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 48 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.2.31081961111079962118821.1	x^18 - 9x^17 + 45x^16 - 156x^15 + 413x^14 - 875x^13 + 1524x^12 - 2215x^11 + 2707x^10 - 2788x^9 + 2416x^8 - 1753x^7 + 1062x^6 - 539x^5 + 238x^4 - 97x^3 + 40x^2 - 14x + 1	\( 31^{12}\cdot 39461 \)	18T656	Trivial (GRH)
18.0.118344186923291529969664.4	x^18 + 3x^16 + 5x^14 + 5x^12 + 5x^10 + 28x^8 + 4x^6 + 2x^4 + x^2 + 1	\( -\,2^{18}\cdot 7^{8}\cdot 23^{8} \)	18T656	Trivial (GRH)
18.0.118344186923291529969664.5	x^18 - 4x^16 + 10x^14 - 22x^12 + 38x^10 - 29x^8 + 44x^6 - 14x^4 + 12x^2 + 1	\( -\,2^{18}\cdot 7^{8}\cdot 23^{8} \)	18T656	Trivial (GRH)
18.2.828409308463040709787648.1	x^18 - 14x^16 + 81x^14 - 252x^12 + 460x^10 - 503x^8 + 325x^6 - 124x^4 + 34x^2 - 7	\( 2^{18}\cdot 7^{9}\cdot 23^{8} \)	18T656	Trivial (GRH)
18.10.78190236448698608037083217920.1	x^18 - 6x^17 + 2x^16 + 64x^15 - 186x^14 + 104x^13 + 344x^12 - 176x^11 - 936x^10 + 224x^9 + 1388x^8 - 1556x^7 + 792x^6 + 4548x^5 + 416x^4 - 7720x^3 - 3932x^2 + 2368x - 148	\( 2^{18}\cdot 5\cdot 19^{8}\cdot 37^{8} \)	18T656	Trivial (GRH)
18.6.78190236448698608037083217920.1	x^18 + 15x^16 + 36x^14 - 52x^12 - 194x^10 - 34x^8 + 160x^6 + 48x^4 - 27x^2 - 5	\( 2^{18}\cdot 5\cdot 19^{8}\cdot 37^{8} \)	18T656	Trivial (GRH)
18.4.121194866495482842457478987776.1	x^18 - 2x^17 - 14x^16 + 76x^15 - 166x^14 + 98x^13 + 546x^12 - 2302x^11 + 4460x^10 - 3450x^9 - 4932x^8 + 19348x^7 - 30924x^6 + 30640x^5 - 19400x^4 + 7168x^3 - 1200x^2 + 8x + 8	\( -\,2^{16}\cdot 19^{8}\cdot 31\cdot 37^{8} \)	18T656	Trivial (GRH)
18.8.121194866495482842457478987776.1	x^18 - 9x^17 + 38x^16 - 84x^15 - 58x^14 + 1028x^13 - 3238x^12 + 5236x^11 - 3927x^10 - 1119x^9 + 5192x^8 - 6988x^7 + 13786x^6 - 22796x^5 + 17332x^4 - 1056x^3 - 5626x^2 + 2516x - 226	\( -\,2^{16}\cdot 19^{8}\cdot 31\cdot 37^{8} \)	18T656	Trivial (GRH)
18.4.168109008364702007279728918528.1	x^18 - 9x^17 + 55x^16 - 236x^15 + 786x^14 - 2086x^13 + 4404x^12 - 7392x^11 + 9183x^10 - 7041x^9 - 1233x^8 + 13732x^7 - 24250x^6 + 26532x^5 - 19414x^4 + 9212x^3 - 2517x^2 + 273x + 19	\( -\,2^{16}\cdot 19^{8}\cdot 37^{8}\cdot 43 \)	18T656	Trivial (GRH)
18.8.168109008364702007279728918528.1	x^18 - 9x^17 + 45x^16 - 156x^15 + 308x^14 - 140x^13 - 1344x^12 + 5438x^11 - 11421x^10 + 15217x^9 - 10407x^8 - 4338x^7 + 21310x^6 - 29266x^5 + 23964x^4 - 12530x^3 + 3719x^2 - 391x + 13	\( -\,2^{16}\cdot 19^{8}\cdot 37^{8}\cdot 43 \)	18T656	Trivial (GRH)
