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 90)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.370297890940243544960000.1	x^20 + 9x^18 + 35x^16 + 80x^14 + 123x^12 + 141x^10 + 140x^8 + 129x^6 + 99x^4 + 49x^2 + 11	\( 2^{10}\cdot 5^{4}\cdot 11\cdot 47^{10} \)	20T852	Trivial (GRH)
20.0.1052995387977179557764813.1	x^20 - 10x^19 + 52x^18 - 183x^17 + 481x^16 - 992x^15 + 1653x^14 - 2269x^13 + 2604x^12 - 2533x^11 + 2116x^10 - 1533x^9 + 969x^8 - 539x^7 + 269x^6 - 123x^5 + 52x^4 - 20x^3 + 6x^2 - x + 1	\( 3^{4}\cdot 79^{10}\cdot 1373 \)	20T852	Trivial
20.2.110088938158843764415696897024.1	x^20 + 7x^18 - 20x^16 - 299x^14 - 1199x^12 - 2807x^10 - 4345x^8 - 4357x^6 - 2596x^4 - 783x^2 - 81	\( -\,2^{10}\cdot 401^{10} \)	20T852	Trivial (GRH)
20.2.110088938158843764415696897024.2	x^20 - 2x^18 + 10x^16 + 11x^14 - 3x^12 + 104x^10 + 150x^8 + 26x^6 - 28x^4 - 11x^2 - 1	\( -\,2^{10}\cdot 401^{10} \)	20T852	Trivial (GRH)
20.6.110088938158843764415696897024.2	x^20 + 4x^18 + 21x^16 + 56x^14 - 351x^12 - 1006x^10 + 283x^8 + 82x^6 - 70x^4 + 18x^2 - 1	\( -\,2^{10}\cdot 401^{10} \)	20T852	Trivial (GRH)
20.10.110088938158843764415696897024.3	x^20 - 12x^18 + 47x^16 - 45x^14 - 173x^12 + 424x^10 + 65x^8 - 497x^6 - 223x^4 + 495x^2 - 81	\( -\,2^{10}\cdot 401^{10} \)	20T852	Trivial (GRH)
20.2.110088938158843764415696897024.3	x^20 + 8x^18 + 32x^16 + 62x^14 - 125x^12 - 1072x^10 - 3113x^8 - 5470x^6 - 5625x^4 - 2706x^2 - 361	\( -\,2^{10}\cdot 401^{10} \)	20T852	Trivial (GRH)
20.6.110088938158843764415696897024.3	x^20 + 11x^18 + 8x^16 - 200x^14 - 772x^12 - 1058x^10 - 288x^8 + 513x^6 + 256x^4 - 71x^2 - 1	\( -\,2^{10}\cdot 401^{10} \)	20T852	Trivial (GRH)
20.6.110088938158843764415696897024.4	x^20 - 2x^18 - 10x^16 + 18x^14 - 23x^12 + x^10 + 29x^8 - 54x^6 + 40x^4 - 8x^2 - 1	\( -\,2^{10}\cdot 401^{10} \)	20T852	Trivial (GRH)
20.6.110088938158843764415696897024.5	x^20 - 3x^18 + 16x^16 + 27x^14 - 74x^12 - 76x^10 + 36x^8 - 18x^4 + 11x^2 - 1	\( -\,2^{10}\cdot 401^{10} \)	20T852	Trivial (GRH)
20.6.990800443429593879741272073216.1	x^20 - x^19 + 4x^18 + 7x^17 + 4x^15 - 104x^14 - 301x^13 - 650x^12 - 470x^11 + 180x^10 + 2116x^9 + 5406x^8 + 6560x^7 + 1549x^6 - 4647x^5 - 3498x^4 - 422x^3 + 1067x^2 + 75x - 153	\( -\,2^{10}\cdot 3^{2}\cdot 401^{10} \)	20T852	Trivial (GRH)
20.2.8917203990866344917671448658944.1	x^20 + 6x^18 + 16x^16 + 122x^14 + 292x^12 - 700x^10 + 4079x^8 - 3314x^6 - 13260x^4 - 6446x^2 - 169	\( -\,2^{10}\cdot 3^{4}\cdot 401^{10} \)	20T852	$[2]$ (GRH)
