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 60)

Label	Polynomial	Discriminant	Galois group	Class group
16.8.755848063425150770281.2	x^16 - 7x^15 + 17x^14 - 11x^13 - 31x^12 + 76x^11 - 65x^10 + 7x^9 + 28x^8 - 8x^7 + 40x^6 - 96x^5 + 63x^4 - 25x^3 + 17x^2 - 4x - 1	\( 17^{14}\cdot 67^{2} \)	16T1194	Trivial (GRH)
16.8.755848063425150770281.3	x^16 - 3x^15 + x^14 + 11x^13 - 17x^12 + 35x^11 - 48x^10 - 43x^9 + 240x^8 - 55x^7 - 182x^6 + 2x^5 - 20x^3 + 4x^2 + 6x + 1	\( 17^{14}\cdot 67^{2} \)	16T1194	Trivial (GRH)
16.4.1717622208732448876729.1	x^16 - 5x^15 + 9x^14 - 4x^13 + 3x^12 - 69x^11 + 269x^10 - 579x^9 + 839x^8 - 907x^7 + 725x^6 - 420x^5 + 165x^4 - 45x^3 + 38x^2 - 2x - 1	\( 17^{14}\cdot 101^{2} \)	16T1194	Trivial
16.8.1717622208732448876729.1	x^16 - x^15 - 12x^14 + 21x^13 + 32x^12 - 93x^11 + 3x^10 + 148x^9 - 70x^8 - 118x^7 + 45x^6 + 109x^5 - 25x^4 - 61x^3 - 6x^2 + 29x - 1	\( 17^{14}\cdot 101^{2} \)	16T1194	Trivial
16.4.3160283426693396036401.1	x^16 - 3x^15 + 20x^13 - 37x^12 + 50x^11 - 29x^10 + 56x^9 - 40x^8 - x^7 + 75x^6 - 48x^5 - 29x^4 + x^3 + 17x^2 - 15x - 1	\( 17^{14}\cdot 137^{2} \)	16T1194	Trivial
16.8.3160283426693396036401.1	x^16 - 2x^15 - 11x^14 + 31x^13 + 19x^12 - 133x^11 + 125x^10 + 53x^9 - 271x^8 + 459x^7 - 425x^6 + 17x^5 + 425x^4 - 459x^3 + 187x^2 - 17	\( 17^{14}\cdot 137^{2} \)	16T1194	Trivial
16.12.11034809241396899282944.1	x^16 - 4x^14 - 10x^12 + 78x^10 - 155x^8 + 130x^6 - 41x^4 + x^2 + 1	\( 2^{16}\cdot 17^{14} \)	16T1194	Trivial (GRH)
16.4.11034809241396899282944.1	x^16 + 4x^14 - 10x^12 - 44x^10 - 2x^8 + 74x^6 + 61x^4 + 16x^2 + 1	\( 2^{16}\cdot 17^{14} \)	16T1194	Trivial
16.12.11034809241396899282944.2	x^16 - 4x^14 - 10x^12 + 44x^10 - 2x^8 - 74x^6 + 61x^4 - 16x^2 + 1	\( 2^{16}\cdot 17^{14} \)	16T1194	Trivial (GRH)
16.4.11034809241396899282944.2	x^16 + 4x^14 - 10x^12 - 78x^10 - 155x^8 - 130x^6 - 41x^4 - x^2 + 1	\( 2^{16}\cdot 17^{14} \)	16T1194	$[2]$
16.12.3393001956715501807791409.1	x^16 - 4x^15 - 16x^14 + 65x^13 + 97x^12 - 333x^11 - 211x^10 - 3x^9 - 601x^8 + 5676x^7 + 4109x^6 - 16107x^5 - 9109x^4 + 12503x^3 + 6343x^2 - 1082x - 307	\( 17^{14}\cdot 67^{4} \)	16T1194	Trivial (GRH)
16.4.3393001956715501807791409.1	x^16 - 3x^15 + 11x^14 - 11x^13 - 60x^12 + 300x^11 - 1213x^10 + 2461x^9 - 4741x^8 + 5556x^7 - 4672x^6 + 491x^5 + 4456x^4 - 7090x^3 + 3779x^2 - 1713x - 2789	\( 17^{14}\cdot 67^{4} \)	16T1194	$[2]$ (GRH)
16.4.3393001956715501807791409.2	x^16 - 5x^15 + 10x^14 - 19x^13 + 30x^12 - 199x^11 + 503x^10 - 773x^9 - 657x^8 + 3402x^7 - 5195x^6 + 9313x^5 - 7926x^4 + 7472x^3 - 2560x^2 + 2145x + 1021	\( 17^{14}\cdot 67^{4} \)	16T1194	$[2]$ (GRH)
