^9 + 44x^8 - 7x^7 - 213x^6 + 265x^5 - 251x^4 + 392x^3 - 184x^2 - 33x + 121	\( -\,2^{8}\cdot 5^{10}\cdot 29^{4}\cdot 89^{4} \)	16T1719	Trivial (GRH)
16.6.110940987391802500000000.1	x^16 - 2x^15 - 14x^14 + 26x^13 + 71x^12 - 108x^11 - 176x^10 + 87x^9 + 312x^8 + 412x^7 - 527x^6 - 1000x^5 + 618x^4 + 863x^3 - 892x^2 + 415x - 61	\( -\,2^{8}\cdot 5^{10}\cdot 29^{4}\cdot 89^{4} \)	16T1719	Trivial (GRH)
16.6.110940987391802500000000.2	x^16 - 2x^15 - 3x^14 - 9x^13 - 29x^12 + 118x^11 + 36x^10 - 204x^9 - 245x^8 + 269x^7 + 543x^6 - 321x^5 - 255x^4 - 361x^3 + 383x^2 + 79x - 41	\( -\,2^{8}\cdot 5^{10}\cdot 29^{4}\cdot 89^{4} \)	16T1719	Trivial (GRH)
16.4.181943219322556100000000.1	x^16 + 20x^14 + 160x^12 + 650x^10 + 1387x^8 + 1370x^6 + 235x^4 - 325x^2 + 41	\( 2^{8}\cdot 5^{8}\cdot 29^{4}\cdot 41\cdot 89^{4} \)	16T1719	Trivial (GRH)
16.14.394949915114816900000000.1	x^16 - 4x^15 - 6x^14 + 51x^13 - 73x^12 - 120x^11 + 632x^10 - 657x^9 - 978x^8 + 2624x^7 - 1454x^6 - 1075x^5 + 1804x^4 - 959x^3 + 238x^2 - 26x + 1	\( -\,2^{8}\cdot 5^{8}\cdot 29^{4}\cdot 89^{5} \)	16T1719	Trivial (GRH)
16.12.483702705028258900000000.1	x^16 - 12x^14 + 48x^12 - 54x^10 - 93x^8 + 234x^6 - 45x^4 - 189x^2 + 109	\( 2^{8}\cdot 5^{8}\cdot 29^{4}\cdot 89^{4}\cdot 109 \)	16T1719	Trivial (GRH)
16.16.2200254466977203050390625.1	x^16 - 8x^15 + 8x^14 + 84x^13 - 190x^12 - 316x^11 + 1078x^10 + 462x^9 - 2852x^8 + 12x^7 + 3862x^6 - 788x^5 - 2488x^4 + 900x^3 + 560x^2 - 325x + 41	\( 5^{8}\cdot 11^{2}\cdot 29^{4}\cdot 89^{4}\cdot 1049 \)	16T1719	Trivial (GRH)
16.12.6199677062451683175390625.1	x^16 - 8x^15 + 24x^14 - 28x^13 - 22x^12 + 132x^11 - 194x^10 + 46x^9 + 240x^8 - 356x^7 + 142x^6 + 180x^5 - 184x^4 - 28x^3 + 48x^2 + 7x - 1	\( 5^{8}\cdot 29^{4}\cdot 89^{4}\cdot 357649 \)	16T1719	Trivial (GRH)
16.16.20090743594492734347265625.1	x^16 - 8x^15 + 10x^14 + 70x^13 - 185x^12 - 164x^11 + 844x^10 - 95x^9 - 1644x^8 + 766x^7 + 1469x^6 - 860x^5 - 554x^4 + 285x^3 + 72x^2 - 7x - 1	\( 5^{8}\cdot 23^{2}\cdot 29^{4}\cdot 101^{4}\cdot 1321 \)	16T1719	Trivial (GRH)
16.0.22873841513195110400000000.1	x^16 - 10x^14 + 61x^12 - 36x^10 - 282x^8 + 1742x^6 + 8956x^4 + 5508x^2 + 3509	\( 2^{24}\cdot 5^{8}\cdot 19^{4}\cdot 29\cdot 31^{4} \)	16T1719	$[8]$ (GRH)
16.8.52222277247435505100000000.1	x^16 + 2x^14 - 36x^12 - 82x^10 + 229x^8 + 468x^6 - 373x^4 - 695x^2 + 11	\( 2^{8}\cdot 5^{8}\cdot 11\cdot 29^{4}\cdot 509^{4} \)	16T1719	Trivial (GRH)
16.8.52222277247435505100000000.2	x^16 - 24x^14 - 16x^13 + 246x^12 + 288x^11 - 1298x^10 - 2128x^9 + 3476x^8 + 7920x^7 - 3598x^6 - 14680x^5 - 1637x^4 + 11616x^3 + 4332x^2 - 3160x - 1669	\( 2^{8}\cdot 5^{8}\cdot 11\cdot 29^{4}\cdot 509^{4} \)	16T1719	Trivial (GRH)
16.8.52222277247435505100000000.3	x^16 - 5x^15 - 3x^14 + 47x^13 + 40x^12 - 447x^11 - 210x^10 + 2630x^9 + 1066x^8 - 8828x^7 - 15935x^6 + 34586x^5 + 73962x^4 - 98427x^3 - 118200x^2 + 80375x + 68249	\( 2^{8}\cdot 5^{8}\cdot 11\cdot 29^{4}\cdot 509^{4} \)	16T1719	Trivial (GRH)
