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 40 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.232001679347763200000000000.1	x^20 - 3x^18 - 5x^16 + 21x^14 + 4x^12 - 38x^10 + 12x^8 + 18x^6 - 4x^4 - 10x^2 + 5	\( 2^{20}\cdot 5^{11}\cdot 1459^{4} \)	20T1010	Trivial (GRH)
20.4.232001679347763200000000000.1	x^20 - 9x^18 + 37x^16 - 99x^14 + 194x^12 - 291x^10 + 334x^8 - 293x^6 + 186x^4 - 70x^2 + 5	\( 2^{20}\cdot 5^{11}\cdot 1459^{4} \)	20T1010	Trivial (GRH)
20.0.232001679347763200000000000.2	x^20 + 4x^18 + 8x^16 + 8x^14 + 2x^12 - 4x^10 - 9x^8 - 5x^6 - 4x^4 + 5x^2 + 5	\( 2^{20}\cdot 5^{11}\cdot 1459^{4} \)	20T1010	Trivial (GRH)
20.4.232001679347763200000000000.2	x^20 - 3x^18 + 3x^16 - 3x^14 + 7x^12 + 16x^10 + 16x^8 - 71x^4 - 50x^2 + 5	\( 2^{20}\cdot 5^{11}\cdot 1459^{4} \)	20T1010	Trivial (GRH)
20.4.18835106651668995200000000000.1	x^20 - 5x^19 + 20x^18 - 50x^17 + 100x^16 - 151x^15 + 146x^14 - 66x^13 - 197x^12 + 428x^11 - 536x^10 + 532x^9 + 222x^8 + 8x^7 + 1084x^6 + 70x^5 - 183x^4 - 143x^3 - 4x^2 + 10x + 5	\( 2^{16}\cdot 5^{11}\cdot 19^{4}\cdot 461^{4} \)	20T1010	Trivial (GRH)
20.4.301361706426703923200000000000.1	x^20 - 15x^18 - 2x^17 + 65x^16 + 62x^15 - 56x^14 - 326x^13 - 245x^12 + 112x^11 + 937x^10 + 1856x^9 + 795x^8 - 602x^7 - 2508x^6 - 2006x^5 - 1399x^4 - 300x^3 - 85x^2 + 50x - 5	\( 2^{20}\cdot 5^{11}\cdot 19^{4}\cdot 461^{4} \)	20T1010	Trivial (GRH)
20.8.4346030133803056596710205078125.1	x^20 - 10x^19 + 46x^18 - 129x^17 + 222x^16 - 144x^15 - 342x^14 + 1140x^13 - 1493x^12 + 404x^11 + 1861x^10 - 3228x^9 + 1938x^8 + 1116x^7 - 2773x^6 + 1689x^5 + 97x^4 - 696x^3 + 407x^2 - 106x + 11	\( 5^{15}\cdot 11^{4}\cdot 9931^{4} \)	20T1010	Trivial (GRH)
20.8.4821787302827262771200000000000.1	x^20 - 15x^18 + 63x^16 + 58x^14 - 851x^12 + 407x^10 + 4293x^8 - 698x^6 - 8189x^4 - 2675x^2 + 1805	\( 2^{24}\cdot 5^{11}\cdot 19^{4}\cdot 461^{4} \)	20T1010	Trivial (GRH)
20.8.4821787302827262771200000000000.2	x^20 - 11x^18 + 11x^16 + 366x^14 - 2459x^12 + 7439x^10 - 11423x^8 + 7966x^6 - 2761x^4 + 1485x^2 + 405	\( 2^{24}\cdot 5^{11}\cdot 19^{4}\cdot 461^{4} \)	20T1010	Trivial (GRH)
20.4.77148596845236204339200000000000.1	x^20 + 11x^18 + 11x^16 - 366x^14 - 2459x^12 - 7439x^10 - 11423x^8 - 7966x^6 - 2761x^4 - 1485x^2 + 405	\( 2^{28}\cdot 5^{11}\cdot 19^{4}\cdot 461^{4} \)	20T1010	Trivial (GRH)