16.12.3393001956715501807791409.3	x^16 - 4x^15 - 10x^14 + 61x^13 - 155x^12 + 419x^11 - 228x^10 - 934x^9 + 1157x^8 - 1343x^7 - 612x^6 + 4063x^5 + 34x^4 - 2856x^3 - 187x^2 + 510x + 17	\( 17^{14}\cdot 67^{4} \)	16T1194	Trivial (GRH)
16.12.17521464151279710991512529.1	x^16 - 2x^15 - 4x^14 + 23x^13 - 182x^12 - 46x^11 + 1179x^10 - 1502x^9 + 776x^8 + 12647x^7 - 11064x^6 - 26215x^5 + 10486x^4 + 15687x^3 - 1182x^2 - 2572x - 239	\( 17^{14}\cdot 101^{4} \)	16T1194	Trivial (GRH)
16.8.17521464151279710991512529.1	x^16 - 4x^15 - 16x^14 + 48x^13 + 97x^12 - 231x^11 - 568x^10 + 1136x^9 + 2901x^8 - 3249x^7 - 5156x^6 - 2558x^5 + 479x^4 + 28908x^3 - 9246x^2 - 37700x + 25261	\( 17^{14}\cdot 101^{4} \)	16T1194	Trivial (GRH)
16.12.17521464151279710991512529.2	x^16 - 3x^15 - 23x^14 + 91x^13 + 59x^12 - 703x^11 + 1473x^10 - 718x^9 - 6339x^8 + 15450x^7 - 8871x^6 - 4354x^5 + 10882x^4 - 9742x^3 - 6353x^2 + 3234x + 1427	\( 17^{14}\cdot 101^{4} \)	16T1194	Trivial (GRH)
16.8.17521464151279710991512529.2	x^16 - 6x^15 + 11x^14 - 55x^13 + 140x^12 - 125x^11 + 295x^10 + 424x^9 - 1932x^8 + 3263x^7 - 8562x^6 + 5689x^5 + 10442x^4 - 27935x^3 + 31002x^2 - 5990x - 3229	\( 17^{14}\cdot 101^{4} \)	16T1194	Trivial (GRH)
16.0.49535258684630680881135616.1	x^16 + 35x^14 + 486x^12 + 3428x^10 + 13207x^8 + 28366x^6 + 33276x^4 + 19631x^2 + 4489	\( 2^{16}\cdot 17^{14}\cdot 67^{2} \)	16T1194	$[2, 2, 78]$ (GRH)
16.12.49535258684630680881135616.1	x^16 - 16x^14 - 75x^12 + 1405x^10 - 2008x^8 - 12179x^6 + 30777x^4 - 21373x^2 + 4489	\( 2^{16}\cdot 17^{14}\cdot 67^{2} \)	16T1194	Trivial (GRH)
16.16.49535258684630680881135616.1	x^16 - 35x^14 + 486x^12 - 3428x^10 + 13207x^8 - 28366x^6 + 33276x^4 - 19631x^2 + 4489	\( 2^{16}\cdot 17^{14}\cdot 67^{2} \)	16T1194	Trivial (GRH)
16.4.49535258684630680881135616.1	x^16 + 16x^14 - 41x^12 - 1116x^10 - 4422x^8 - 5552x^6 + 2064x^4 + 8844x^2 + 4489	\( 2^{16}\cdot 17^{14}\cdot 67^{2} \)	16T1194	$[2]$
16.8.49535258684630680881135616.1	x^16 + x^14 - 75x^12 + 11x^10 + 1222x^8 - 143x^6 - 4413x^4 + 268x^2 + 4489	\( 2^{16}\cdot 17^{14}\cdot 67^{2} \)	16T1194	Trivial (GRH)
16.0.49535258684630680881135616.2	x^16 + 33x^14 + 435x^12 + 2981x^10 + 11592x^8 + 26051x^6 + 32613x^4 + 20234x^2 + 4489	\( 2^{16}\cdot 17^{14}\cdot 67^{2} \)	16T1194	$[2, 2, 72]$ (GRH)
16.12.49535258684630680881135616.2	x^16 - 13x^14 - 10x^12 + 687x^10 - 2399x^8 - 1405x^6 + 15412x^4 - 15879x^2 + 4489	\( 2^{16}\cdot 17^{14}\cdot 67^{2} \)	16T1194	Trivial (GRH)
16.16.49535258684630680881135616.2	x^16 - 33x^14 + 435x^12 - 2981x^10 + 11592x^8 - 26051x^6 + 32613x^4 - 20234x^2 + 4489	\( 2^{16}\cdot 17^{14}\cdot 67^{2} \)	16T1194	Trivial (GRH)
16.4.49535258684630680881135616.2	x^16 + 21x^14 + 109x^12 - 248x^10 - 2637x^8 - 2034x^6 + 9564x^4 + 14874x^2 + 4489	\( 2^{16}\cdot 17^{14}\cdot 67^{2} \)	16T1194	$[2]$