20.6.8917203990866344917671448658944.1	x^20 - 5x^19 + 46x^17 - 149x^16 + 234x^15 - 82x^14 - 589x^13 + 1792x^12 - 2790x^11 + 2339x^10 - 218x^9 - 2078x^8 + 2410x^7 - 809x^6 - 818x^5 + 794x^4 + 21x^3 - 297x^2 + 81	\( -\,2^{10}\cdot 3^{4}\cdot 401^{10} \)	20T852	Trivial (GRH)
20.2.8917203990866344917671448658944.2	x^20 - 3x^18 + 4x^16 - 154x^14 + 622x^12 - 1510x^10 + 6140x^8 - 3575x^6 + 786x^4 + 1249x^2 - 169	\( -\,2^{10}\cdot 3^{4}\cdot 401^{10} \)	20T852	$[2]$ (GRH)
20.2.44145664201696349530694455706624.1	x^20 + 12x^18 + 116x^16 + 398x^14 + 411x^12 + 2577x^10 + 10391x^8 + 6416x^6 - 13634x^4 - 11228x^2 - 401	\( -\,2^{10}\cdot 401^{11} \)	20T852	Trivial (GRH)
20.10.44145664201696349530694455706624.4	x^20 - 5x^19 - x^18 + 74x^17 - 222x^16 - 58x^15 + 1675x^14 - 3385x^13 - 1065x^12 + 14949x^11 - 19998x^10 - 8818x^9 + 49219x^8 - 38044x^7 - 26526x^6 + 57161x^5 - 20112x^4 - 16395x^3 + 14762x^2 - 3264x - 9	\( -\,2^{10}\cdot 401^{11} \)	20T852	Trivial (GRH)
20.10.44145664201696349530694455706624.5	x^20 - 8x^19 + 10x^18 + 68x^17 - 238x^16 + 174x^15 + 984x^14 - 4306x^13 + 6353x^12 + 1930x^11 - 15570x^10 + 12248x^9 + 8177x^8 - 15564x^7 + 768x^6 + 6272x^5 - 465x^4 - 954x^3 - 134x^2 + 48x + 13	\( -\,2^{10}\cdot 401^{11} \)	20T852	Trivial (GRH)
20.6.44145664201696349530694455706624.5	x^20 - x^18 + 6x^16 - 68x^14 - 554x^12 - 938x^10 + 658x^8 + 15469x^6 - 12180x^4 - 6889x^2 - 401	\( -\,2^{10}\cdot 401^{11} \)	20T852	Trivial (GRH)
20.10.44145664201696349530694455706624.6	x^20 - 15x^18 - 5x^17 + 91x^16 + 102x^15 - 500x^14 - 284x^13 + 1753x^12 + 51x^11 - 3389x^10 - 989x^9 + 6988x^8 + 308x^7 - 8168x^6 + 3547x^5 + 354x^4 + 428x^3 + 352x^2 - 912x + 288	\( -\,2^{10}\cdot 401^{11} \)	20T852	Trivial (GRH)
20.6.44145664201696349530694455706624.6	x^20 - x^18 + 34x^16 + 96x^14 + 197x^12 - 581x^10 - 5029x^8 - 3252x^6 + 5281x^4 + 1292x^2 - 401	\( -\,2^{10}\cdot 401^{11} \)	20T852	Trivial (GRH)
20.4.54262773113256889032978788220729.1	x^20 - 10x^19 + 55x^18 - 210x^17 + 594x^16 - 1284x^15 + 2137x^14 - 2689x^13 + 2389x^12 - 1113x^11 - 547x^10 + 1673x^9 - 1810x^8 + 1267x^7 - 645x^6 + 266x^5 - 94x^4 + 20x^3 - 5x^2 + 5x - 1	\( 3^{2}\cdot 401^{10}\cdot 56081 \)	20T852	Trivial (GRH)
20.8.152647020964259209777322411247857.1	x^20 - 8x^19 + 12x^18 + 44x^17 - 156x^16 + 215x^15 - 235x^14 + 161x^13 - 23x^12 - 74x^11 + 109x^10 - 74x^9 - 23x^8 + 161x^7 - 235x^6 + 215x^5 - 156x^4 + 44x^3 + 12x^2 - 8x + 1	\( 17^{5}\cdot 401^{10} \)	20T852	Trivial (GRH)