20.8.77148596845236204339200000000000.1	x^20 - 52x^16 + 184x^14 + 352x^12 - 1764x^10 + 1328x^8 + 352x^6 + 64x^4 - 400x^2 + 80	\( 2^{28}\cdot 5^{11}\cdot 19^{4}\cdot 461^{4} \)	20T1010	Trivial (GRH)
20.4.77148596845236204339200000000000.2	x^20 + 15x^18 + 63x^16 - 58x^14 - 851x^12 - 407x^10 + 4293x^8 + 698x^6 - 8189x^4 + 2675x^2 + 1805	\( 2^{28}\cdot 5^{11}\cdot 19^{4}\cdot 461^{4} \)	20T1010	Trivial (GRH)
20.8.77148596845236204339200000000000.2	x^20 - 10x^18 + x^16 + 276x^14 - 934x^12 - 112x^10 + 5970x^8 - 12004x^6 + 9141x^4 - 2150x^2 + 125	\( 2^{28}\cdot 5^{11}\cdot 19^{4}\cdot 461^{4} \)	20T1010	Trivial (GRH)
20.12.525869646190169848201934814453125.1	x^20 - 4x^19 - 15x^18 + 62x^17 + 61x^16 - 98x^15 - 195x^14 - 3221x^13 + 2095x^12 + 30457x^11 - 20568x^10 - 130158x^9 + 104483x^8 + 301874x^7 - 288014x^6 - 352758x^5 + 387768x^4 + 183454x^3 - 231764x^2 - 33500x + 50051	\( 5^{15}\cdot 11^{6}\cdot 9931^{4} \)	20T1010	Trivial (GRH)
20.0.1740665216320641860403200000000000.1	x^20 - 10x^19 + 57x^18 - 204x^17 + 597x^16 - 1542x^15 + 3584x^14 - 6528x^13 + 9059x^12 - 9576x^11 + 6821x^10 - 2116x^9 + 3245x^8 - 60408x^7 + 219396x^6 - 491660x^5 + 821043x^4 - 863398x^3 + 572299x^2 - 468806x + 369151	\( 2^{24}\cdot 5^{11}\cdot 19^{6}\cdot 461^{4} \)	20T1010	$[2, 2]$ (GRH)
20.0.1740665216320641860403200000000000.2	x^20 - 3x^18 - 40x^17 + 19x^16 + 12x^15 + 1192x^14 - 848x^13 - 3341x^12 - 11284x^11 + 48551x^10 - 68258x^9 + 85675x^8 - 79844x^7 + 31556x^6 - 34124x^5 + 41709x^4 - 24494x^3 + 61531x^2 - 22760x + 5345	\( 2^{24}\cdot 5^{11}\cdot 19^{6}\cdot 461^{4} \)	20T1010	$[2, 2]$ (GRH)
20.8.13146741154754246205048370361328125.1	x^20 - 2x^19 - 14x^18 + 65x^17 - 39x^16 - 329x^15 + 622x^14 - 2074x^13 - 1721x^12 + 11724x^11 - 3202x^10 - 2334x^9 + 38319x^8 + 13654x^7 - 21038x^6 - 121x^5 + 65866x^4 - 75655x^3 - 34699x^2 + 60617x - 16189	\( 5^{17}\cdot 11^{6}\cdot 9931^{4} \)	20T1010	Trivial (GRH)
20.12.14023021703309967392000000000000000.1	x^20 - 9x^18 + 22x^16 + 14x^14 - 104x^12 + 35x^10 + 155x^8 - 50x^6 - 95x^4 - 5x^2 + 5	\( 2^{20}\cdot 5^{15}\cdot 11^{4}\cdot 2339^{4} \)	20T1010	Trivial (GRH)
20.12.19750040792380468310835200000000000.1	x^20 - 19x^18 + 131x^16 - 498x^14 + 1383x^12 - 1917x^10 + 4913x^8 - 8168x^6 + 3959x^4 - 565x^2 + 5	\( 2^{36}\cdot 5^{11}\cdot 19^{4}\cdot 461^{4} \)	20T1010	Trivial (GRH)