18.10.203294614766616380896416366592.1	x^18 - 6x^17 + 18x^16 - 36x^15 - 70x^14 + 504x^13 - 772x^12 + 556x^11 - 1952x^10 + 3968x^9 + 1364x^8 - 9752x^7 + 5028x^6 + 5060x^5 - 4020x^4 - 704x^3 + 944x^2 - 40x - 92	\( 2^{18}\cdot 13\cdot 19^{8}\cdot 37^{8} \)	18T656	Trivial (GRH)
18.6.203294614766616380896416366592.1	x^18 - 6x^17 - 8x^16 + 78x^15 + 64x^14 - 620x^13 - 6x^12 + 2734x^11 - 2240x^10 - 5872x^9 + 10480x^8 + 6516x^7 - 31020x^6 + 8468x^5 + 33076x^4 - 3564x^3 - 10232x^2 - 2896x - 244	\( 2^{18}\cdot 13\cdot 19^{8}\cdot 37^{8} \)	18T656	Trivial (GRH)
18.10.238480221168530754513103814656.1	x^18 - 4x^17 - 18x^16 + 78x^15 + 92x^14 - 508x^13 - 144x^12 + 1432x^11 + 134x^10 - 2144x^9 - 912x^8 + 3464x^7 + 1916x^6 - 6060x^5 - 380x^4 + 4196x^3 - 1172x^2 + 44x + 52	\( 2^{16}\cdot 19^{8}\cdot 37^{8}\cdot 61 \)	18T656	Trivial (GRH)
18.10.238480221168530754513103814656.2	x^18 - 6x^17 + 8x^16 + 20x^15 - 106x^14 + 212x^13 - 246x^12 + 434x^11 + 128x^10 - 2448x^9 + 2148x^8 + 392x^7 - 1860x^6 + 2680x^5 + 1016x^4 - 616x^3 + 440x^2 + 216x - 20	\( 2^{16}\cdot 19^{8}\cdot 37^{8}\cdot 61 \)	18T656	Trivial (GRH)
18.10.254118268458270476120520458240.1	x^18 - 9x^17 + 28x^16 - 20x^15 - 134x^14 + 574x^13 - 978x^12 + 148x^11 + 2775x^10 - 6461x^9 + 5366x^8 + 4448x^7 - 14846x^6 + 15284x^5 + 620x^4 - 15388x^3 + 9016x^2 - 424x - 482	\( 2^{16}\cdot 5\cdot 13\cdot 19^{8}\cdot 37^{8} \)	18T656	Trivial (GRH)
18.2.254118268458270476120520458240.1	x^18 - 9x^17 + 54x^16 - 212x^15 + 642x^14 - 1504x^13 + 2820x^12 - 3902x^11 + 3025x^10 + 1721x^9 - 8946x^8 + 11988x^7 - 5076x^6 - 4594x^5 + 5540x^4 - 252x^3 - 1882x^2 + 610x + 50	\( 2^{16}\cdot 5\cdot 13\cdot 19^{8}\cdot 37^{8} \)	18T656	$[2]$ (GRH)
18.12.261937292103140336924228780032.1	x^18 - 3x^17 - 27x^16 + 90x^15 + 234x^14 - 968x^13 - 610x^12 + 4758x^11 - 1113x^10 - 11855x^9 + 8305x^8 + 16048x^7 - 15800x^6 - 12950x^5 + 14568x^4 + 6650x^3 - 6993x^2 - 1813x + 1369	\( -\,2^{16}\cdot 19^{8}\cdot 37^{8}\cdot 67 \)	18T656	Trivial (GRH)
18.8.261937292103140336924228780032.1	x^18 - 9x^17 + 39x^16 - 108x^15 + 78x^14 + 630x^13 - 2890x^12 + 6888x^11 - 10525x^10 + 10077x^9 - 4127x^8 - 3832x^7 + 7418x^6 - 4786x^5 + 282x^4 + 1724x^3 - 779x^2 - 81x + 115	\( -\,2^{16}\cdot 19^{8}\cdot 37^{8}\cdot 67 \)	18T656	Trivial (GRH)
18.14.265846803925575267326082940928.1	x^18 - 4x^17 - 22x^16 + 84x^15 + 206x^14 - 662x^13 - 1134x^12 + 2656x^11 + 3644x^10 - 6244x^9 - 6112x^8 + 9208x^7 + 4524x^6 - 7072x^5 - 552x^4 + 1544x^3 + 48x^2 - 80x - 8	\( 2^{18}\cdot 17\cdot 19^{8}\cdot 37^{8} \)	18T656	Trivial (GRH)