16.8.49535258684630680881135616.2	x^16 + 18x^14 + 44x^12 - 482x^10 - 784x^8 + 5042x^6 - 2271x^4 - 6566x^2 + 4489	\( 2^{16}\cdot 17^{14}\cdot 67^{2} \)	16T1194	Trivial (GRH)
16.8.49535258684630680881135616.3	x^16 + 16x^14 - 24x^12 - 674x^10 + 610x^8 + 7232x^6 - 13899x^4 + 2010x^2 + 4489	\( 2^{16}\cdot 17^{14}\cdot 67^{2} \)	16T1194	$[2]$ (GRH)
16.8.49535258684630680881135616.4	x^16 + 4x^14 - 95x^12 - 299x^10 + 1936x^8 + 1791x^6 - 12281x^4 + 6901x^2 + 4489	\( 2^{16}\cdot 17^{14}\cdot 67^{2} \)	16T1194	Trivial (GRH)
16.8.49535258684630680881135616.5	x^16 + 4x^14 - 61x^12 - 95x^10 + 1222x^8 - 589x^6 - 4563x^4 + 2345x^2 + 4489	\( 2^{16}\cdot 17^{14}\cdot 67^{2} \)	16T1194	$[2]$ (GRH)
16.8.49535258684630680881135616.6	x^16 + 13x^14 + 7x^12 - 313x^10 - 342x^8 + 2663x^6 + 1251x^4 - 8040x^2 + 4489	\( 2^{16}\cdot 17^{14}\cdot 67^{2} \)	16T1194	Trivial (GRH)
16.0.166907320970544740432871424.1	x^16 - 8x^14 + 28x^12 - 120x^10 + 410x^8 - 872x^6 + 1956x^4 - 1880x^2 + 2209	\( 2^{76}\cdot 47^{2} \)	16T1194	Trivial (GRH)
16.0.166907320970544740432871424.2	x^16 + 24x^14 + 252x^12 + 1512x^10 + 5662x^8 + 13256x^6 + 17612x^4 + 9400x^2 + 2209	\( 2^{76}\cdot 47^{2} \)	16T1194	Trivial (GRH)
16.8.15231185783695887615175635001.1	x^16 - 4x^15 + 24x^14 - 109x^13 - 70x^12 + 997x^11 - 8796x^10 + 33984x^9 - 56320x^8 + 31671x^7 + 527680x^6 - 1308864x^5 + 2302820x^4 - 286790x^3 - 4367181x^2 + 4418113x - 1248497	\( 17^{14}\cdot 67^{6} \)	16T1194	$[2]$ (GRH)
16.8.15231185783695887615175635001.3	x^16 - 4x^15 - 27x^14 + 61x^13 - 274x^12 - 312x^11 + 4906x^10 - 10862x^9 + 8739x^8 + 75531x^7 - 277525x^6 + 285090x^5 + 89828x^4 - 921468x^3 + 3589244x^2 - 6103952x + 2529311	\( 17^{14}\cdot 67^{6} \)	16T1194	$[2]$ (GRH)
16.12.24292037884309209334711647701449.1	x^16 - 2x^15 - 58x^14 + 37x^13 + 1350x^12 + 786x^11 - 14262x^10 - 22454x^9 + 55928x^8 + 149437x^7 - 7339x^6 - 296732x^5 - 267330x^4 - 24747x^3 + 50232x^2 + 13177x + 673	\( 61^{2}\cdot 97^{14} \)	16T1194	Trivial (GRH)
16.8.24292037884309209334711647701449.1	x^16 - 2x^15 - 58x^14 + 134x^13 + 1059x^12 - 3482x^11 - 4562x^10 + 34388x^9 - 56010x^8 - 27200x^7 + 365820x^6 - 823539x^5 + 770667x^4 - 181208x^3 - 219331x^2 + 400013x - 326993	\( 61^{2}\cdot 97^{14} \)	16T1194	Trivial (GRH)
16.8.90390672967514567934462041097091729.1	x^16 - 4x^15 - 49x^14 + 286x^13 + 658x^12 - 8165x^11 + 11235x^10 + 45433x^9 - 202626x^8 + 266588x^7 + 134579x^6 - 900440x^5 + 1227748x^4 - 496607x^3 - 512251x^2 + 602034x - 171211	\( 61^{4}\cdot 97^{14} \)	16T1194	Trivial (GRH)
16.4.90390672967514567934462041097091729.3	x^16 - 3x^15 + x^14 + 295x^13 - 1285x^12 - 150x^11 + 24126x^10 - 115640x^9 + 127136x^8 + 335929x^7 - 1549932x^6 + 2210218x^5 + 1404898x^4 + 1432911x^3 - 4972170x^2 - 3390345x - 1778071	\( 61^{4}\cdot 97^{14} \)	16T1194	$[6]$ (GRH)