20.8.152647020964259209777322411247857.2	x^20 - 6x^18 - 33x^17 + 52x^16 + 218x^15 - 597x^14 + 212x^13 + 1689x^12 - 3608x^11 + 2074x^10 + 3738x^9 - 7911x^8 + 7390x^7 - 5438x^6 + 1157x^5 + 6880x^4 - 11818x^3 + 8814x^2 - 3428x + 487	\( 17^{5}\cdot 401^{10} \)	20T852	Trivial (GRH)
20.4.312981668589577444029325718995221.1	x^20 - 10x^19 + 56x^18 - 219x^17 + 651x^16 - 1536x^15 + 2961x^14 - 4761x^13 + 6444x^12 - 7321x^11 + 6940x^10 - 5501x^9 + 3707x^8 - 2183x^7 + 1107x^6 - 413x^5 + 46x^4 + 62x^3 - 42x^2 + 11x - 1	\( 3^{4}\cdot 127\cdot 283\cdot 401^{10} \)	20T852	Trivial (GRH)
20.12.543949443442847039977958368195584.1	x^20 - 15x^18 + 97x^16 - 370x^14 + 967x^12 - 1849x^10 + 2554x^8 - 2429x^6 + 1510x^4 - 536x^2 + 61	\( 2^{10}\cdot 3^{4}\cdot 61\cdot 401^{10} \)	20T852	Trivial (GRH)
20.4.813788289251768851893063870405509.1	x^20 - 10x^19 + 60x^18 - 255x^17 + 848x^16 - 2296x^15 + 5210x^14 - 10060x^13 + 16705x^12 - 23972x^11 + 29760x^10 - 31865x^9 + 29173x^8 - 22502x^7 + 14207x^6 - 6977x^5 + 2340x^4 - 299x^3 - 164x^2 + 96x - 9	\( 401^{10}\cdot 7569509 \)	20T852	Trivial (GRH)
20.8.949770250182943861335026416786432.1	x^20 - 13x^18 + 47x^16 - 38x^14 - 87x^12 + 103x^10 + 104x^8 - 95x^6 - 60x^4 + 12x^2 + 7	\( 2^{10}\cdot 7\cdot 19^{10}\cdot 43^{10} \)	20T852	Trivial (GRH)
20.10.2592814671517088339518493318709248.1	x^20 - 2x^19 - 17x^18 - 52x^16 + 52x^15 + 506x^14 - 108x^13 + 908x^12 - 2722x^11 + 7509x^10 + 5980x^9 - 18299x^8 + 1038x^7 + 13852x^6 - 6192x^5 - 2540x^4 + 1890x^3 - 266x^2 + 1	\( -\,2^{20}\cdot 23\cdot 401^{10} \)	20T852	Trivial (GRH)
20.14.2592814671517088339518493318709248.1	x^20 - 4x^19 - 8x^18 + 48x^17 - 15x^16 - 276x^15 + 216x^14 + 1706x^13 + 910x^12 - 6726x^11 - 12074x^10 + 2148x^9 + 28324x^8 + 33250x^7 + 4039x^6 - 19804x^5 - 12395x^4 + 282x^3 + 2258x^2 + 662x + 57	\( -\,2^{20}\cdot 23\cdot 401^{10} \)	20T852	Trivial (GRH)
20.4.6425671142455392841415396485496832.1	x^20 - 2x^19 + 9x^18 - 2x^17 + 16x^16 + 92x^15 - 122x^14 + 648x^13 - 938x^12 + 1860x^11 - 1835x^10 + 174x^9 + 443x^8 - 9482x^7 - 2822x^6 - 24228x^5 - 23078x^4 - 30512x^3 - 29232x^2 - 16758x - 7533	\( 2^{20}\cdot 3\cdot 19\cdot 401^{10} \)	20T852	$[2]$ (GRH)