18.12.297122898505054710540916228096.1	x^18 - 23x^16 - 12x^15 + 168x^14 + 232x^13 - 508x^12 - 1312x^11 + 422x^10 + 2964x^9 + 842x^8 - 2684x^7 - 648x^6 + 640x^5 - 2980x^4 - 344x^3 + 3769x^2 + 740x - 851	\( -\,2^{18}\cdot 19^{9}\cdot 37^{8} \)	18T656	Trivial (GRH)
18.8.297122898505054710540916228096.1	x^18 - 2x^17 - 20x^16 + 10x^15 + 140x^14 - 156x^13 - 1268x^12 - 1088x^11 + 2960x^10 + 4760x^9 - 5784x^8 - 12544x^7 + 15144x^6 + 46544x^5 + 11840x^4 - 51472x^3 - 52416x^2 - 17264x - 1840	\( -\,2^{18}\cdot 19^{9}\cdot 37^{8} \)	18T656	Trivial (GRH)
18.4.320799749736333025107469378612.1	x^18 - 3x^17 + 19x^16 - 20x^15 + 50x^14 - 204x^13 - 281x^12 - 170x^11 - 331x^10 + 2078x^9 + 3x^8 + 828x^7 - 4883x^6 - 4414x^5 - 5354x^4 - 80x^3 - 400x^2 + 1072x - 224	\( -\,2^{2}\cdot 13^{9}\cdot 229^{8} \)	18T656	$[2]$ (GRH)
18.12.359675087664013596970582802432.1	x^18 - 12x^16 - 4x^14 + 608x^12 - 3028x^10 + 5436x^8 - 2980x^6 - 640x^4 + 564x^2 + 92	\( -\,2^{18}\cdot 19^{8}\cdot 23\cdot 37^{8} \)	18T656	Trivial (GRH)
18.4.359675087664013596970582802432.1	x^18 - 4x^17 + 10x^16 - 48x^15 + 46x^14 - 296x^13 + 142x^12 - 1132x^11 + 132x^10 - 2404x^9 - 1320x^8 - 2880x^7 - 7636x^6 - 3648x^5 - 13656x^4 - 4304x^3 - 5080x^2 - 4200x + 1000	\( -\,2^{18}\cdot 19^{8}\cdot 23\cdot 37^{8} \)	18T656	$[2]$ (GRH)
18.12.371403623131318388176145285120.1	x^18 - 3x^17 - 22x^16 + 64x^15 + 172x^14 - 576x^13 - 400x^12 + 2952x^11 - 1591x^10 - 8939x^9 + 11818x^8 + 13926x^7 - 29088x^6 - 5352x^5 + 31862x^4 - 10294x^3 - 11026x^2 + 7890x - 1390	\( -\,2^{16}\cdot 5\cdot 19^{9}\cdot 37^{8} \)	18T656	Trivial (GRH)
18.8.402679717710797831390978572288.1	x^18 - 7x^17 + 2x^16 + 80x^15 - 112x^14 - 372x^13 + 602x^12 + 1552x^11 - 3035x^10 - 2273x^9 + 6232x^8 + 1644x^7 - 7198x^6 + 424x^5 + 3412x^4 + 188x^3 - 600x^2 + 8	\( -\,2^{16}\cdot 19^{8}\cdot 37^{8}\cdot 103 \)	18T656	Trivial (GRH)
18.14.488688977804366300231770112000.1	x^18 - 5x^17 - 23x^16 + 144x^15 + 74x^14 - 1240x^13 + 900x^12 + 3682x^11 - 5595x^10 - 2105x^9 + 9049x^8 - 2000x^7 - 6080x^6 + 958x^5 + 928x^4 - 926x^3 - 559x^2 - 95x - 5	\( 2^{16}\cdot 5^{3}\cdot 19^{8}\cdot 37^{8} \)	18T656	Trivial (GRH)
18.10.535603119673585465054020042752.1	x^18 - 5x^17 - 14x^16 + 106x^15 - 72x^14 - 258x^13 - 120x^12 + 144x^11 + 5353x^10 - 9211x^9 - 11516x^8 + 50784x^7 - 49810x^6 - 29054x^5 + 123328x^4 - 136686x^3 + 61164x^2 + 8768x - 12634	\( 2^{16}\cdot 19^{8}\cdot 37^{8}\cdot 137 \)	18T656	Trivial (GRH)