16.4.90390672967514567934462041097091729.4	x^16 - 2x^15 + 6x^14 + 22x^13 + 462x^12 - 1962x^11 - 17124x^10 + 492x^9 + 103052x^8 + 375809x^7 + 102689x^6 - 1452595x^5 - 2379393x^4 - 213178x^3 + 1549406x^2 + 246417x - 979969	\( 61^{4}\cdot 97^{14} \)	16T1194	$[2]$ (GRH)
16.8.90390672967514567934462041097091729.4	x^16 - 3x^15 - 96x^14 + 101x^13 + 3080x^12 + 2081x^11 - 33298x^10 - 54627x^9 + 76987x^8 + 114284x^7 - 228695x^6 - 241942x^5 + 269222x^4 + 1297305x^3 + 1010790x^2 - 2315682x + 2366739	\( 61^{4}\cdot 97^{14} \)	16T1194	Trivial (GRH)
16.12.1571275555715210001755383712793895489.2	x^16 - 2x^15 - 72x^14 - 64x^13 + 739x^12 + 6298x^11 + 33232x^10 - 43795x^9 - 559066x^8 - 617694x^7 + 801331x^6 + 820974x^5 - 235098x^4 - 223555x^3 - 48690x^2 - 3767x + 139	\( 23^{10}\cdot 41^{14} \)	16T1194	Trivial (GRH)
16.8.1571275555715210001755383712793895489.2	x^16 - 6x^15 + 3x^14 + 174x^13 - 1513x^12 + 5874x^11 - 20194x^10 + 89059x^9 - 245805x^8 + 50169x^7 + 2103327x^6 - 6774158x^5 + 7693019x^4 + 2712470x^3 - 23723409x^2 + 30809257x - 5481397	\( 23^{10}\cdot 41^{14} \)	16T1194	$[2]$ (GRH)
16.12.1571275555715210001755383712793895489.3	x^16 - 58x^14 - 281x^12 + 45464x^10 - 336639x^8 - 7059712x^6 + 84575163x^4 - 153963334x^2 + 10220809	\( 23^{10}\cdot 41^{14} \)	16T1194	Trivial (GRH)
16.8.1571275555715210001755383712793895489.4	x^16 - 6x^15 + 78x^14 - 722x^13 + 3256x^12 - 12212x^11 + 48486x^10 - 138518x^9 + 93887x^8 + 1175012x^7 - 5313570x^6 + 8817560x^5 + 3162395x^4 - 37693454x^3 + 56984839x^2 - 27302620x - 1009009	\( 23^{10}\cdot 41^{14} \)	16T1194	$[2]$ (GRH)
16.8.1571275555715210001755383712793895489.5	x^16 - 6x^15 - 130x^14 + 616x^13 + 5302x^12 - 21932x^11 - 56878x^10 + 339490x^9 - 316281x^8 - 1177018x^7 + 3353338x^6 - 1067350x^5 - 6133505x^4 + 8919920x^3 - 3939369x^2 - 263472x + 505613	\( 23^{10}\cdot 41^{14} \)	16T1194	$[2]$ (GRH)
16.4.1571275555715210001755383712793895489.6	x^16 - 4x^15 + 63x^14 - 408x^13 + 1614x^12 - 6300x^11 + 24089x^10 - 61437x^9 + 90222x^8 - 137237x^7 + 374301x^6 - 299541x^5 - 1784877x^4 + 4589903x^3 - 1756820x^2 - 5065413x + 4559237	\( 23^{10}\cdot 41^{14} \)	16T1194	$[2, 2]$ (GRH)
16.8.1571275555715210001755383712793895489.6	x^16 - 2x^15 - 31x^14 - 64x^13 - 819x^12 + 4002x^11 + 27164x^10 - 48182x^9 - 262349x^8 + 106202x^7 + 1107150x^6 + 1147826x^5 - 1607860x^4 - 6299140x^3 - 2370356x^2 + 8298938x + 6534883	\( 23^{10}\cdot 41^{14} \)	16T1194	$[2]$ (GRH)
16.4.1571275555715210001755383712793895489.7	x^16 - 4x^15 + 2x^14 - 92x^13 - 3068x^12 - 8082x^11 + 11452x^10 + 87776x^9 + 51900x^8 - 396964x^7 + 77866x^6 + 1458350x^5 - 750133x^4 - 6068974x^3 - 8010384x^2 + 6145284x + 20054449	\( 23^{10}\cdot 41^{14} \)	16T1194	$[2, 2]$ (GRH)