20.12.19750040792380468310835200000000000.2	x^20 - 21x^18 + 221x^16 - 1520x^14 + 7113x^12 - 22369x^10 + 46399x^8 - 61610x^6 + 49225x^4 - 20625x^2 + 3125	\( 2^{36}\cdot 5^{11}\cdot 19^{4}\cdot 461^{4} \)	20T1010	Trivial (GRH)
20.8.2270054028671330373808947200000000000.1	x^20 + 12x^18 + 37x^16 - 32x^14 - 251x^12 - 156x^10 + 295x^8 + 248x^6 - 49x^4 - 30x^2 + 5	\( 2^{32}\cdot 5^{11}\cdot 41^{4}\cdot 1399^{4} \)	20T1010	Trivial (GRH)
20.12.4557142893582673873952000000000000000.1	x^20 - 16x^18 + 5x^16 + 722x^14 - 916x^12 - 10685x^10 + 6915x^8 + 50640x^6 + 32000x^4 - 1710x^2 + 5	\( 2^{20}\cdot 5^{15}\cdot 11^{4}\cdot 9931^{4} \)	20T1010	Trivial (GRH)
20.16.4557142893582673873952000000000000000.1	x^20 - 27x^18 + 215x^16 + 341x^14 - 14451x^12 + 84845x^10 - 214125x^8 + 233495x^6 - 95565x^4 + 7395x^2 + 1805	\( 2^{20}\cdot 5^{15}\cdot 11^{4}\cdot 9931^{4} \)	20T1010	Trivial (GRH)
20.20.4557142893582673873952000000000000000.1	x^20 - 36x^18 + 555x^16 - 4783x^14 + 25189x^12 - 82980x^10 + 167040x^8 - 188380x^6 + 92705x^4 - 2775x^2 + 5	\( 2^{20}\cdot 5^{15}\cdot 11^{4}\cdot 9931^{4} \)	20T1010	Trivial (GRH)
20.4.4557142893582673873952000000000000000.1	x^20 + 32x^18 + 393x^16 + 2317x^14 + 6576x^12 + 6710x^10 - 4400x^8 - 9740x^6 - 405x^4 + 90x^2 + 5	\( 2^{20}\cdot 5^{15}\cdot 11^{4}\cdot 9931^{4} \)	20T1010	Trivial (GRH)
20.8.4557142893582673873952000000000000000.1	x^20 + 11x^18 - 123x^16 - 1426x^14 - 1429x^12 + 8650x^10 + 8140x^8 - 6415x^6 - 3985x^4 + 560x^2 + 5	\( 2^{20}\cdot 5^{15}\cdot 11^{4}\cdot 9931^{4} \)	20T1010	Trivial (GRH)
20.12.4557142893582673873952000000000000000.2	x^20 + 3x^18 - 125x^16 - 139x^14 + 4539x^12 - 3580x^10 - 34485x^8 + 67725x^6 - 30200x^4 + 125x^2 + 125	\( 2^{20}\cdot 5^{15}\cdot 11^{4}\cdot 9931^{4} \)	20T1010	Trivial (GRH)
20.16.4557142893582673873952000000000000000.2	x^20 - 27x^18 + 158x^16 - 117x^14 - 709x^12 + 1145x^10 + 205x^8 - 1165x^6 + 585x^4 - 100x^2 + 5	\( 2^{20}\cdot 5^{15}\cdot 11^{4}\cdot 9931^{4} \)	20T1010	Trivial (GRH)
20.4.4557142893582673873952000000000000000.2	x^20 + 14x^18 + 10x^16 - 733x^14 - 4561x^12 - 9935x^10 - 2315x^8 + 20380x^6 + 24470x^4 + 7435x^2 + 5	\( 2^{20}\cdot 5^{15}\cdot 11^{4}\cdot 9931^{4} \)	20T1010	Trivial (GRH)
20.16.4557142893582673873952000000000000000.3	x^20 - 19x^18 + 67x^16 + 409x^14 - 3374x^12 + 8560x^10 - 8680x^8 + 2020x^6 + 1105x^4 - 155x^2 + 5	\( 2^{20}\cdot 5^{15}\cdot 11^{4}\cdot 9931^{4} \)	20T1010	Trivial (GRH)