18.8.543422143318455325857728364544.1	x^18 - 7x^17 + 3x^16 + 80x^15 - 190x^14 - 80x^13 + 682x^12 - 486x^11 + 377x^10 - 1235x^9 - 3897x^8 + 19742x^7 - 8696x^6 - 61440x^5 + 53780x^4 + 77514x^3 - 43061x^2 - 20743x - 1279	\( -\,2^{16}\cdot 19^{8}\cdot 37^{8}\cdot 139 \)	18T656	Trivial (GRH)
18.8.746716758085071706754144731136.1	x^18 - 6x^17 + 16x^16 - 62x^15 + 114x^14 + 20x^13 - 128x^12 + 1292x^11 - 1516x^10 + 440x^9 - 1688x^8 - 5776x^7 - 2168x^6 - 7272x^5 + 2528x^4 - 2224x^3 - 384x^2 + 7696x - 2960	\( -\,2^{16}\cdot 19^{8}\cdot 37^{8}\cdot 191 \)	18T656	Trivial (GRH)
18.8.4003340106173368731498660757504.1	x^18 - 6x^17 + 16x^16 - 34x^15 + 76x^14 - 96x^13 - 224x^12 + 908x^11 - 614x^10 - 248x^9 - 2756x^8 + 4404x^7 + 8888x^6 - 17052x^5 - 6556x^4 + 20160x^3 + 2884x^2 - 8216x - 1828	\( -\,2^{26}\cdot 19^{8}\cdot 37^{8} \)	18T656	Trivial (GRH)
18.2.9402375932956007616459256954880.1	x^18 - 6x^17 + 13x^16 - 38x^15 + 68x^14 + 22x^13 + 504x^12 + 1162x^11 + 4302x^10 + 7074x^9 + 17266x^8 + 23670x^7 + 35660x^6 + 48834x^5 + 41952x^4 + 17734x^3 + 993x^2 - 36x + 137	\( 2^{16}\cdot 5\cdot 13\cdot 19^{8}\cdot 37^{9} \)	18T656	$[2, 8]$ (GRH)
18.16.25404311813314286172470287269888.1	x^18 - 324x^14 + 3168x^12 - 11052x^10 + 16596x^8 - 10896x^6 + 3420x^4 - 504x^2 + 28	\( -\,2^{22}\cdot 3^{36}\cdot 7^{9} \)	18T656	Trivial (GRH)
18.16.64053441698773899703978572120064.1	x^18 - 16x^16 + 66x^14 + 112x^12 - 1400x^10 + 3444x^8 - 3480x^6 + 1424x^4 - 172x^2 + 4	\( -\,2^{30}\cdot 19^{8}\cdot 37^{8} \)	18T656	Trivial (GRH)
18.6.92076822441987480824469197422592.1	x^18 + 12x^16 - 4x^14 - 608x^12 - 3028x^10 - 5436x^8 - 2980x^6 + 640x^4 + 564x^2 - 92	\( 2^{26}\cdot 19^{8}\cdot 23\cdot 37^{8} \)	18T656	$[2]$ (GRH)
18.12.328498943730005017710048643698688.1	x^18 - 3x^17 - 23x^16 + 36x^15 + 184x^14 + 304x^13 - 1434x^12 - 3157x^11 + 4412x^10 + 13908x^9 - 5052x^8 - 33258x^7 - 507x^6 + 42503x^5 + 5358x^4 - 27709x^3 - 1646x^2 + 5453x + 692	\( -\,2^{12}\cdot 13^{9}\cdot 229^{8} \)	18T656	Trivial (GRH)
18.12.328498943730005017710048643698688.2	x^18 - 3x^17 - 6x^16 + 64x^15 - 179x^14 - 413x^13 + 2165x^12 + 116x^11 - 9155x^10 + 6214x^9 + 16744x^8 - 18364x^7 - 12595x^6 + 19075x^5 + 3041x^4 - 7577x^3 + 216x^2 + 832x - 7	\( -\,2^{12}\cdot 13^{9}\cdot 229^{8} \)	18T656	Trivial (GRH)
18.6.328498943730005017710048643698688.1	x^18 + 24x^16 + 44x^14 - 799x^12 - 2094x^10 + 3769x^8 + 4996x^6 - 3041x^4 - 3336x^2 - 208	\( 2^{12}\cdot 13^{9}\cdot 229^{8} \)	18T656	$[2]$ (GRH)