20.8.6425671142455392841415396485496832.1	x^20 - 10x^19 + 45x^18 - 120x^17 + 246x^16 - 540x^15 + 294x^14 + 4332x^13 - 18904x^12 + 42704x^11 - 47606x^10 - 13084x^9 + 126853x^8 - 202726x^7 + 142449x^6 + 13898x^5 - 104552x^4 + 80894x^3 - 27324x^2 + 3150x + 729	\( 2^{20}\cdot 3\cdot 19\cdot 401^{10} \)	20T852	$[2]$ (GRH)
20.8.6425671142455392841415396485496832.2	x^20 - 6x^19 + 17x^18 - 40x^17 + 129x^16 - 502x^15 + 606x^14 + 2818x^13 - 9074x^12 + 6836x^11 + 5977x^10 - 31002x^9 + 86602x^8 - 132122x^7 + 129997x^6 - 132002x^5 + 104262x^4 - 31332x^3 + 5691x^2 - 3236x - 3317	\( 2^{20}\cdot 3\cdot 19\cdot 401^{10} \)	20T852	Trivial (GRH)
20.8.6425671142455392841415396485496832.3	x^20 - 10x^19 + 53x^18 - 160x^17 + 224x^16 + 346x^15 - 3422x^14 + 11924x^13 - 22597x^12 + 17810x^11 + 14447x^10 - 51538x^9 + 83787x^8 - 204508x^7 + 552342x^6 - 1067830x^5 + 1399293x^4 - 1249038x^3 + 742424x^2 - 267498x + 43959	\( 2^{20}\cdot 3\cdot 19\cdot 401^{10} \)	20T852	$[2]$ (GRH)
20.14.9194738203964790047763420536341504.1	x^20 + 12x^18 - 142x^16 - 575x^14 + 5884x^12 - 6285x^10 - 20019x^8 + 32440x^6 - 12421x^4 + 1079x^2 - 1	\( -\,2^{10}\cdot 17^{4}\cdot 401^{10} \)	20T852	Trivial (GRH)
20.18.9194738203964790047763420536341504.1	x^20 - 45x^18 + 639x^16 - 3014x^14 + 4891x^12 - 385x^10 - 5102x^8 + 4425x^6 - 1477x^4 + 203x^2 - 9	\( -\,2^{10}\cdot 17^{4}\cdot 401^{10} \)	20T852	Trivial (GRH)
20.6.9194738203964790047763420536341504.1	x^20 + 17x^18 + 46x^16 - 611x^14 - 4217x^12 - 7571x^10 + 2829x^8 + 14513x^6 + 1958x^4 - 6229x^2 - 529	\( -\,2^{10}\cdot 17^{4}\cdot 401^{10} \)	20T852	Trivial (GRH)
20.18.9194738203964790047763420536341504.2	x^20 - 40x^18 + 531x^16 - 3442x^14 + 12429x^12 - 26045x^10 + 31129x^8 - 19494x^6 + 5072x^4 - 171x^2 - 1	\( -\,2^{10}\cdot 17^{4}\cdot 401^{10} \)	20T852	Trivial (GRH)
20.6.9194738203964790047763420536341504.2	x^20 + 8x^18 - 110x^16 - 716x^14 + 648x^12 + 6814x^10 + 5839x^8 - 7926x^6 - 12330x^4 - 4340x^2 - 289	\( -\,2^{10}\cdot 17^{4}\cdot 401^{10} \)	20T852	$[2]$ (GRH)
20.10.9194738203964790047763420536341504.3	x^20 - 15x^18 - 92x^16 + 516x^14 + 758x^12 - 462x^10 - 594x^8 + 181x^6 + 136x^4 - 23x^2 - 9	\( -\,2^{10}\cdot 17^{4}\cdot 401^{10} \)	20T852	Trivial (GRH)
20.10.9194738203964790047763420536341504.4	x^20 + 12x^18 - 92x^16 - 1048x^14 - 1699x^12 + 3878x^10 + 5783x^8 - 6650x^6 + 931x^4 + 64x^2 - 1	\( -\,2^{10}\cdot 17^{4}\cdot 401^{10} \)	20T852	Trivial (GRH)
20.10.9194738203964790047763420536341504.5	x^20 + 6x^18 - 87x^16 - 372x^14 + 1800x^12 + 6235x^10 - 7572x^8 - 15408x^6 + 5568x^4 + 3072x^2 - 1024	\( -\,2^{10}\cdot 17^{4}\cdot 401^{10} \)	20T852	Trivial (GRH)