20.4.4557142893582673873952000000000000000.3	x^20 + 15x^18 + 31x^16 - 485x^14 - 3126x^12 - 6710x^10 - 3485x^8 + 5850x^6 + 7300x^4 + 2375x^2 + 125	\( 2^{20}\cdot 5^{15}\cdot 11^{4}\cdot 9931^{4} \)	20T1010	$[2]$ (GRH)
20.4.4557142893582673873952000000000000000.4	x^20 + 39x^18 + 557x^16 + 3536x^14 + 9236x^12 + 2805x^10 - 23995x^8 - 25745x^6 - 1580x^4 + 660x^2 + 5	\( 2^{20}\cdot 5^{15}\cdot 11^{4}\cdot 9931^{4} \)	20T1010	Trivial (GRH)
20.12.113928572339566846848800000000000000000.1	x^20 - 25x^18 + 105x^16 + 1620x^14 - 12675x^12 - 8010x^10 + 180305x^8 - 48650x^6 - 95575x^4 + 750x^2 + 125	\( 2^{20}\cdot 5^{17}\cdot 11^{4}\cdot 9931^{4} \)	20T1010	Trivial (GRH)
20.16.113928572339566846848800000000000000000.1	x^20 - 30x^18 + 5x^16 + 5160x^14 - 42740x^12 + 120635x^10 - 114980x^8 + 15000x^6 + 14150x^4 - 2875x^2 + 125	\( 2^{20}\cdot 5^{17}\cdot 11^{4}\cdot 9931^{4} \)	20T1010	Trivial (GRH)
20.8.113928572339566846848800000000000000000.1	x^20 + 15x^18 - 105x^16 - 1820x^14 + 595x^12 + 52715x^10 + 142970x^8 + 38950x^6 - 129550x^4 + 24875x^2 + 125	\( 2^{20}\cdot 5^{17}\cdot 11^{4}\cdot 9931^{4} \)	20T1010	Trivial (GRH)
20.12.113928572339566846848800000000000000000.2	x^20 + 10x^18 - 115x^16 - 690x^14 + 3495x^12 + 9205x^10 - 43980x^8 - 12250x^6 + 185850x^4 - 196750x^2 + 45125	\( 2^{20}\cdot 5^{17}\cdot 11^{4}\cdot 9931^{4} \)	20T1010	Trivial (GRH)
20.8.113928572339566846848800000000000000000.2	x^20 + 25x^18 - 2465x^14 - 690x^12 + 73620x^10 - 48270x^8 - 477300x^6 + 56325x^4 + 377250x^2 + 120125	\( 2^{20}\cdot 5^{17}\cdot 11^{4}\cdot 9931^{4} \)	20T1010	Trivial (GRH)
20.0.449447128722439644559460125472000000000000000.1	x^20 + 166x^18 + 10675x^16 + 353573x^14 + 6717429x^12 + 76284670x^10 + 518418700x^8 + 2034961210x^6 + 4213127440x^4 + 3683209280x^2 + 493123805	\( 2^{20}\cdot 5^{15}\cdot 11^{4}\cdot 9931^{6} \)	20T1010	$[2, 2, 3987620]$ (GRH)
20.20.449447128722439644559460125472000000000000000.1	x^20 - 273x^18 + 28558x^16 - 1477318x^14 + 40983526x^12 - 625485945x^10 + 5158670340x^8 - 21487038030x^6 + 36848807880x^4 - 8542596545x^2 + 493123805	\( 2^{20}\cdot 5^{15}\cdot 11^{4}\cdot 9931^{6} \)	20T1010	Trivial (GRH)
20.0.54383102575415196991694675182112000000000000000.1	x^20 + 391x^18 + 55991x^16 + 3687046x^14 + 118265156x^12 + 2038773950x^10 + 19835671615x^8 + 108465111260x^6 + 310756387810x^4 + 375696185150x^2 + 59667980405	\( 2^{20}\cdot 5^{15}\cdot 11^{6}\cdot 9931^{6} \)	20T1010	$[2, 2, 2, 21353032]$ (GRH)