18.6.328498943730005017710048643698688.2	x^18 + 17x^16 - 75x^14 - 1520x^12 - 591x^10 + 4931x^8 + 3310x^6 - 595x^4 - 217x^2 - 13	\( 2^{12}\cdot 13^{9}\cdot 229^{8} \)	18T656	Trivial (GRH)
18.0.1617225569132332394880239476670464.1	x^18 + 30x^16 + 298x^14 + 1453x^12 + 3945x^10 + 6162x^8 + 5379x^6 + 2364x^4 + 397x^2 + 4	\( -\,2^{18}\cdot 13^{8}\cdot 229^{8} \)	18T656	$[2, 2, 320]$ (GRH)
18.10.2814348094639878218243558512525312.1	x^18 - 6x^17 + 21x^16 + 10x^15 - 386x^14 + 1166x^13 - 898x^12 - 4254x^11 + 17478x^10 - 28374x^9 + 8158x^8 + 64982x^7 - 170442x^6 + 232734x^5 - 192126x^4 + 95542x^3 - 27219x^2 + 3952x - 215	\( 2^{26}\cdot 19^{9}\cdot 37^{9} \)	18T656	Trivial (GRH)
18.14.2814348094639878218243558512525312.1	x^18 - 8x^17 - 30x^16 + 304x^15 + 302x^14 - 4100x^13 - 1486x^12 + 24632x^11 + 4634x^10 - 66622x^9 - 4730x^8 + 83916x^7 - 4304x^6 - 47668x^5 + 7864x^4 + 10408x^3 - 2892x^2 - 228x + 38	\( 2^{26}\cdot 19^{9}\cdot 37^{9} \)	18T656	Trivial (GRH)
18.6.2814348094639878218243558512525312.1	x^18 - 6x^17 + 46x^16 - 210x^15 + 700x^14 - 1768x^13 + 182x^12 + 16772x^11 - 98398x^10 + 330956x^9 - 862540x^8 + 1847208x^7 - 2851560x^6 + 2365244x^5 + 794812x^4 - 3987136x^3 + 4500304x^2 - 1527896x - 2142956	\( 2^{26}\cdot 19^{9}\cdot 37^{9} \)	18T656	Trivial (GRH)
18.10.2814348094639878218243558512525312.2	x^18 - 19x^16 - 56x^14 + 288x^12 + 682x^10 - 966x^8 - 1752x^6 + 1352x^4 + 1073x^2 - 703	\( 2^{26}\cdot 19^{9}\cdot 37^{9} \)	18T656	Trivial (GRH)
18.14.2814348094639878218243558512525312.2	x^18 - 4x^17 - 68x^16 + 292x^15 + 1762x^14 - 8276x^13 - 22128x^12 + 118944x^11 + 138738x^10 - 948722x^9 - 360754x^8 + 4345520x^7 - 329114x^6 - 11341964x^5 + 4582920x^4 + 14427212x^3 - 10213556x^2 - 3094036x + 2589586	\( 2^{26}\cdot 19^{9}\cdot 37^{9} \)	18T656	Trivial (GRH)
18.0.4270486268490065230230632368082944.1	x^18 + 57x^16 + 1055x^14 + 8143x^12 + 31842x^10 + 67882x^8 + 78617x^6 + 45620x^4 + 10699x^2 + 676	\( -\,2^{12}\cdot 13^{10}\cdot 229^{8} \)	18T656	$[2, 204]$ (GRH)
18.18.45029569514238051491896936200404992.1	x^18 - 6x^17 - 58x^16 + 378x^15 + 1130x^14 - 8762x^13 - 7180x^12 + 92108x^11 - 23052x^10 - 422000x^9 + 370866x^8 + 616044x^7 - 740360x^6 - 178552x^5 + 285632x^4 + 40440x^3 - 25872x^2 - 1600x + 650	\( 2^{30}\cdot 19^{9}\cdot 37^{9} \)	18T656	Trivial (GRH)
18.18.45029569514238051491896936200404992.2	x^18 - 67x^16 + 1824x^14 - 25880x^12 + 205162x^10 - 920022x^8 + 2340952x^6 - 3299088x^4 + 2374845x^2 - 675583	\( 2^{30}\cdot 19^{9}\cdot 37^{9} \)	18T656	Trivial (GRH)