20.10.9194738203964790047763420536341504.6	x^20 + 16x^18 + 5x^16 - 739x^14 - 767x^12 + 12440x^10 + 2227x^8 - 61631x^6 + 1285x^4 + 79335x^2 - 23409	\( -\,2^{10}\cdot 17^{4}\cdot 401^{10} \)	20T852	Trivial (GRH)
20.0.10727396401012212935958752736709632.1	x^20 + 9x^18 - 66x^16 - 303x^14 + 1038x^12 + 5236x^10 + 5353x^8 + 3393x^6 + 4951x^4 + 401x^2 + 1203	\( 2^{10}\cdot 3^{5}\cdot 401^{11} \)	20T852	$[4]$ (GRH)
20.4.10727396401012212935958752736709632.1	x^20 - 4x^19 + 5x^18 - 8x^17 - 83x^16 + 633x^15 - 1124x^14 - 65x^13 + 3513x^12 - 9183x^11 + 17503x^10 - 29308x^9 + 42998x^8 - 49881x^7 + 44079x^6 - 29346x^5 + 12813x^4 - 2997x^3 + 427x^2 + 13x + 1	\( 2^{10}\cdot 3^{5}\cdot 401^{11} \)	20T852	$[2]$ (GRH)
20.0.10727396401012212935958752736709632.2	x^20 - 7x^19 + 34x^18 - 102x^17 + 216x^16 - 311x^15 + 268x^14 - 435x^13 + 1282x^12 - 3098x^11 + 4588x^10 + 4292x^9 - 2681x^8 + 27550x^7 - 20394x^6 + 52377x^5 - 34980x^4 - 55208x^3 + 91430x^2 - 96384x + 55053	\( 2^{10}\cdot 3^{5}\cdot 401^{11} \)	20T852	$[4]$ (GRH)
20.4.10727396401012212935958752736709632.2	x^20 - 10x^18 - 8x^16 + 222x^14 - 3488x^12 - 14624x^10 + 4827x^8 - 7790x^6 - 92236x^4 - 61754x^2 + 10827	\( 2^{10}\cdot 3^{5}\cdot 401^{11} \)	20T852	$[2]$ (GRH)
20.10.21531634880859298819479661907542016.1	x^20 - 8x^19 + 20x^18 + 12x^17 - 183x^16 + 262x^15 + 481x^14 - 1094x^13 - 918x^12 + 3284x^11 - 1068x^10 + 1258x^9 - 5727x^8 - 7816x^7 + 23162x^6 - 1428x^5 - 36585x^4 + 3382x^3 + 32037x^2 + 15858x + 2241	\( -\,2^{20}\cdot 191\cdot 401^{10} \)	20T852	Trivial (GRH)
20.10.21531634880859298819479661907542016.2	x^20 - 2x^19 - 27x^18 + 60x^17 + 81x^16 - 366x^15 + 1710x^14 - 3384x^13 - 6189x^12 + 32264x^11 - 37563x^10 - 42732x^9 + 172372x^8 - 118640x^7 - 96505x^6 + 120714x^5 - 20207x^4 - 4234x^3 + 3997x^2 - 738x - 81	\( -\,2^{20}\cdot 191\cdot 401^{10} \)	20T852	Trivial (GRH)
20.8.44114989058670911625646176850630673.1	x^20 - 5x^19 - 11x^18 + 69x^17 + 113x^16 - 510x^15 - 1033x^14 + 2482x^13 + 6231x^12 - 5982x^11 - 30814x^10 + 8127x^9 + 108473x^8 - 24903x^7 - 229311x^6 + 90558x^5 + 258425x^4 - 154725x^3 - 112796x^2 + 98079x - 12469	\( 17^{7}\cdot 401^{10} \)	20T852	Trivial (GRH)
20.8.44114989058670911625646176850630673.2	x^20 - 5x^18 - 172x^16 + 890x^14 + 5794x^12 - 14418x^10 - 93211x^8 - 112761x^6 - 12138x^4 + 23120x^2 + 4913	\( 17^{7}\cdot 401^{10} \)	20T852	Trivial (GRH)