16.8.52222277247435505100000000.4	x^16 - 4x^15 + 2x^14 + 63x^13 - 76x^12 - 250x^11 + 824x^10 + 374x^9 - 3021x^8 + 2352x^7 + 3912x^6 - 7116x^5 + 2625x^4 + 923x^3 - 565x^2 - 2x + 19	\( 2^{8}\cdot 5^{8}\cdot 11\cdot 29^{4}\cdot 509^{4} \)	16T1719	Trivial (GRH)
16.8.57341738797144638761328125.1	x^16 - 3x^15 - 8x^14 + 20x^13 - 21x^12 + 443x^11 - 1561x^10 + 2072x^9 - 3335x^8 + 8610x^7 - 10332x^6 + 4628x^5 + 3827x^4 - 4972x^3 + 968x^2 + 203x - 19	\( 5^{8}\cdot 29^{4}\cdot 89^{4}\cdot 149^{3} \)	16T1719	Trivial (GRH)
16.4.141874618546577094761328125.1	x^16 - 6x^15 + 7x^14 + 9x^13 - 40x^12 + 95x^11 - 223x^10 + 572x^9 - 490x^8 + 30x^7 + 1527x^6 - 2979x^5 + 3390x^4 + 1972x^3 - 2219x^2 - 10028x + 11881	\( 5^{8}\cdot 19^{4}\cdot 29\cdot 31^{4}\cdot 101^{4} \)	16T1719	Trivial (GRH)
16.4.141874618546577094761328125.2	x^16 - 6x^15 + 15x^14 - 51x^13 + 145x^12 - 310x^11 + 591x^10 - 736x^9 + 2034x^8 - 2383x^7 + 762x^6 - 4738x^5 + 8177x^4 - 917x^3 + 730x^2 - 9499x + 3481	\( 5^{8}\cdot 19^{4}\cdot 29\cdot 31^{4}\cdot 101^{4} \)	16T1719	Trivial (GRH)
16.0.192453229606633127823828125.1	x^16 - 6x^15 + 3x^14 + 49x^13 - 85x^12 - 136x^11 + 556x^10 - 141x^9 - 1260x^8 + 1371x^7 + 563x^6 - 1840x^5 + 4959x^4 + 232x^3 + 535x^2 - 27x + 1	\( 5^{8}\cdot 19^{4}\cdot 29\cdot 31^{4}\cdot 109^{4} \)	16T1719	$[24]$ (GRH)
16.12.2521354970203350630400000000.1	x^16 - 30x^14 + 39x^12 + 2872x^10 - 8347x^8 - 35456x^6 + 34259x^4 - 8866x^2 + 589	\( 2^{24}\cdot 5^{8}\cdot 19\cdot 29^{4}\cdot 31^{5} \)	16T1719	Trivial (GRH)
16.8.2521354970203350630400000000.1	x^16 - 4x^15 - 28x^14 + 84x^13 + 169x^12 - 12x^11 - 572x^10 - 4706x^9 + 2413x^8 + 22934x^7 + 2712x^6 - 20178x^5 + 7213x^4 - 2302x^3 - 20380x^2 + 5354x + 9011	\( 2^{24}\cdot 5^{8}\cdot 19\cdot 29^{4}\cdot 31^{5} \)	16T1719	Trivial (GRH)
16.12.2521354970203350630400000000.2	x^16 - 8x^15 + 12x^14 + 32x^13 - 200x^12 + 820x^11 - 1320x^10 + 218x^9 + 12078x^8 - 34192x^7 - 43374x^6 + 73780x^5 + 56317x^4 - 24022x^3 - 7770x^2 - 62x + 1	\( 2^{24}\cdot 5^{8}\cdot 19\cdot 29^{4}\cdot 31^{5} \)	16T1719	Trivial (GRH)
16.8.2521354970203350630400000000.2	x^16 - 4x^15 - 8x^14 + 74x^13 - 187x^12 + 254x^11 - 1962x^10 + 2874x^9 - 392x^8 + 4542x^7 + 18416x^6 - 19442x^5 - 11254x^4 - 72424x^3 + 15662x^2 + 64102x + 19069	\( 2^{24}\cdot 5^{8}\cdot 19\cdot 29^{4}\cdot 31^{5} \)	16T1719	Trivial (GRH)
16.0.8257456786263434854400000000.1	x^16 - 2x^15 + 10x^14 + 46x^13 + 261x^12 + 570x^11 + 1798x^10 + 6188x^9 + 23677x^8 + 50688x^7 + 97180x^6 + 140166x^5 + 221873x^4 + 296034x^3 + 272912x^2 + 137910x + 28449	\( 2^{24}\cdot 5^{8}\cdot 19^{6}\cdot 29\cdot 31^{4} \)	16T1719	$[2, 2, 58]$ (GRH)
16.0.6944521157247548712550400000000.1	x^16 - 6x^15 + 58x^14 - 150x^13 + 1015x^12 - 2812x^11 + 10766x^10 - 27256x^9 + 54324x^8 - 164802x^7 + 156958x^6 - 705304x^5 + 1223950x^4 - 1382320x^3 + 7647038x^2 + 37860x + 12543759	\( 2^{24}\cdot 5^{8}\cdot 19^{6}\cdot 29^{3}\cdot 31^{4} \)	16T1719	$[2, 2, 2, 2, 820]$ (GRH)